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Finite element discretization library
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fe.hpp
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1 // Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
2 // the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
3 // reserved. See file COPYRIGHT for details.
4 //
5 // This file is part of the MFEM library. For more information and source code
6 // availability see http://mfem.org.
7 //
8 // MFEM is free software; you can redistribute it and/or modify it under the
9 // terms of the GNU Lesser General Public License (as published by the Free
10 // Software Foundation) version 2.1 dated February 1999.
11 
12 #ifndef MFEM_FE
13 #define MFEM_FE
14 
15 #include "../config/config.hpp"
16 #include "../general/array.hpp"
17 #include "../linalg/linalg.hpp"
18 #include "intrules.hpp"
19 #include "geom.hpp"
20 
21 #include <map>
22 
23 namespace mfem
24 {
25 
26 // Base and derived classes for finite elements
27 
28 /// Describes the space on each element
29 class FunctionSpace
30 {
31 public:
32  enum
33  {
34  Pk, ///< Polynomials of order k
35  Qk, ///< Tensor products of polynomials of order k
36  rQk ///< Refined tensor products of polynomials of order k
37  };
38 };
39 
40 class ElementTransformation;
41 class Coefficient;
42 class VectorCoefficient;
43 class MatrixCoefficient;
44 class KnotVector;
45 
46 /// Abstract class for Finite Elements
47 class FiniteElement
48 {
49 protected:
50  int Dim, ///< Dimension of reference space
51  GeomType, ///< Geometry::Type of the reference element
52  Dof, ///< Number of degrees of freedom
53  Order, ///< Order/degree of the shape functions
54  FuncSpace, RangeType, MapType,
55  DerivType, DerivRangeType, DerivMapType;
56  IntegrationRule Nodes;
57 #ifndef MFEM_THREAD_SAFE
58  mutable DenseMatrix vshape; // Dof x Dim
59 #endif
60 
61 public:
62  /// Enumeration for RangeType and DerivRangeType
63  enum { SCALAR, VECTOR };
64 
65  /** @brief Enumeration for MapType: defines how reference functions are
66  mapped to physical space.
67 
68  A reference function, `uh(xh)`, can be mapped to a function, `u(x)`, on a
69  general physical element in following ways:
70 
71  VALUE u(x) = uh(xh)
72  INTEGRAL u(x) = (1/w) * uh(xh)
73  H_DIV u(x) = (J/w) * uh(xh)
74  H_CURL u(x) = J^{-t} * uh(xh) (square J)
75  H_CURL u(x) = J*(J^t*J)^{-1} * uh(xh) (general J)
76 
77  where
78 
79  x = T(xh) is the image of the reference point xh ("x hat"),
80  J = J(xh) is the Jacobian matrix of the transformation T, and
81  w = w(xh) = / det(J), for square J,
82  \ det(J^t*J)^{1/2}, for general J,
83  is the transformation weight factor.
84  */
85  enum { VALUE, ///< For scalar fields; preserves point values
86  INTEGRAL, ///< For scalar fields; preserves volume integrals
87  H_DIV, /**< For vector fields; preserves surface integrals of the
88  normal component */
89  H_CURL /**< For vector fields; preserves line integrals of the
90  tangential component */
91  };
92 
93  /** @brief Enumeration for DerivType: defines which derivative method
94  is implemented.
95 
96  Each FiniteElement class implements only one type of derivative. The
97  value returned by GetDerivType() indicates which derivative method is
98  implemented.
99  */
100  enum { NONE, ///< No derivatives implemented
101  GRAD, ///< Implements CalcDShape methods
102  DIV, ///< Implements CalcDivShape methods
103  CURL ///< Implements CalcCurlShape methods
104  };
105 
106  /** Construct FiniteElement with given
107  @param D Reference space dimension
108  @param G Geometry type (of type Geometry::Type)
109  @param Do Number of degrees of freedom in the FiniteElement
110  @param O Order/degree of the FiniteElement
111  @param F FunctionSpace type of the FiniteElement
112  */
113  FiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk);
114 
115  /// Returns the reference space dimension for the finite element
116  int GetDim() const { return Dim; }
117 
118  /// Returns the Geometry::Type of the reference element
119  int GetGeomType() const { return GeomType; }
120 
121  /// Returns the number of degrees of freedom in the finite element
122  int GetDof() const { return Dof; }
123 
124  /// Returns the order of the finite element
125  int GetOrder() const { return Order; }
126 
127  /// Returns the type of space on each element
128  int Space() const { return FuncSpace; }
129 
130  int GetRangeType() const { return RangeType; }
131 
132  int GetDerivRangeType() const { return DerivRangeType; }
133 
134  int GetMapType() const { return MapType; }
135 
136  int GetDerivType() const { return DerivType; }
137 
138  int GetDerivMapType() const { return DerivMapType; }
139 
140  /** @brief Evaluate the values of all shape functions of a scalar finite
141  element in reference space at the given point @a ip. */
142  /** The size (#Dof) of the result Vector @a shape must be set in advance. */
143  virtual void CalcShape(const IntegrationPoint &ip,
144  Vector &shape) const = 0;
145 
146  /** @brief Evaluate the values of all shape functions of a scalar finite
147  element in physical space at the point described by @a Trans. */
148  /** The size (#Dof) of the result Vector @a shape must be set in advance. */
149  void CalcPhysShape(ElementTransformation &Trans, Vector &shape) const;
150 
151  /** @brief Evaluate the gradients of all shape functions of a scalar finite
152  element in reference space at the given point @a ip. */
153  /** Each row of the result DenseMatrix @a dshape contains the derivatives of
154  one shape function. The size (#Dof x #Dim) of @a dshape must be set in
155  advance. */
156  virtual void CalcDShape(const IntegrationPoint &ip,
157  DenseMatrix &dshape) const = 0;
158 
159  /** @brief Evaluate the gradients of all shape functions of a scalar finite
160  element in physical space at the point described by @a Trans. */
161  /** Each row of the result DenseMatrix @a dshape contains the derivatives of
162  one shape function. The size (#Dof x SDim) of @a dshape must be set in
163  advance, where SDim >= #Dim is the physical space dimension as described
164  by @a Trans. */
165  void CalcPhysDShape(ElementTransformation &Trans, DenseMatrix &dshape) const;
166 
167  const IntegrationRule & GetNodes() const { return Nodes; }
168 
169  // virtual functions for finite elements on vector spaces
170 
171  /** @brief Evaluate the values of all shape functions of a *vector* finite
172  element in reference space at the given point @a ip. */
173  /** Each row of the result DenseMatrix @a shape contains the components of
174  one vector shape function. The size (#Dof x #Dim) of @a shape must be set
175  in advance. */
176  virtual void CalcVShape(const IntegrationPoint &ip,
177  DenseMatrix &shape) const;
178 
179  /** @brief Evaluate the values of all shape functions of a *vector* finite
180  element in physical space at the point described by @a Trans. */
181  /** Each row of the result DenseMatrix @a shape contains the components of
182  one vector shape function. The size (#Dof x SDim) of @a shape must be set
183  in advance, where SDim >= #Dim is the physical space dimension as
184  described by @a Trans. */
185  virtual void CalcVShape(ElementTransformation &Trans,
186  DenseMatrix &shape) const;
187 
188  /// Equivalent to the CalcVShape() method with the same arguments.
189  void CalcPhysVShape(ElementTransformation &Trans, DenseMatrix &shape) const
190  { CalcVShape(Trans, shape); }
191 
192  /** @brief Evaluate the divergence of all shape functions of a *vector*
193  finite element in reference space at the given point @a ip. */
194  /** The size (#Dof) of the result Vector @a divshape must be set in advance.
195  */
196  virtual void CalcDivShape(const IntegrationPoint &ip,
197  Vector &divshape) const;
198 
199  /** @brief Evaluate the divergence of all shape functions of a *vector*
200  finite element in physical space at the point described by @a Trans. */
201  /** The size (#Dof) of the result Vector @a divshape must be set in advance.
202  */
203  void CalcPhysDivShape(ElementTransformation &Trans, Vector &divshape) const;
204 
205  /** @brief Evaluate the curl of all shape functions of a *vector* finite
206  element in reference space at the given point @a ip. */
207  /** Each row of the result DenseMatrix @a curl_shape contains the components
208  of the curl of one vector shape function. The size (#Dof x CDim) of
209  @a curl_shape must be set in advance, where CDim = 3 for #Dim = 3 and
210  CDim = 1 for #Dim = 2. */
211  virtual void CalcCurlShape(const IntegrationPoint &ip,
212  DenseMatrix &curl_shape) const;
213 
214  /** @brief Evaluate the curl of all shape functions of a *vector* finite
215  element in physical space at the point described by @a Trans. */
216  /** Each row of the result DenseMatrix @a curl_shape contains the components
217  of the curl of one vector shape function. The size (#Dof x CDim) of
218  @a curl_shape must be set in advance, where CDim = 3 for #Dim = 3 and
219  CDim = 1 for #Dim = 2. */
220  void CalcPhysCurlShape(ElementTransformation &Trans,
221  DenseMatrix &curl_shape) const;
222 
223  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
224 
225  /** each row of h contains the upper triangular part of the hessian
226  of one shape function; the order in 2D is {u_xx, u_xy, u_yy} */
227  virtual void CalcHessian (const IntegrationPoint &ip,
228  DenseMatrix &h) const;
229 
230  /** Return the local interpolation matrix I (Dof x Dof) where the
231  fine element is the image of the base geometry under the given
232  transformation. */
233  virtual void GetLocalInterpolation (ElementTransformation &Trans,
234  DenseMatrix &I) const;
235 
236  /** Given a coefficient and a transformation, compute its projection
237  (approximation) in the local finite dimensional space in terms
238  of the degrees of freedom. */
239  virtual void Project (Coefficient &coeff,
240  ElementTransformation &Trans, Vector &dofs) const;
241 
242  /** Given a vector coefficient and a transformation, compute its
243  projection (approximation) in the local finite dimensional space
244  in terms of the degrees of freedom. (VectorFiniteElements) */
245  virtual void Project (VectorCoefficient &vc,
246  ElementTransformation &Trans, Vector &dofs) const;
247 
248  /** Given a matrix coefficient and a transformation, compute an approximation
249  ("projection") in the local finite dimensional space in terms of the
250  degrees of freedom. For VectorFiniteElements, the rows of the coefficient
251  are projected in the vector space. */
252  virtual void ProjectMatrixCoefficient(
253  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
254 
255  /** Compute a representation (up to multiplicative constant) for
256  the delta function at the vertex with the given index. */
257  virtual void ProjectDelta(int vertex, Vector &dofs) const;
258 
259  /** Compute the embedding/projection matrix from the given FiniteElement
260  onto 'this' FiniteElement. The ElementTransformation is included to
261  support cases when the projection depends on it. */
262  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
263  DenseMatrix &I) const;
264 
265  /** Compute the discrete gradient matrix from the given FiniteElement onto
266  'this' FiniteElement. The ElementTransformation is included to support
267  cases when the matrix depends on it. */
268  virtual void ProjectGrad(const FiniteElement &fe,
269  ElementTransformation &Trans,
270  DenseMatrix &grad) const;
271 
272  /** Compute the discrete curl matrix from the given FiniteElement onto
273  'this' FiniteElement. The ElementTransformation is included to support
274  cases when the matrix depends on it. */
275  virtual void ProjectCurl(const FiniteElement &fe,
276  ElementTransformation &Trans,
277  DenseMatrix &curl) const;
278 
279  /** Compute the discrete divergence matrix from the given FiniteElement onto
280  'this' FiniteElement. The ElementTransformation is included to support
281  cases when the matrix depends on it. */
282  virtual void ProjectDiv(const FiniteElement &fe,
283  ElementTransformation &Trans,
284  DenseMatrix &div) const;
285 
286  virtual ~FiniteElement () { }
287 
288  static int VerifyClosed(int pt_type)
289  {
290  int cp_type = Quadrature1D::CheckClosed(pt_type);
291  MFEM_VERIFY(cp_type != Quadrature1D::Invalid,
292  "invalid closed point type: " << pt_type);
293  return cp_type;
294  }
295  static int VerifyOpen(int pt_type)
296  {
297  int op_type = Quadrature1D::CheckOpen(pt_type);
298  MFEM_VERIFY(op_type != Quadrature1D::Invalid,
299  "invalid open point type: " << pt_type);
300  return op_type;
301  }
302 };
303 
304 class ScalarFiniteElement : public FiniteElement
305 {
306 public:
307  ScalarFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
308  : FiniteElement(D, G, Do, O, F)
309  { DerivType = GRAD; DerivRangeType = VECTOR; DerivMapType = H_CURL; }
310 
311  void SetMapType(int M)
312  {
313  MFEM_VERIFY(M == VALUE || M == INTEGRAL, "unknown MapType");
314  MapType = M;
315  DerivType = (M == VALUE) ? GRAD : NONE;
316  }
317 };
318 
319 class NodalFiniteElement : public ScalarFiniteElement
320 {
321 protected:
322  void NodalLocalInterpolation (ElementTransformation &Trans,
323  DenseMatrix &I,
324  const NodalFiniteElement &fine_fe) const;
325 
326  void ProjectCurl_2D(const FiniteElement &fe,
327  ElementTransformation &Trans,
328  DenseMatrix &curl) const;
329 
330 #ifndef MFEM_THREAD_SAFE
331  mutable Vector c_shape;
332 #endif
333 
334 public:
335 #ifdef MFEM_THREAD_SAFE
336  NodalFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
337  : ScalarFiniteElement(D, G, Do, O, F) { }
338 #else
339  NodalFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
340  : ScalarFiniteElement(D, G, Do, O, F), c_shape(Do) { }
341 #endif
342 
343  virtual void GetLocalInterpolation (ElementTransformation &Trans,
344  DenseMatrix &I) const
345  { NodalLocalInterpolation (Trans, I, *this); }
346 
347  virtual void Project (Coefficient &coeff,
348  ElementTransformation &Trans, Vector &dofs) const;
349 
350  virtual void Project (VectorCoefficient &vc,
351  ElementTransformation &Trans, Vector &dofs) const;
352 
353  // (mc.height x mc.width) @ DOFs -> (Dof x mc.width x mc.height) in dofs
354  virtual void ProjectMatrixCoefficient(
355  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
356 
357  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
358  DenseMatrix &I) const;
359 
360  virtual void ProjectGrad(const FiniteElement &fe,
361  ElementTransformation &Trans,
362  DenseMatrix &grad) const;
363 
364  virtual void ProjectDiv(const FiniteElement &fe,
365  ElementTransformation &Trans,
366  DenseMatrix &div) const;
367 };
368 
369 
370 class PositiveFiniteElement : public ScalarFiniteElement
371 {
372 protected:
373  void PositiveLocalInterpolation(ElementTransformation &Trans,
374  DenseMatrix &I,
375  const PositiveFiniteElement &fine_fe) const;
376 
377 public:
378  PositiveFiniteElement(int D, int G, int Do, int O,
379  int F = FunctionSpace::Pk) :
380  ScalarFiniteElement(D, G, Do, O, F)
381  { }
382 
383  virtual void GetLocalInterpolation(ElementTransformation &Trans,
384  DenseMatrix &I) const
385  { PositiveLocalInterpolation(Trans, I, *this); }
386 
387  using FiniteElement::Project;
388 
389  // Low-order monotone "projection" (actually it is not a projection): the
390  // dofs are set to be the Coefficient values at the nodes.
391  virtual void Project(Coefficient &coeff,
392  ElementTransformation &Trans, Vector &dofs) const;
393 
394  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
395  DenseMatrix &I) const;
396 };
397 
398 class VectorFiniteElement : public FiniteElement
399 {
400  // Hide the scalar functions CalcShape and CalcDShape.
401 private:
402  /// Overrides the scalar CalcShape function to print an error.
403  virtual void CalcShape(const IntegrationPoint &ip,
404  Vector &shape) const;
405 
406  /// Overrides the scalar CalcDShape function to print an error.
407  virtual void CalcDShape(const IntegrationPoint &ip,
408  DenseMatrix &dshape) const;
409 
410 protected:
411 #ifndef MFEM_THREAD_SAFE
412  mutable DenseMatrix J, Jinv;
413  mutable DenseMatrix curlshape, curlshape_J;
414 #endif
415  void SetDerivMembers();
416 
417  void CalcVShape_RT(ElementTransformation &Trans,
418  DenseMatrix &shape) const;
419 
420  void CalcVShape_ND(ElementTransformation &Trans,
421  DenseMatrix &shape) const;
422 
423  void Project_RT(const double *nk, const Array<int> &d2n,
424  VectorCoefficient &vc, ElementTransformation &Trans,
425  Vector &dofs) const;
426 
427  // project the rows of the matrix coefficient in an RT space
428  void ProjectMatrixCoefficient_RT(
429  const double *nk, const Array<int> &d2n,
430  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
431 
432  void Project_RT(const double *nk, const Array<int> &d2n,
433  const FiniteElement &fe, ElementTransformation &Trans,
434  DenseMatrix &I) const;
435 
436  // rotated gradient in 2D
437  void ProjectGrad_RT(const double *nk, const Array<int> &d2n,
438  const FiniteElement &fe, ElementTransformation &Trans,
439  DenseMatrix &grad) const;
440 
441  // Compute the curl as a discrete operator from ND FE (fe) to ND FE (this).
442  // The natural FE for the range is RT, so this is an approximation.
443  void ProjectCurl_ND(const double *tk, const Array<int> &d2t,
444  const FiniteElement &fe, ElementTransformation &Trans,
445  DenseMatrix &curl) const;
446 
447  void ProjectCurl_RT(const double *nk, const Array<int> &d2n,
448  const FiniteElement &fe, ElementTransformation &Trans,
449  DenseMatrix &curl) const;
450 
451  void Project_ND(const double *tk, const Array<int> &d2t,
452  VectorCoefficient &vc, ElementTransformation &Trans,
453  Vector &dofs) const;
454 
455  // project the rows of the matrix coefficient in an ND space
456  void ProjectMatrixCoefficient_ND(
457  const double *tk, const Array<int> &d2t,
458  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
459 
460  void Project_ND(const double *tk, const Array<int> &d2t,
461  const FiniteElement &fe, ElementTransformation &Trans,
462  DenseMatrix &I) const;
463 
464  void ProjectGrad_ND(const double *tk, const Array<int> &d2t,
465  const FiniteElement &fe, ElementTransformation &Trans,
466  DenseMatrix &grad) const;
467 
468  void LocalInterpolation_RT(const double *nk, const Array<int> &d2n,
469  ElementTransformation &Trans,
470  DenseMatrix &I) const;
471 
472  void LocalInterpolation_ND(const double *tk, const Array<int> &d2t,
473  ElementTransformation &Trans,
474  DenseMatrix &I) const;
475 
476 public:
477  VectorFiniteElement (int D, int G, int Do, int O, int M,
478  int F = FunctionSpace::Pk) :
479 #ifdef MFEM_THREAD_SAFE
480  FiniteElement(D, G, Do, O, F)
481  { RangeType = VECTOR; MapType = M; SetDerivMembers(); }
482 #else
483  FiniteElement(D, G, Do, O, F), Jinv(D)
484  { RangeType = VECTOR; MapType = M; SetDerivMembers(); }
485 #endif
486 };
487 
488 class PointFiniteElement : public NodalFiniteElement
489 {
490 public:
491  PointFiniteElement();
492 
493  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
494 
495  virtual void CalcDShape(const IntegrationPoint &ip,
496  DenseMatrix &dshape) const;
497 };
498 
499 /// Class for linear FE on interval
500 class Linear1DFiniteElement : public NodalFiniteElement
501 {
502 public:
503  /// Construct a linear FE on interval
504  Linear1DFiniteElement();
505 
506  /** virtual function which evaluates the values of all
507  shape functions at a given point ip and stores
508  them in the vector shape of dimension Dof (2) */
509  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
510 
511  /** virtual function which evaluates the derivatives of all
512  shape functions at a given point ip and stores them in
513  the matrix dshape (Dof x Dim) (2 x 1) so that each row
514  contains the derivative of one shape function */
515  virtual void CalcDShape(const IntegrationPoint &ip,
516  DenseMatrix &dshape) const;
517 };
518 
519 /// Class for linear FE on triangle
520 class Linear2DFiniteElement : public NodalFiniteElement
521 {
522 public:
523  /// Construct a linear FE on triangle
524  Linear2DFiniteElement();
525 
526  /** virtual function which evaluates the values of all
527  shape functions at a given point ip and stores
528  them in the vector shape of dimension Dof (3) */
529  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
530 
531  /** virtual function which evaluates the values of all
532  partial derivatives of all shape functions at a given
533  point ip and stores them in the matrix dshape (Dof x Dim) (3 x 2)
534  so that each row contains the derivatives of one shape function */
535  virtual void CalcDShape(const IntegrationPoint &ip,
536  DenseMatrix &dshape) const;
537  virtual void ProjectDelta(int vertex, Vector &dofs) const
538  { dofs = 0.0; dofs(vertex) = 1.0; }
539 };
540 
541 /// Class for bilinear FE on quadrilateral
542 class BiLinear2DFiniteElement : public NodalFiniteElement
543 {
544 public:
545  /// Construct a bilinear FE on quadrilateral
546  BiLinear2DFiniteElement();
547 
548  /** virtual function which evaluates the values of all
549  shape functions at a given point ip and stores
550  them in the vector shape of dimension Dof (4) */
551  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
552 
553  /** virtual function which evaluates the values of all
554  partial derivatives of all shape functions at a given
555  point ip and stores them in the matrix dshape (Dof x Dim) (4 x 2)
556  so that each row contains the derivatives of one shape function */
557  virtual void CalcDShape(const IntegrationPoint &ip,
558  DenseMatrix &dshape) const;
559  virtual void CalcHessian (const IntegrationPoint &ip,
560  DenseMatrix &h) const;
561  virtual void ProjectDelta(int vertex, Vector &dofs) const
562  { dofs = 0.0; dofs(vertex) = 1.0; } // { dofs = 1.0; }
563 };
564 
565 /// Class for linear FE on triangle with nodes at the 3 "Gaussian" points
566 class GaussLinear2DFiniteElement : public NodalFiniteElement
567 {
568 public:
569  GaussLinear2DFiniteElement();
570  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
571  virtual void CalcDShape(const IntegrationPoint &ip,
572  DenseMatrix &dshape) const;
573  virtual void ProjectDelta(int vertex, Vector &dofs) const;
574 };
575 
576 /// Class for bilinear FE on quad with nodes at the 4 Gaussian points
577 class GaussBiLinear2DFiniteElement : public NodalFiniteElement
578 {
579 private:
580  static const double p[2];
581 
582 public:
583  GaussBiLinear2DFiniteElement();
584  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
585  virtual void CalcDShape(const IntegrationPoint &ip,
586  DenseMatrix &dshape) const;
587  virtual void ProjectDelta(int vertex, Vector &dofs) const;
588 };
589 
590 class P1OnQuadFiniteElement : public NodalFiniteElement
591 {
592 public:
593  P1OnQuadFiniteElement();
594  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
595  virtual void CalcDShape(const IntegrationPoint &ip,
596  DenseMatrix &dshape) const;
597  virtual void ProjectDelta(int vertex, Vector &dofs) const
598  { dofs = 1.0; }
599 };
600 
601 /// Class for quadratic FE on interval
602 class Quad1DFiniteElement : public NodalFiniteElement
603 {
604 public:
605  /// Construct a quadratic FE on interval
606  Quad1DFiniteElement();
607 
608  /** virtual function which evaluates the values of all
609  shape functions at a given point ip and stores
610  them in the vector shape of dimension Dof (3) */
611  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
612 
613  /** virtual function which evaluates the derivatives of all
614  shape functions at a given point ip and stores them in
615  the matrix dshape (Dof x Dim) (3 x 1) so that each row
616  contains the derivative of one shape function */
617  virtual void CalcDShape(const IntegrationPoint &ip,
618  DenseMatrix &dshape) const;
619 };
620 
621 class QuadPos1DFiniteElement : public PositiveFiniteElement
622 {
623 public:
624  QuadPos1DFiniteElement();
625  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
626  virtual void CalcDShape(const IntegrationPoint &ip,
627  DenseMatrix &dshape) const;
628 };
629 
630 /// Class for quadratic FE on triangle
631 class Quad2DFiniteElement : public NodalFiniteElement
632 {
633 public:
634  /// Construct a quadratic FE on triangle
635  Quad2DFiniteElement();
636 
637  /** virtual function which evaluates the values of all
638  shape functions at a given point ip and stores
639  them in the vector shape of dimension Dof (6) */
640  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
641 
642  /** virtual function which evaluates the values of all
643  partial derivatives of all shape functions at a given
644  point ip and stores them in the matrix dshape (Dof x Dim) (6 x 2)
645  so that each row contains the derivatives of one shape function */
646  virtual void CalcDShape(const IntegrationPoint &ip,
647  DenseMatrix &dshape) const;
648 
649  virtual void CalcHessian (const IntegrationPoint &ip,
650  DenseMatrix &h) const;
651  virtual void ProjectDelta(int vertex, Vector &dofs) const;
652 };
653 
654 /// Class for quadratic FE on triangle with nodes at the "Gaussian" points
655 class GaussQuad2DFiniteElement : public NodalFiniteElement
656 {
657 private:
658  static const double p[2];
659  DenseMatrix A;
660  mutable DenseMatrix D;
661  mutable Vector pol;
662 public:
663  GaussQuad2DFiniteElement();
664  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
665  virtual void CalcDShape(const IntegrationPoint &ip,
666  DenseMatrix &dshape) const;
667  // virtual void ProjectDelta(int vertex, Vector &dofs) const;
668 };
669 
670 /// Class for bi-quadratic FE on quadrilateral
671 class BiQuad2DFiniteElement : public NodalFiniteElement
672 {
673 public:
674  /// Construct a biquadratic FE on quadrilateral
675  BiQuad2DFiniteElement();
676 
677  /** virtual function which evaluates the values of all
678  shape functions at a given point ip and stores
679  them in the vector shape of dimension Dof (9) */
680  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
681 
682  /** virtual function which evaluates the values of all
683  partial derivatives of all shape functions at a given
684  point ip and stores them in the matrix dshape (Dof x Dim) (9 x 2)
685  so that each row contains the derivatives of one shape function */
686  virtual void CalcDShape(const IntegrationPoint &ip,
687  DenseMatrix &dshape) const;
688  virtual void ProjectDelta(int vertex, Vector &dofs) const;
689 };
690 
691 class BiQuadPos2DFiniteElement : public PositiveFiniteElement
692 {
693 public:
694  BiQuadPos2DFiniteElement();
695  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
696  virtual void CalcDShape(const IntegrationPoint &ip,
697  DenseMatrix &dshape) const;
698  virtual void GetLocalInterpolation(ElementTransformation &Trans,
699  DenseMatrix &I) const;
700  using FiniteElement::Project;
701  virtual void Project(Coefficient &coeff, ElementTransformation &Trans,
702  Vector &dofs) const;
703  virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans,
704  Vector &dofs) const;
705  virtual void ProjectDelta(int vertex, Vector &dofs) const
706  { dofs = 0.; dofs(vertex) = 1.; }
707 };
708 
709 /// Bi-quadratic element on quad with nodes at the 9 Gaussian points
710 class GaussBiQuad2DFiniteElement : public NodalFiniteElement
711 {
712 public:
713  GaussBiQuad2DFiniteElement();
714  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
715  virtual void CalcDShape(const IntegrationPoint &ip,
716  DenseMatrix &dshape) const;
717  // virtual void ProjectDelta(int vertex, Vector &dofs) const { dofs = 1.; }
718 };
719 
720 class BiCubic2DFiniteElement : public NodalFiniteElement
721 {
722 public:
723  BiCubic2DFiniteElement();
724  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
725  virtual void CalcDShape(const IntegrationPoint &ip,
726  DenseMatrix &dshape) const;
727  virtual void CalcHessian (const IntegrationPoint &ip,
728  DenseMatrix &h) const;
729 };
730 
731 class Cubic1DFiniteElement : public NodalFiniteElement
732 {
733 public:
734  Cubic1DFiniteElement();
735 
736  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
737 
738  virtual void CalcDShape(const IntegrationPoint &ip,
739  DenseMatrix &dshape) const;
740 };
741 
742 class Cubic2DFiniteElement : public NodalFiniteElement
743 {
744 public:
745  Cubic2DFiniteElement();
746 
747  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
748 
749  virtual void CalcDShape(const IntegrationPoint &ip,
750  DenseMatrix &dshape) const;
751 
752  virtual void CalcHessian (const IntegrationPoint &ip,
753  DenseMatrix &h) const;
754 };
755 
756 /// Class for cubic FE on tetrahedron
757 class Cubic3DFiniteElement : public NodalFiniteElement
758 {
759 public:
760  /// Construct a cubic FE on tetrahedron
761  Cubic3DFiniteElement();
762 
763  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
764 
765  virtual void CalcDShape(const IntegrationPoint &ip,
766  DenseMatrix &dshape) const;
767 };
768 
769 /// Class for constant FE on triangle
770 class P0TriangleFiniteElement : public NodalFiniteElement
771 {
772 public:
773  /// Construct P0 triangle finite element
774  P0TriangleFiniteElement();
775 
776  /// evaluate shape function - constant 1
777  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
778 
779  /// evaluate derivatives of shape function - constant 0
780  virtual void CalcDShape(const IntegrationPoint &ip,
781  DenseMatrix &dshape) const;
782  virtual void ProjectDelta(int vertex, Vector &dofs) const
783  { dofs(0) = 1.0; }
784 };
785 
786 
787 class P0QuadFiniteElement : public NodalFiniteElement
788 {
789 public:
790  P0QuadFiniteElement();
791  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
792  virtual void CalcDShape(const IntegrationPoint &ip,
793  DenseMatrix &dshape) const;
794  virtual void ProjectDelta(int vertex, Vector &dofs) const
795  { dofs(0) = 1.0; }
796 };
797 
798 
799 /// Class for linear FE on tetrahedron
800 class Linear3DFiniteElement : public NodalFiniteElement
801 {
802 public:
803  /// Construct a linear FE on tetrahedron
804  Linear3DFiniteElement();
805 
806  /** virtual function which evaluates the values of all
807  shape functions at a given point ip and stores
808  them in the vector shape of dimension Dof (4) */
809  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
810 
811  /** virtual function which evaluates the values of all
812  partial derivatives of all shape functions at a given
813  point ip and stores them in the matrix dshape (Dof x Dim) (4 x 3)
814  so that each row contains the derivatives of one shape function */
815  virtual void CalcDShape(const IntegrationPoint &ip,
816  DenseMatrix &dshape) const;
817 
818  virtual void ProjectDelta(int vertex, Vector &dofs) const
819  { dofs = 0.0; dofs(vertex) = 1.0; }
820 
821  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
822 };
823 
824 /// Class for quadratic FE on tetrahedron
825 class Quadratic3DFiniteElement : public NodalFiniteElement
826 {
827 public:
828  /// Construct a quadratic FE on tetrahedron
829  Quadratic3DFiniteElement();
830 
831  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
832 
833  virtual void CalcDShape(const IntegrationPoint &ip,
834  DenseMatrix &dshape) const;
835 };
836 
837 /// Class for tri-linear FE on cube
838 class TriLinear3DFiniteElement : public NodalFiniteElement
839 {
840 public:
841  /// Construct a tri-linear FE on cube
842  TriLinear3DFiniteElement();
843 
844  /** virtual function which evaluates the values of all
845  shape functions at a given point ip and stores
846  them in the vector shape of dimension Dof (8) */
847  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
848 
849  /** virtual function which evaluates the values of all
850  partial derivatives of all shape functions at a given
851  point ip and stores them in the matrix dshape (Dof x Dim) (8 x 3)
852  so that each row contains the derivatives of one shape function */
853  virtual void CalcDShape(const IntegrationPoint &ip,
854  DenseMatrix &dshape) const;
855 
856  virtual void ProjectDelta(int vertex, Vector &dofs) const
857  { dofs = 0.0; dofs(vertex) = 1.0; }
858 };
859 
860 /// Crouzeix-Raviart finite element on triangle
861 class CrouzeixRaviartFiniteElement : public NodalFiniteElement
862 {
863 public:
864  CrouzeixRaviartFiniteElement();
865  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
866  virtual void CalcDShape(const IntegrationPoint &ip,
867  DenseMatrix &dshape) const;
868  virtual void ProjectDelta(int vertex, Vector &dofs) const
869  { dofs = 1.0; }
870 };
871 
872 /// Crouzeix-Raviart finite element on quadrilateral
873 class CrouzeixRaviartQuadFiniteElement : public NodalFiniteElement
874 {
875 public:
876  CrouzeixRaviartQuadFiniteElement();
877  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
878  virtual void CalcDShape(const IntegrationPoint &ip,
879  DenseMatrix &dshape) const;
880 };
881 
882 class P0SegmentFiniteElement : public NodalFiniteElement
883 {
884 public:
885  P0SegmentFiniteElement(int Ord = 0);
886  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
887  virtual void CalcDShape(const IntegrationPoint &ip,
888  DenseMatrix &dshape) const;
889 };
890 
891 class RT0TriangleFiniteElement : public VectorFiniteElement
892 {
893 private:
894  static const double nk[3][2];
895 
896 public:
897  RT0TriangleFiniteElement();
898 
899  virtual void CalcVShape(const IntegrationPoint &ip,
900  DenseMatrix &shape) const;
901 
902  virtual void CalcVShape(ElementTransformation &Trans,
903  DenseMatrix &shape) const
904  { CalcVShape_RT(Trans, shape); }
905 
906  virtual void CalcDivShape(const IntegrationPoint &ip,
907  Vector &divshape) const;
908 
909  virtual void GetLocalInterpolation (ElementTransformation &Trans,
910  DenseMatrix &I) const;
911 
912  using FiniteElement::Project;
913 
914  virtual void Project (VectorCoefficient &vc,
915  ElementTransformation &Trans, Vector &dofs) const;
916 };
917 
918 class RT0QuadFiniteElement : public VectorFiniteElement
919 {
920 private:
921  static const double nk[4][2];
922 
923 public:
924  RT0QuadFiniteElement();
925 
926  virtual void CalcVShape(const IntegrationPoint &ip,
927  DenseMatrix &shape) const;
928 
929  virtual void CalcVShape(ElementTransformation &Trans,
930  DenseMatrix &shape) const
931  { CalcVShape_RT(Trans, shape); }
932 
933  virtual void CalcDivShape(const IntegrationPoint &ip,
934  Vector &divshape) const;
935 
936  virtual void GetLocalInterpolation (ElementTransformation &Trans,
937  DenseMatrix &I) const;
938 
939  using FiniteElement::Project;
940 
941  virtual void Project (VectorCoefficient &vc,
942  ElementTransformation &Trans, Vector &dofs) const;
943 };
944 
945 class RT1TriangleFiniteElement : public VectorFiniteElement
946 {
947 private:
948  static const double nk[8][2];
949 
950 public:
951  RT1TriangleFiniteElement();
952 
953  virtual void CalcVShape(const IntegrationPoint &ip,
954  DenseMatrix &shape) const;
955 
956  virtual void CalcVShape(ElementTransformation &Trans,
957  DenseMatrix &shape) const
958  { CalcVShape_RT(Trans, shape); }
959 
960  virtual void CalcDivShape(const IntegrationPoint &ip,
961  Vector &divshape) const;
962 
963  virtual void GetLocalInterpolation (ElementTransformation &Trans,
964  DenseMatrix &I) const;
965 
966  using FiniteElement::Project;
967 
968  virtual void Project (VectorCoefficient &vc,
969  ElementTransformation &Trans, Vector &dofs) const;
970 };
971 
972 class RT1QuadFiniteElement : public VectorFiniteElement
973 {
974 private:
975  static const double nk[12][2];
976 
977 public:
978  RT1QuadFiniteElement();
979 
980  virtual void CalcVShape(const IntegrationPoint &ip,
981  DenseMatrix &shape) const;
982 
983  virtual void CalcVShape(ElementTransformation &Trans,
984  DenseMatrix &shape) const
985  { CalcVShape_RT(Trans, shape); }
986 
987  virtual void CalcDivShape(const IntegrationPoint &ip,
988  Vector &divshape) const;
989 
990  virtual void GetLocalInterpolation (ElementTransformation &Trans,
991  DenseMatrix &I) const;
992 
993  using FiniteElement::Project;
994 
995  virtual void Project (VectorCoefficient &vc,
996  ElementTransformation &Trans, Vector &dofs) const;
997 };
998 
999 class RT2TriangleFiniteElement : public VectorFiniteElement
1000 {
1001 private:
1002  static const double M[15][15];
1003 public:
1004  RT2TriangleFiniteElement();
1005 
1006  virtual void CalcVShape(const IntegrationPoint &ip,
1007  DenseMatrix &shape) const;
1008 
1009  virtual void CalcVShape(ElementTransformation &Trans,
1010  DenseMatrix &shape) const
1011  { CalcVShape_RT(Trans, shape); }
1012 
1013  virtual void CalcDivShape(const IntegrationPoint &ip,
1014  Vector &divshape) const;
1015 };
1016 
1017 class RT2QuadFiniteElement : public VectorFiniteElement
1018 {
1019 private:
1020  static const double nk[24][2];
1021  static const double pt[4];
1022  static const double dpt[3];
1023 
1024 public:
1025  RT2QuadFiniteElement();
1026 
1027  virtual void CalcVShape(const IntegrationPoint &ip,
1028  DenseMatrix &shape) const;
1029 
1030  virtual void CalcVShape(ElementTransformation &Trans,
1031  DenseMatrix &shape) const
1032  { CalcVShape_RT(Trans, shape); }
1033 
1034  virtual void CalcDivShape(const IntegrationPoint &ip,
1035  Vector &divshape) const;
1036 
1037  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1038  DenseMatrix &I) const;
1039 
1040  using FiniteElement::Project;
1041 
1042  virtual void Project (VectorCoefficient &vc,
1043  ElementTransformation &Trans, Vector &dofs) const;
1044 };
1045 
1046 /// Linear 1D element with nodes 1/3 and 2/3 (trace of RT1)
1047 class P1SegmentFiniteElement : public NodalFiniteElement
1048 {
1049 public:
1050  P1SegmentFiniteElement();
1051  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1052  virtual void CalcDShape(const IntegrationPoint &ip,
1053  DenseMatrix &dshape) const;
1054 };
1055 
1056 /// Quadratic 1D element with nodes the Gaussian points in [0,1] (trace of RT2)
1057 class P2SegmentFiniteElement : public NodalFiniteElement
1058 {
1059 public:
1060  P2SegmentFiniteElement();
1061  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1062  virtual void CalcDShape(const IntegrationPoint &ip,
1063  DenseMatrix &dshape) const;
1064 };
1065 
1066 class Lagrange1DFiniteElement : public NodalFiniteElement
1067 {
1068 private:
1069  Vector rwk;
1070 #ifndef MFEM_THREAD_SAFE
1071  mutable Vector rxxk;
1072 #endif
1073 public:
1074  Lagrange1DFiniteElement (int degree);
1075  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1076  virtual void CalcDShape(const IntegrationPoint &ip,
1077  DenseMatrix &dshape) const;
1078 };
1079 
1080 class P1TetNonConfFiniteElement : public NodalFiniteElement
1081 {
1082 public:
1083  P1TetNonConfFiniteElement();
1084  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1085  virtual void CalcDShape(const IntegrationPoint &ip,
1086  DenseMatrix &dshape) const;
1087 };
1088 
1089 class P0TetFiniteElement : public NodalFiniteElement
1090 {
1091 public:
1092  P0TetFiniteElement ();
1093  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1094  virtual void CalcDShape(const IntegrationPoint &ip,
1095  DenseMatrix &dshape) const;
1096  virtual void ProjectDelta(int vertex, Vector &dofs) const
1097  { dofs(0) = 1.0; }
1098 };
1099 
1100 class P0HexFiniteElement : public NodalFiniteElement
1101 {
1102 public:
1103  P0HexFiniteElement ();
1104  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1105  virtual void CalcDShape(const IntegrationPoint &ip,
1106  DenseMatrix &dshape) const;
1107  virtual void ProjectDelta(int vertex, Vector &dofs) const
1108  { dofs(0) = 1.0; }
1109 };
1110 
1111 /// Tensor products of 1D FEs (only degree 2 is functional)
1112 class LagrangeHexFiniteElement : public NodalFiniteElement
1113 {
1114 private:
1115  Lagrange1DFiniteElement * fe1d;
1116  int dof1d;
1117  int *I, *J, *K;
1118 #ifndef MFEM_THREAD_SAFE
1119  mutable Vector shape1dx, shape1dy, shape1dz;
1120  mutable DenseMatrix dshape1dx, dshape1dy, dshape1dz;
1121 #endif
1122 
1123 public:
1124  LagrangeHexFiniteElement (int degree);
1125  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1126  virtual void CalcDShape(const IntegrationPoint &ip,
1127  DenseMatrix &dshape) const;
1128  ~LagrangeHexFiniteElement ();
1129 };
1130 
1131 
1132 /// Class for refined linear FE on interval
1133 class RefinedLinear1DFiniteElement : public NodalFiniteElement
1134 {
1135 public:
1136  /// Construct a quadratic FE on interval
1137  RefinedLinear1DFiniteElement();
1138 
1139  /** virtual function which evaluates the values of all
1140  shape functions at a given point ip and stores
1141  them in the vector shape of dimension Dof (3) */
1142  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1143 
1144  /** virtual function which evaluates the derivatives of all
1145  shape functions at a given point ip and stores them in
1146  the matrix dshape (Dof x Dim) (3 x 1) so that each row
1147  contains the derivative of one shape function */
1148  virtual void CalcDShape(const IntegrationPoint &ip,
1149  DenseMatrix &dshape) const;
1150 };
1151 
1152 /// Class for refined linear FE on triangle
1153 class RefinedLinear2DFiniteElement : public NodalFiniteElement
1154 {
1155 public:
1156  /// Construct a quadratic FE on triangle
1157  RefinedLinear2DFiniteElement();
1158 
1159  /** virtual function which evaluates the values of all
1160  shape functions at a given point ip and stores
1161  them in the vector shape of dimension Dof (6) */
1162  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1163 
1164  /** virtual function which evaluates the values of all
1165  partial derivatives of all shape functions at a given
1166  point ip and stores them in the matrix dshape (Dof x Dim) (6 x 2)
1167  so that each row contains the derivatives of one shape function */
1168  virtual void CalcDShape(const IntegrationPoint &ip,
1169  DenseMatrix &dshape) const;
1170 };
1171 
1172 /// Class for refined linear FE on tetrahedron
1173 class RefinedLinear3DFiniteElement : public NodalFiniteElement
1174 {
1175 public:
1176  /// Construct a quadratic FE on tetrahedron
1177  RefinedLinear3DFiniteElement();
1178 
1179  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1180 
1181  virtual void CalcDShape(const IntegrationPoint &ip,
1182  DenseMatrix &dshape) const;
1183 };
1184 
1185 /// Class for refined bi-linear FE on quadrilateral
1186 class RefinedBiLinear2DFiniteElement : public NodalFiniteElement
1187 {
1188 public:
1189  /// Construct a biquadratic FE on quadrilateral
1190  RefinedBiLinear2DFiniteElement();
1191 
1192  /** virtual function which evaluates the values of all
1193  shape functions at a given point ip and stores
1194  them in the vector shape of dimension Dof (9) */
1195  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1196 
1197  /** virtual function which evaluates the values of all
1198  partial derivatives of all shape functions at a given
1199  point ip and stores them in the matrix dshape (Dof x Dim) (9 x 2)
1200  so that each row contains the derivatives of one shape function */
1201  virtual void CalcDShape(const IntegrationPoint &ip,
1202  DenseMatrix &dshape) const;
1203 };
1204 
1205 /// Class for refined trilinear FE on a hexahedron
1206 class RefinedTriLinear3DFiniteElement : public NodalFiniteElement
1207 {
1208 public:
1209  /// Construct a biquadratic FE on quadrilateral
1210  RefinedTriLinear3DFiniteElement();
1211 
1212  /** virtual function which evaluates the values of all
1213  shape functions at a given point ip and stores
1214  them in the vector shape of dimension Dof (9) */
1215  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1216 
1217  /** virtual function which evaluates the values of all
1218  partial derivatives of all shape functions at a given
1219  point ip and stores them in the matrix dshape (Dof x Dim) (9 x 2)
1220  so that each row contains the derivatives of one shape function */
1221  virtual void CalcDShape(const IntegrationPoint &ip,
1222  DenseMatrix &dshape) const;
1223 };
1224 
1225 
1226 class Nedelec1HexFiniteElement : public VectorFiniteElement
1227 {
1228 private:
1229  static const double tk[12][3];
1230 
1231 public:
1232  Nedelec1HexFiniteElement();
1233  virtual void CalcVShape(const IntegrationPoint &ip,
1234  DenseMatrix &shape) const;
1235  virtual void CalcVShape(ElementTransformation &Trans,
1236  DenseMatrix &shape) const
1237  { CalcVShape_ND(Trans, shape); }
1238  virtual void CalcCurlShape(const IntegrationPoint &ip,
1239  DenseMatrix &curl_shape) const;
1240  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1241  DenseMatrix &I) const;
1242  using FiniteElement::Project;
1243  virtual void Project (VectorCoefficient &vc,
1244  ElementTransformation &Trans, Vector &dofs) const;
1245 };
1246 
1247 
1248 class Nedelec1TetFiniteElement : public VectorFiniteElement
1249 {
1250 private:
1251  static const double tk[6][3];
1252 
1253 public:
1254  Nedelec1TetFiniteElement();
1255  virtual void CalcVShape(const IntegrationPoint &ip,
1256  DenseMatrix &shape) const;
1257  virtual void CalcVShape(ElementTransformation &Trans,
1258  DenseMatrix &shape) const
1259  { CalcVShape_ND(Trans, shape); }
1260  virtual void CalcCurlShape(const IntegrationPoint &ip,
1261  DenseMatrix &curl_shape) const;
1262  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1263  DenseMatrix &I) const;
1264  using FiniteElement::Project;
1265  virtual void Project (VectorCoefficient &vc,
1266  ElementTransformation &Trans, Vector &dofs) const;
1267 };
1268 
1269 
1270 class RT0HexFiniteElement : public VectorFiniteElement
1271 {
1272 private:
1273  static const double nk[6][3];
1274 
1275 public:
1276  RT0HexFiniteElement();
1277 
1278  virtual void CalcVShape(const IntegrationPoint &ip,
1279  DenseMatrix &shape) const;
1280 
1281  virtual void CalcVShape(ElementTransformation &Trans,
1282  DenseMatrix &shape) const
1283  { CalcVShape_RT(Trans, shape); }
1284 
1285  virtual void CalcDivShape(const IntegrationPoint &ip,
1286  Vector &divshape) const;
1287 
1288  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1289  DenseMatrix &I) const;
1290 
1291  using FiniteElement::Project;
1292 
1293  virtual void Project (VectorCoefficient &vc,
1294  ElementTransformation &Trans, Vector &dofs) const;
1295 };
1296 
1297 
1298 class RT1HexFiniteElement : public VectorFiniteElement
1299 {
1300 private:
1301  static const double nk[36][3];
1302 
1303 public:
1304  RT1HexFiniteElement();
1305 
1306  virtual void CalcVShape(const IntegrationPoint &ip,
1307  DenseMatrix &shape) const;
1308 
1309  virtual void CalcVShape(ElementTransformation &Trans,
1310  DenseMatrix &shape) const
1311  { CalcVShape_RT(Trans, shape); }
1312 
1313  virtual void CalcDivShape(const IntegrationPoint &ip,
1314  Vector &divshape) const;
1315 
1316  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1317  DenseMatrix &I) const;
1318 
1319  using FiniteElement::Project;
1320 
1321  virtual void Project (VectorCoefficient &vc,
1322  ElementTransformation &Trans, Vector &dofs) const;
1323 };
1324 
1325 
1326 class RT0TetFiniteElement : public VectorFiniteElement
1327 {
1328 private:
1329  static const double nk[4][3];
1330 
1331 public:
1332  RT0TetFiniteElement();
1333 
1334  virtual void CalcVShape(const IntegrationPoint &ip,
1335  DenseMatrix &shape) const;
1336 
1337  virtual void CalcVShape(ElementTransformation &Trans,
1338  DenseMatrix &shape) const
1339  { CalcVShape_RT(Trans, shape); }
1340 
1341  virtual void CalcDivShape(const IntegrationPoint &ip,
1342  Vector &divshape) const;
1343 
1344  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1345  DenseMatrix &I) const;
1346 
1347  using FiniteElement::Project;
1348 
1349  virtual void Project (VectorCoefficient &vc,
1350  ElementTransformation &Trans, Vector &dofs) const;
1351 };
1352 
1353 
1354 class RotTriLinearHexFiniteElement : public NodalFiniteElement
1355 {
1356 public:
1357  RotTriLinearHexFiniteElement();
1358  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1359  virtual void CalcDShape(const IntegrationPoint &ip,
1360  DenseMatrix &dshape) const;
1361 };
1362 
1363 
1364 class Poly_1D
1365 {
1366 public:
1367  class Basis
1368  {
1369  private:
1370  int mode; /* 0 - use change of basis, O(p^2) Evals
1371  1 - use barycentric Lagrangian interpolation, O(p) Evals */
1372  DenseMatrixInverse Ai;
1373  mutable Vector x, w;
1374 
1375  public:
1376  Basis(const int p, const double *nodes, const int _mode = 1);
1377  void Eval(const double x, Vector &u) const;
1378  void Eval(const double x, Vector &u, Vector &d) const;
1379  };
1380 
1381 private:
1382  std::map< int, Array<double*>* > points_container;
1383  std::map< int, Array<Basis*>* > bases_container;
1384 
1385  static Array2D<int> binom;
1386 
1387  static void CalcMono(const int p, const double x, double *u);
1388  static void CalcMono(const int p, const double x, double *u, double *d);
1389 
1390  static void CalcLegendre(const int p, const double x, double *u);
1391  static void CalcLegendre(const int p, const double x, double *u, double *d);
1392 
1393  static void CalcChebyshev(const int p, const double x, double *u);
1394  static void CalcChebyshev(const int p, const double x, double *u, double *d);
1395 
1396  QuadratureFunctions1D quad_func;
1397 
1398 public:
1399  Poly_1D() { }
1400 
1401  /** @brief Get a poiner to an array containing the binomial coefficients "p
1402  choose k" for k=0,...,p for the given p. */
1403  static const int *Binom(const int p);
1404 
1405  /** @brief Get the coordinates of the points of the given Quadrature1D type.
1406  @param p the polynomial degree; the number of points is `p+1`.
1407  @param type the Quadrature1D type.
1408  @return a pointer to an array containing the `p+1` coordiantes of the
1409  quadrature points. */
1410  const double *GetPoints(const int p, const int type);
1411  const double *OpenPoints(const int p,
1412  const int type = Quadrature1D::GaussLegendre)
1413  { return GetPoints(p, type); }
1414  const double *ClosedPoints(const int p,
1415  const int type = Quadrature1D::GaussLobatto)
1416  { return GetPoints(p, type); }
1417 
1418  /** @brief Get a Poly_1D::Basis object of the given degree and Quadrature1D
1419  type.
1420  @param p the polynomial degree of the basis.
1421  @param type the Quadrature1D type.
1422  @return a reference to an object of type Poly_1D::Basis that represents
1423  the requested nodal basis. */
1424  Basis &GetBasis(const int p, const int type);
1425  Basis &OpenBasis(const int p,
1426  const int type = Quadrature1D::GaussLegendre)
1427  { return GetBasis(p, type); }
1428  Basis &ClosedBasis(const int p,
1429  const int type = Quadrature1D::GaussLobatto)
1430  { return GetBasis(p, type); }
1431 
1432  // Evaluate the values of a hierarchical 1D basis at point x
1433  // hierarchical = k-th basis function is degree k polynomial
1434  static void CalcBasis(const int p, const double x, double *u)
1435  // { CalcMono(p, x, u); }
1436  // Bernstein basis is not hierarchical --> does not work for triangles
1437  // and tetrahedra
1438  // { CalcBernstein(p, x, u); }
1439  // { CalcLegendre(p, x, u); }
1440  { CalcChebyshev(p, x, u); }
1441 
1442  // Evaluate the values and derivatives of a hierarchical 1D basis at point x
1443  static void CalcBasis(const int p, const double x, double *u, double *d)
1444  // { CalcMono(p, x, u, d); }
1445  // { CalcBernstein(p, x, u, d); }
1446  // { CalcLegendre(p, x, u, d); }
1447  { CalcChebyshev(p, x, u, d); }
1448 
1449  // Evaluate a representation of a Delta function at point x
1450  static double CalcDelta(const int p, const double x)
1451  { return pow(x, (double) p); }
1452 
1453  static void ChebyshevPoints(const int p, double *x);
1454 
1455  /// Compute the terms in the expansion of the binomial (x + y)^p
1456  static void CalcBinomTerms(const int p, const double x, const double y,
1457  double *u);
1458  /** Compute the terms in the expansion of the binomial (x + y)^p and their
1459  derivatives with respect to x assuming that dy/dx = -1. */
1460  static void CalcBinomTerms(const int p, const double x, const double y,
1461  double *u, double *d);
1462  /** Compute the derivatives (w.r.t. x) of the terms in the expansion of the
1463  binomial (x + y)^p assuming that dy/dx = -1. */
1464  static void CalcDBinomTerms(const int p, const double x, const double y,
1465  double *d);
1466  static void CalcBernstein(const int p, const double x, double *u)
1467  { CalcBinomTerms(p, x, 1. - x, u); }
1468  static void CalcBernstein(const int p, const double x, double *u, double *d)
1469  { CalcBinomTerms(p, x, 1. - x, u, d); }
1470 
1471  ~Poly_1D();
1472 };
1473 
1474 extern Poly_1D poly1d;
1475 
1476 
1477 class H1_SegmentElement : public NodalFiniteElement
1478 {
1479 private:
1480  int pt_type;
1481  Poly_1D::Basis &basis1d;
1482 #ifndef MFEM_THREAD_SAFE
1483  mutable Vector shape_x, dshape_x;
1484 #endif
1485  Array<int> dof_map;
1486 
1487 public:
1488  H1_SegmentElement(const int p, const int type = Quadrature1D::GaussLobatto);
1489  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1490  virtual void CalcDShape(const IntegrationPoint &ip,
1491  DenseMatrix &dshape) const;
1492  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1493  const Array<int> &GetDofMap() const { return dof_map; }
1494 };
1495 
1496 
1497 class H1_QuadrilateralElement : public NodalFiniteElement
1498 {
1499 private:
1500  int pt_type;
1501  Poly_1D::Basis &basis1d;
1502 #ifndef MFEM_THREAD_SAFE
1503  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1504 #endif
1505  Array<int> dof_map;
1506 
1507 public:
1508  H1_QuadrilateralElement(const int p,
1509  const int type = Quadrature1D::GaussLobatto);
1510  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1511  virtual void CalcDShape(const IntegrationPoint &ip,
1512  DenseMatrix &dshape) const;
1513  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1514  const Array<int> &GetDofMap() const { return dof_map; }
1515 };
1516 
1517 
1518 class H1_HexahedronElement : public NodalFiniteElement
1519 {
1520 private:
1521  int pt_type;
1522  Poly_1D::Basis &basis1d;
1523 #ifndef MFEM_THREAD_SAFE
1524  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1525 #endif
1526  Array<int> dof_map;
1527 
1528 public:
1529  H1_HexahedronElement(const int p, const int type = Quadrature1D::GaussLobatto);
1530  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1531  virtual void CalcDShape(const IntegrationPoint &ip,
1532  DenseMatrix &dshape) const;
1533  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1534  const Array<int> &GetDofMap() const { return dof_map; }
1535 };
1536 
1537 class H1Pos_SegmentElement : public PositiveFiniteElement
1538 {
1539 private:
1540 #ifndef MFEM_THREAD_SAFE
1541  // This is to share scratch space between invocations, which helps
1542  // speed things up, but with OpenMP, we need one copy per thread.
1543  // Right now, we solve this by allocating this space within each function
1544  // call every time we call it. Alternatively, we should do some sort
1545  // thread private thing. Brunner, Jan 2014
1546  mutable Vector shape_x, dshape_x;
1547 #endif
1548  Array<int> dof_map;
1549 
1550 public:
1551  H1Pos_SegmentElement(const int p);
1552  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1553  virtual void CalcDShape(const IntegrationPoint &ip,
1554  DenseMatrix &dshape) const;
1555  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1556  const Array<int> &GetDofMap() const { return dof_map; }
1557 };
1558 
1559 
1560 class H1Pos_QuadrilateralElement : public PositiveFiniteElement
1561 {
1562 private:
1563 #ifndef MFEM_THREAD_SAFE
1564  // See comment in H1Pos_SegmentElement
1565  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1566 #endif
1567  Array<int> dof_map;
1568 
1569 public:
1570  H1Pos_QuadrilateralElement(const int p);
1571  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1572  virtual void CalcDShape(const IntegrationPoint &ip,
1573  DenseMatrix &dshape) const;
1574  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1575  const Array<int> &GetDofMap() const { return dof_map; }
1576 };
1577 
1578 
1579 class H1Pos_HexahedronElement : public PositiveFiniteElement
1580 {
1581 private:
1582 #ifndef MFEM_THREAD_SAFE
1583  // See comment in H1Pos_SegementElement.
1584  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1585 #endif
1586  Array<int> dof_map;
1587 
1588 public:
1589  H1Pos_HexahedronElement(const int p);
1590  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1591  virtual void CalcDShape(const IntegrationPoint &ip,
1592  DenseMatrix &dshape) const;
1593  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1594  const Array<int> &GetDofMap() const { return dof_map; }
1595 };
1596 
1597 
1598 class H1_TriangleElement : public NodalFiniteElement
1599 {
1600 private:
1601 #ifndef MFEM_THREAD_SAFE
1602  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1603  mutable DenseMatrix du;
1604 #endif
1605  DenseMatrixInverse Ti;
1606 
1607 public:
1608  H1_TriangleElement(const int p, const int type = Quadrature1D::GaussLobatto);
1609  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1610  virtual void CalcDShape(const IntegrationPoint &ip,
1611  DenseMatrix &dshape) const;
1612 };
1613 
1614 
1615 class H1_TetrahedronElement : public NodalFiniteElement
1616 {
1617 private:
1618 #ifndef MFEM_THREAD_SAFE
1619  mutable Vector shape_x, shape_y, shape_z, shape_l;
1620  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1621  mutable DenseMatrix du;
1622 #endif
1623  DenseMatrixInverse Ti;
1624 
1625 public:
1626  H1_TetrahedronElement(const int p,
1627  const int type = Quadrature1D::GaussLobatto);
1628  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1629  virtual void CalcDShape(const IntegrationPoint &ip,
1630  DenseMatrix &dshape) const;
1631 };
1632 
1633 
1634 class H1Pos_TriangleElement : public PositiveFiniteElement
1635 {
1636 protected:
1637 #ifndef MFEM_THREAD_SAFE
1638  mutable Vector m_shape, dshape_1d;
1639  mutable DenseMatrix m_dshape;
1640 #endif
1641  Array<int> dof_map;
1642 
1643 public:
1644  H1Pos_TriangleElement(const int p);
1645 
1646  // The size of shape is (p+1)(p+2)/2 (dof).
1647  static void CalcShape(const int p, const double x, const double y,
1648  double *shape);
1649 
1650  // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
1651  static void CalcDShape(const int p, const double x, const double y,
1652  double *dshape_1d, double *dshape);
1653 
1654  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1655  virtual void CalcDShape(const IntegrationPoint &ip,
1656  DenseMatrix &dshape) const;
1657 };
1658 
1659 
1660 class H1Pos_TetrahedronElement : public PositiveFiniteElement
1661 {
1662 protected:
1663 #ifndef MFEM_THREAD_SAFE
1664  mutable Vector m_shape, dshape_1d;
1665  mutable DenseMatrix m_dshape;
1666 #endif
1667  Array<int> dof_map;
1668 
1669 public:
1670  H1Pos_TetrahedronElement(const int p);
1671 
1672  // The size of shape is (p+1)(p+2)(p+3)/6 (dof).
1673  static void CalcShape(const int p, const double x, const double y,
1674  const double z, double *shape);
1675 
1676  // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
1677  static void CalcDShape(const int p, const double x, const double y,
1678  const double z, double *dshape_1d, double *dshape);
1679 
1680  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1681  virtual void CalcDShape(const IntegrationPoint &ip,
1682  DenseMatrix &dshape) const;
1683 };
1684 
1685 
1686 class L2_SegmentElement : public NodalFiniteElement
1687 {
1688 private:
1689  int type;
1690  Poly_1D::Basis &basis1d;
1691 #ifndef MFEM_THREAD_SAFE
1692  mutable Vector shape_x, dshape_x;
1693 #endif
1694 
1695 public:
1696  L2_SegmentElement(const int p, const int type = Quadrature1D::GaussLegendre);
1697  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1698  virtual void CalcDShape(const IntegrationPoint &ip,
1699  DenseMatrix &dshape) const;
1700  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1701 };
1702 
1703 
1704 class L2Pos_SegmentElement : public PositiveFiniteElement
1705 {
1706 private:
1707 #ifndef MFEM_THREAD_SAFE
1708  mutable Vector shape_x, dshape_x;
1709 #endif
1710 
1711 public:
1712  L2Pos_SegmentElement(const int p);
1713  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1714  virtual void CalcDShape(const IntegrationPoint &ip,
1715  DenseMatrix &dshape) const;
1716  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1717 };
1718 
1719 
1720 class L2_QuadrilateralElement : public NodalFiniteElement
1721 {
1722 private:
1723  int type;
1724  Poly_1D::Basis &basis1d;
1725 #ifndef MFEM_THREAD_SAFE
1726  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1727 #endif
1728 
1729 public:
1730  L2_QuadrilateralElement(const int p,
1731  const int _type = Quadrature1D::GaussLegendre);
1732  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1733  virtual void CalcDShape(const IntegrationPoint &ip,
1734  DenseMatrix &dshape) const;
1735  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1736  virtual void ProjectCurl(const FiniteElement &fe,
1737  ElementTransformation &Trans,
1738  DenseMatrix &curl) const
1739  { ProjectCurl_2D(fe, Trans, curl); }
1740 };
1741 
1742 
1743 class L2Pos_QuadrilateralElement : public PositiveFiniteElement
1744 {
1745 private:
1746 #ifndef MFEM_THREAD_SAFE
1747  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1748 #endif
1749 
1750 public:
1751  L2Pos_QuadrilateralElement(const int p);
1752  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1753  virtual void CalcDShape(const IntegrationPoint &ip,
1754  DenseMatrix &dshape) const;
1755  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1756 };
1757 
1758 
1759 class L2_HexahedronElement : public NodalFiniteElement
1760 {
1761 private:
1762  int type;
1763  Poly_1D::Basis &basis1d;
1764 #ifndef MFEM_THREAD_SAFE
1765  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1766 #endif
1767 
1768 public:
1769  L2_HexahedronElement(const int p,
1770  const int _type = Quadrature1D::GaussLegendre);
1771  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1772  virtual void CalcDShape(const IntegrationPoint &ip,
1773  DenseMatrix &dshape) const;
1774  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1775 };
1776 
1777 
1778 class L2Pos_HexahedronElement : public PositiveFiniteElement
1779 {
1780 private:
1781 #ifndef MFEM_THREAD_SAFE
1782  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1783 #endif
1784 
1785 public:
1786  L2Pos_HexahedronElement(const int p);
1787  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1788  virtual void CalcDShape(const IntegrationPoint &ip,
1789  DenseMatrix &dshape) const;
1790  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1791 };
1792 
1793 
1794 class L2_TriangleElement : public NodalFiniteElement
1795 {
1796 private:
1797 #ifndef MFEM_THREAD_SAFE
1798  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1799  mutable DenseMatrix du;
1800 #endif
1801  DenseMatrixInverse Ti;
1802 
1803 public:
1804  L2_TriangleElement(const int p,
1805  const int type = Quadrature1D::GaussLegendre);
1806  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1807  virtual void CalcDShape(const IntegrationPoint &ip,
1808  DenseMatrix &dshape) const;
1809  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1810  virtual void ProjectCurl(const FiniteElement &fe,
1811  ElementTransformation &Trans,
1812  DenseMatrix &curl) const
1813  { ProjectCurl_2D(fe, Trans, curl); }
1814 };
1815 
1816 
1817 class L2Pos_TriangleElement : public PositiveFiniteElement
1818 {
1819 private:
1820 #ifndef MFEM_THREAD_SAFE
1821  mutable Vector dshape_1d;
1822 #endif
1823 
1824 public:
1825  L2Pos_TriangleElement(const int p);
1826  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1827  virtual void CalcDShape(const IntegrationPoint &ip,
1828  DenseMatrix &dshape) const;
1829  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1830 };
1831 
1832 
1833 class L2_TetrahedronElement : public NodalFiniteElement
1834 {
1835 private:
1836 #ifndef MFEM_THREAD_SAFE
1837  mutable Vector shape_x, shape_y, shape_z, shape_l;
1838  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1839  mutable DenseMatrix du;
1840 #endif
1841  DenseMatrixInverse Ti;
1842 
1843 public:
1844  L2_TetrahedronElement(const int p,
1845  const int type = Quadrature1D::GaussLegendre);
1846  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1847  virtual void CalcDShape(const IntegrationPoint &ip,
1848  DenseMatrix &dshape) const;
1849  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1850 };
1851 
1852 
1853 class L2Pos_TetrahedronElement : public PositiveFiniteElement
1854 {
1855 private:
1856 #ifndef MFEM_THREAD_SAFE
1857  mutable Vector dshape_1d;
1858 #endif
1859 
1860 public:
1861  L2Pos_TetrahedronElement(const int p);
1862  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1863  virtual void CalcDShape(const IntegrationPoint &ip,
1864  DenseMatrix &dshape) const;
1865  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1866 };
1867 
1868 
1869 class RT_QuadrilateralElement : public VectorFiniteElement
1870 {
1871 private:
1872  static const double nk[8];
1873 
1874  Poly_1D::Basis &cbasis1d, &obasis1d;
1875 #ifndef MFEM_THREAD_SAFE
1876  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
1877  mutable Vector dshape_cx, dshape_cy;
1878 #endif
1879  Array<int> dof_map, dof2nk;
1880 
1881 public:
1882  RT_QuadrilateralElement(const int p,
1883  const int cp_type = Quadrature1D::GaussLobatto,
1884  const int op_type = Quadrature1D::GaussLegendre);
1885  virtual void CalcVShape(const IntegrationPoint &ip,
1886  DenseMatrix &shape) const;
1887  virtual void CalcVShape(ElementTransformation &Trans,
1888  DenseMatrix &shape) const
1889  { CalcVShape_RT(Trans, shape); }
1890  virtual void CalcDivShape(const IntegrationPoint &ip,
1891  Vector &divshape) const;
1892  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1893  DenseMatrix &I) const
1894  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1895  using FiniteElement::Project;
1896  virtual void Project(VectorCoefficient &vc,
1897  ElementTransformation &Trans, Vector &dofs) const
1898  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1899  virtual void ProjectMatrixCoefficient(
1900  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
1901  { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
1902  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1903  DenseMatrix &I) const
1904  { Project_RT(nk, dof2nk, fe, Trans, I); }
1905  // Gradient + rotation = Curl: H1 -> H(div)
1906  virtual void ProjectGrad(const FiniteElement &fe,
1907  ElementTransformation &Trans,
1908  DenseMatrix &grad) const
1909  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1910  // Curl = Gradient + rotation: H1 -> H(div)
1911  virtual void ProjectCurl(const FiniteElement &fe,
1912  ElementTransformation &Trans,
1913  DenseMatrix &curl) const
1914  { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
1915 };
1916 
1917 
1918 class RT_HexahedronElement : public VectorFiniteElement
1919 {
1920  static const double nk[18];
1921 
1922  Poly_1D::Basis &cbasis1d, &obasis1d;
1923 #ifndef MFEM_THREAD_SAFE
1924  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
1925  mutable Vector dshape_cx, dshape_cy, dshape_cz;
1926 #endif
1927  Array<int> dof_map, dof2nk;
1928 
1929 public:
1930  RT_HexahedronElement(const int p,
1931  const int cp_type = Quadrature1D::GaussLobatto,
1932  const int op_type = Quadrature1D::GaussLegendre);
1933 
1934  virtual void CalcVShape(const IntegrationPoint &ip,
1935  DenseMatrix &shape) const;
1936  virtual void CalcVShape(ElementTransformation &Trans,
1937  DenseMatrix &shape) const
1938  { CalcVShape_RT(Trans, shape); }
1939  virtual void CalcDivShape(const IntegrationPoint &ip,
1940  Vector &divshape) const;
1941  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1942  DenseMatrix &I) const
1943  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1944  using FiniteElement::Project;
1945  virtual void Project(VectorCoefficient &vc,
1946  ElementTransformation &Trans, Vector &dofs) const
1947  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1948  virtual void ProjectMatrixCoefficient(
1949  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
1950  { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
1951  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1952  DenseMatrix &I) const
1953  { Project_RT(nk, dof2nk, fe, Trans, I); }
1954  virtual void ProjectCurl(const FiniteElement &fe,
1955  ElementTransformation &Trans,
1956  DenseMatrix &curl) const
1957  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
1958 };
1959 
1960 
1961 class RT_TriangleElement : public VectorFiniteElement
1962 {
1963  static const double nk[6], c;
1964 
1965 #ifndef MFEM_THREAD_SAFE
1966  mutable Vector shape_x, shape_y, shape_l;
1967  mutable Vector dshape_x, dshape_y, dshape_l;
1968  mutable DenseMatrix u;
1969  mutable Vector divu;
1970 #endif
1971  Array<int> dof2nk;
1972  DenseMatrixInverse Ti;
1973 
1974 public:
1975  RT_TriangleElement(const int p);
1976  virtual void CalcVShape(const IntegrationPoint &ip,
1977  DenseMatrix &shape) const;
1978  virtual void CalcVShape(ElementTransformation &Trans,
1979  DenseMatrix &shape) const
1980  { CalcVShape_RT(Trans, shape); }
1981  virtual void CalcDivShape(const IntegrationPoint &ip,
1982  Vector &divshape) const;
1983  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1984  DenseMatrix &I) const
1985  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1986  using FiniteElement::Project;
1987  virtual void Project(VectorCoefficient &vc,
1988  ElementTransformation &Trans, Vector &dofs) const
1989  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1990  virtual void ProjectMatrixCoefficient(
1991  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
1992  { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
1993  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1994  DenseMatrix &I) const
1995  { Project_RT(nk, dof2nk, fe, Trans, I); }
1996  // Gradient + rotation = Curl: H1 -> H(div)
1997  virtual void ProjectGrad(const FiniteElement &fe,
1998  ElementTransformation &Trans,
1999  DenseMatrix &grad) const
2000  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
2001  // Curl = Gradient + rotation: H1 -> H(div)
2002  virtual void ProjectCurl(const FiniteElement &fe,
2003  ElementTransformation &Trans,
2004  DenseMatrix &curl) const
2005  { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
2006 };
2007 
2008 
2009 class RT_TetrahedronElement : public VectorFiniteElement
2010 {
2011  static const double nk[12], c;
2012 
2013 #ifndef MFEM_THREAD_SAFE
2014  mutable Vector shape_x, shape_y, shape_z, shape_l;
2015  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
2016  mutable DenseMatrix u;
2017  mutable Vector divu;
2018 #endif
2019  Array<int> dof2nk;
2020  DenseMatrixInverse Ti;
2021 
2022 public:
2023  RT_TetrahedronElement(const int p);
2024  virtual void CalcVShape(const IntegrationPoint &ip,
2025  DenseMatrix &shape) const;
2026  virtual void CalcVShape(ElementTransformation &Trans,
2027  DenseMatrix &shape) const
2028  { CalcVShape_RT(Trans, shape); }
2029  virtual void CalcDivShape(const IntegrationPoint &ip,
2030  Vector &divshape) const;
2031  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2032  DenseMatrix &I) const
2033  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
2034  using FiniteElement::Project;
2035  virtual void Project(VectorCoefficient &vc,
2036  ElementTransformation &Trans, Vector &dofs) const
2037  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
2038  virtual void ProjectMatrixCoefficient(
2039  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
2040  { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
2041  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
2042  DenseMatrix &I) const
2043  { Project_RT(nk, dof2nk, fe, Trans, I); }
2044  virtual void ProjectCurl(const FiniteElement &fe,
2045  ElementTransformation &Trans,
2046  DenseMatrix &curl) const
2047  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
2048 };
2049 
2050 
2051 class ND_HexahedronElement : public VectorFiniteElement
2052 {
2053  static const double tk[18];
2054 
2055  Poly_1D::Basis &cbasis1d, &obasis1d;
2056 #ifndef MFEM_THREAD_SAFE
2057  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
2058  mutable Vector dshape_cx, dshape_cy, dshape_cz;
2059 #endif
2060  Array<int> dof_map, dof2tk;
2061 
2062 public:
2063  ND_HexahedronElement(const int p,
2064  const int cp_type = Quadrature1D::GaussLobatto,
2065  const int op_type = Quadrature1D::GaussLegendre);
2066 
2067  virtual void CalcVShape(const IntegrationPoint &ip,
2068  DenseMatrix &shape) const;
2069 
2070  virtual void CalcVShape(ElementTransformation &Trans,
2071  DenseMatrix &shape) const
2072  { CalcVShape_ND(Trans, shape); }
2073 
2074  virtual void CalcCurlShape(const IntegrationPoint &ip,
2075  DenseMatrix &curl_shape) const;
2076 
2077  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2078  DenseMatrix &I) const
2079  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2080 
2081  using FiniteElement::Project;
2082 
2083  virtual void Project(VectorCoefficient &vc,
2084  ElementTransformation &Trans, Vector &dofs) const
2085  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2086 
2087  virtual void ProjectMatrixCoefficient(
2088  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
2089  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
2090 
2091  virtual void Project(const FiniteElement &fe,
2092  ElementTransformation &Trans,
2093  DenseMatrix &I) const
2094  { Project_ND(tk, dof2tk, fe, Trans, I); }
2095 
2096  virtual void ProjectGrad(const FiniteElement &fe,
2097  ElementTransformation &Trans,
2098  DenseMatrix &grad) const
2099  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2100 
2101  virtual void ProjectCurl(const FiniteElement &fe,
2102  ElementTransformation &Trans,
2103  DenseMatrix &curl) const
2104  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
2105 };
2106 
2107 
2108 class ND_QuadrilateralElement : public VectorFiniteElement
2109 {
2110  static const double tk[8];
2111 
2112  Poly_1D::Basis &cbasis1d, &obasis1d;
2113 #ifndef MFEM_THREAD_SAFE
2114  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
2115  mutable Vector dshape_cx, dshape_cy;
2116 #endif
2117  Array<int> dof_map, dof2tk;
2118 
2119 public:
2120  ND_QuadrilateralElement(const int p,
2121  const int cp_type = Quadrature1D::GaussLobatto,
2122  const int op_type = Quadrature1D::GaussLegendre);
2123  virtual void CalcVShape(const IntegrationPoint &ip,
2124  DenseMatrix &shape) const;
2125  virtual void CalcVShape(ElementTransformation &Trans,
2126  DenseMatrix &shape) const
2127  { CalcVShape_ND(Trans, shape); }
2128  virtual void CalcCurlShape(const IntegrationPoint &ip,
2129  DenseMatrix &curl_shape) const;
2130  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2131  DenseMatrix &I) const
2132  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2133  using FiniteElement::Project;
2134  virtual void Project(VectorCoefficient &vc,
2135  ElementTransformation &Trans, Vector &dofs) const
2136  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2137  virtual void ProjectMatrixCoefficient(
2138  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
2139  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
2140  virtual void Project(const FiniteElement &fe,
2141  ElementTransformation &Trans,
2142  DenseMatrix &I) const
2143  { Project_ND(tk, dof2tk, fe, Trans, I); }
2144  virtual void ProjectGrad(const FiniteElement &fe,
2145  ElementTransformation &Trans,
2146  DenseMatrix &grad) const
2147  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2148 };
2149 
2150 
2151 class ND_TetrahedronElement : public VectorFiniteElement
2152 {
2153  static const double tk[18], c;
2154 
2155 #ifndef MFEM_THREAD_SAFE
2156  mutable Vector shape_x, shape_y, shape_z, shape_l;
2157  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
2158  mutable DenseMatrix u;
2159 #endif
2160  Array<int> dof2tk;
2161  DenseMatrixInverse Ti;
2162 
2163 public:
2164  ND_TetrahedronElement(const int p);
2165  virtual void CalcVShape(const IntegrationPoint &ip,
2166  DenseMatrix &shape) const;
2167  virtual void CalcVShape(ElementTransformation &Trans,
2168  DenseMatrix &shape) const
2169  { CalcVShape_ND(Trans, shape); }
2170  virtual void CalcCurlShape(const IntegrationPoint &ip,
2171  DenseMatrix &curl_shape) const;
2172  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2173  DenseMatrix &I) const
2174  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2175  using FiniteElement::Project;
2176  virtual void Project(VectorCoefficient &vc,
2177  ElementTransformation &Trans, Vector &dofs) const
2178  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2179  virtual void ProjectMatrixCoefficient(
2180  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
2181  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
2182  virtual void Project(const FiniteElement &fe,
2183  ElementTransformation &Trans,
2184  DenseMatrix &I) const
2185  { Project_ND(tk, dof2tk, fe, Trans, I); }
2186  virtual void ProjectGrad(const FiniteElement &fe,
2187  ElementTransformation &Trans,
2188  DenseMatrix &grad) const
2189  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2190 
2191  virtual void ProjectCurl(const FiniteElement &fe,
2192  ElementTransformation &Trans,
2193  DenseMatrix &curl) const
2194  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
2195 };
2196 
2197 class ND_TriangleElement : public VectorFiniteElement
2198 {
2199  static const double tk[8], c;
2200 
2201 #ifndef MFEM_THREAD_SAFE
2202  mutable Vector shape_x, shape_y, shape_l;
2203  mutable Vector dshape_x, dshape_y, dshape_l;
2204  mutable DenseMatrix u;
2205  mutable Vector curlu;
2206 #endif
2207  Array<int> dof2tk;
2208  DenseMatrixInverse Ti;
2209 
2210 public:
2211  ND_TriangleElement(const int p);
2212  virtual void CalcVShape(const IntegrationPoint &ip,
2213  DenseMatrix &shape) const;
2214  virtual void CalcVShape(ElementTransformation &Trans,
2215  DenseMatrix &shape) const
2216  { CalcVShape_ND(Trans, shape); }
2217  virtual void CalcCurlShape(const IntegrationPoint &ip,
2218  DenseMatrix &curl_shape) const;
2219  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2220  DenseMatrix &I) const
2221  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2222  using FiniteElement::Project;
2223  virtual void Project(VectorCoefficient &vc,
2224  ElementTransformation &Trans, Vector &dofs) const
2225  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2226  virtual void ProjectMatrixCoefficient(
2227  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
2228  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
2229  virtual void Project(const FiniteElement &fe,
2230  ElementTransformation &Trans,
2231  DenseMatrix &I) const
2232  { Project_ND(tk, dof2tk, fe, Trans, I); }
2233  virtual void ProjectGrad(const FiniteElement &fe,
2234  ElementTransformation &Trans,
2235  DenseMatrix &grad) const
2236  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2237 };
2238 
2239 
2240 class ND_SegmentElement : public VectorFiniteElement
2241 {
2242  static const double tk[1];
2243 
2244  Poly_1D::Basis &obasis1d;
2245  Array<int> dof2tk;
2246 
2247 public:
2248  ND_SegmentElement(const int p,
2249  const int op_type = Quadrature1D::GaussLegendre );
2250  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
2251  { obasis1d.Eval(ip.x, shape); }
2252  virtual void CalcVShape(const IntegrationPoint &ip,
2253  DenseMatrix &shape) const;
2254  virtual void CalcVShape(ElementTransformation &Trans,
2255  DenseMatrix &shape) const
2256  { CalcVShape_ND(Trans, shape); }
2257  // virtual void CalcCurlShape(const IntegrationPoint &ip,
2258  // DenseMatrix &curl_shape) const;
2259  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2260  DenseMatrix &I) const
2261  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2262  using FiniteElement::Project;
2263  virtual void Project(VectorCoefficient &vc,
2264  ElementTransformation &Trans, Vector &dofs) const
2265  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2266  virtual void ProjectMatrixCoefficient(
2267  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
2268  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
2269  virtual void Project(const FiniteElement &fe,
2270  ElementTransformation &Trans,
2271  DenseMatrix &I) const
2272  { Project_ND(tk, dof2tk, fe, Trans, I); }
2273  virtual void ProjectGrad(const FiniteElement &fe,
2274  ElementTransformation &Trans,
2275  DenseMatrix &grad) const
2276  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2277 };
2278 
2279 
2280 class NURBSFiniteElement : public ScalarFiniteElement
2281 {
2282 protected:
2283  mutable Array <KnotVector*> kv;
2284  mutable int *ijk, patch, elem;
2285  mutable Vector weights;
2286 
2287 public:
2288  NURBSFiniteElement(int D, int G, int Do, int O, int F)
2289  : ScalarFiniteElement(D, G, Do, O, F)
2290  {
2291  ijk = NULL;
2292  patch = elem = -1;
2293  kv.SetSize(Dim);
2294  weights.SetSize(Dof);
2295  weights = 1.0;
2296  }
2297 
2298  void Reset () const { patch = elem = -1; }
2299  void SetIJK (int *IJK) const { ijk = IJK; }
2300  int GetPatch () const { return patch; }
2301  void SetPatch (int p) const { patch = p; }
2302  int GetElement () const { return elem; }
2303  void SetElement (int e) const { elem = e; }
2304  Array <KnotVector*> &KnotVectors() const { return kv; }
2305  Vector &Weights () const { return weights; }
2306 };
2307 
2308 class NURBS1DFiniteElement : public NURBSFiniteElement
2309 {
2310 protected:
2311  mutable Vector shape_x;
2312 
2313 public:
2314  NURBS1DFiniteElement(int p)
2315  : NURBSFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
2316  shape_x(p + 1) { }
2317 
2318  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2319  virtual void CalcDShape(const IntegrationPoint &ip,
2320  DenseMatrix &dshape) const;
2321 };
2322 
2323 class NURBS2DFiniteElement : public NURBSFiniteElement
2324 {
2325 protected:
2326  mutable Vector u, shape_x, shape_y, dshape_x, dshape_y;
2327 
2328 public:
2329  NURBS2DFiniteElement(int p)
2330  : NURBSFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
2331  FunctionSpace::Qk), u(Dof),
2332  shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1), dshape_y(p + 1) { }
2333 
2334  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2335  virtual void CalcDShape(const IntegrationPoint &ip,
2336  DenseMatrix &dshape) const;
2337 };
2338 
2339 class NURBS3DFiniteElement : public NURBSFiniteElement
2340 {
2341 protected:
2342  mutable Vector u, shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
2343 
2344 public:
2345  NURBS3DFiniteElement(int p)
2346  : NURBSFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
2347  FunctionSpace::Qk), u(Dof),
2348  shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
2349  dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1) { }
2350 
2351  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2352  virtual void CalcDShape(const IntegrationPoint &ip,
2353  DenseMatrix &dshape) const;
2354 };
2355 
2356 } // namespace mfem
2357 
2358 #endif
mfem::FiniteElement
Abstract class for Finite Elements.
Definition: fe.hpp:47
mfem::RefinedLinear3DFiniteElement::RefinedLinear3DFiniteElement
RefinedLinear3DFiniteElement()
Construct a quadratic FE on tetrahedron.
Definition: fe.cpp:4270
mfem::RT0TetFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1337
mfem::BiQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1383
mfem::L2_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8285
mfem::ND_SegmentElement
Definition: fe.hpp:2240
mfem::VectorFiniteElement::curlshape_J
DenseMatrix curlshape_J
Definition: fe.hpp:413
mfem::H1Pos_SegmentElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1556
mfem::RT0TetFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:6069
mfem::RT_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1945
mfem::FiniteElement::GetDim
int GetDim() const
Returns the reference space dimension for the finite element.
Definition: fe.hpp:116
mfem::H1Pos_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7185
mfem::RT1TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2907
mfem::L2_SegmentElement::L2_SegmentElement
L2_SegmentElement(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8159
mfem::RT1HexFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1309
mfem::P1TetNonConfFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:3848
mfem::P1OnQuadFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1131
mfem::Poly_1D::CalcBernstein
static void CalcBernstein(const int p, const double x, double *u, double *d)
Definition: fe.hpp:1468
mfem::RT_QuadrilateralElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1911
mfem::IntegrationRule
Class for an integration rule - an Array of IntegrationPoint.
Definition: intrules.hpp:83
mfem::P1SegmentFiniteElement
Linear 1D element with nodes 1/3 and 2/3 (trace of RT1)
Definition: fe.hpp:1047
mfem::P2SegmentFiniteElement
Quadratic 1D element with nodes the Gaussian points in [0,1] (trace of RT2)
Definition: fe.hpp:1057
mfem::L2Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8680
mfem::NURBS2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:10998
mfem::Linear3DFiniteElement::Linear3DFiniteElement
Linear3DFiniteElement()
Construct a linear FE on tetrahedron.
Definition: fe.cpp:2306
mfem::Poly_1D::CalcDelta
static double CalcDelta(const int p, const double x)
Definition: fe.hpp:1450
mfem::RT1QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:3089
mfem::RT_TriangleElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1978
mfem::RT_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2031
mfem::L2Pos_TriangleElement
Definition: fe.hpp:1817
mfem::L2Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8437
mfem::VectorFiniteElement::ProjectMatrixCoefficient_RT
void ProjectMatrixCoefficient_RT(const double *nk, const Array< int > &d2n, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.cpp:577
mfem::VectorFiniteElement::ProjectMatrixCoefficient_ND
void ProjectMatrixCoefficient_ND(const double *tk, const Array< int > &d2t, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.cpp:753
mfem::RT_TetrahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:9854
mfem::FiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:38
mfem::RefinedBiLinear2DFiniteElement::RefinedBiLinear2DFiniteElement
RefinedBiLinear2DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:4502
mfem::GaussBiQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1701
mfem::L2Pos_TriangleElement::L2Pos_TriangleElement
L2Pos_TriangleElement(const int p)
Definition: fe.cpp:8824
mfem::ND_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2144
mfem::RT0TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:902
mfem::H1Pos_SegmentElement::H1Pos_SegmentElement
H1Pos_SegmentElement(const int p)
Definition: fe.cpp:7123
mfem::NURBSFiniteElement::GetPatch
int GetPatch() const
Definition: fe.hpp:2300
mfem::RT_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2044
mfem::FiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:162
mfem::L2_TriangleElement
Definition: fe.hpp:1794
mfem::P0QuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:794
mfem::Nedelec1HexFiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:5114
mfem::FiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:115
mfem::BiQuadPos2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:705
mfem::P0SegmentFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2544
mfem::FiniteElement::CalcPhysDivShape
void CalcPhysDivShape(ElementTransformation &Trans, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in physical space at the po...
Definition: fe.cpp:59
mfem::Linear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2323
mfem::Poly_1D::OpenPoints
const double * OpenPoints(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.hpp:1411
mfem::Poly_1D::Poly_1D
Poly_1D()
Definition: fe.hpp:1399
mfem::L2Pos_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8863
mfem::ND_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2191
mfem::RT1TriangleFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:2861
mfem::RT1QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:3141
mfem::BiQuadPos2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1497
mfem::H1Pos_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:7165
mfem::L2_HexahedronElement
Definition: fe.hpp:1759
mfem::VectorFiniteElement::FiniteElement
FiniteElement(D, G, Do, O, F)
mfem::FiniteElement::GetDerivMapType
int GetDerivMapType() const
Definition: fe.hpp:138
mfem::L2Pos_TetrahedronElement::L2Pos_TetrahedronElement
L2Pos_TetrahedronElement(const int p)
Definition: fe.cpp:9018
mfem::NURBSFiniteElement::kv
Array< KnotVector * > kv
Definition: fe.hpp:2283
mfem::NodalFiniteElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.cpp:282
mfem::VectorFiniteElement::CalcVShape_RT
void CalcVShape_RT(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:534
mfem::L2_TriangleElement::L2_TriangleElement
L2_TriangleElement(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8699
mfem::Vector::SetSize
void SetSize(int s)
Resize the vector to size s.
Definition: vector.hpp:320
mfem::RT_QuadrilateralElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:9236
mfem::Nedelec1HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5176
mfem::P1SegmentFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:3631
mfem::GaussLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1052
mfem::NodalFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:243
mfem::BiQuadPos2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1521
mfem::VectorFiniteElement::LocalInterpolation_ND
void LocalInterpolation_ND(const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:881
mfem::BiCubic2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1879
mfem::RT_TriangleElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2002
mfem::BiCubic2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1790
mfem::RT0TriangleFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:2626
mfem::P0TriangleFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
evaluate derivatives of shape function - constant 0
Definition: fe.cpp:2277
mfem::Nedelec1TetFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1257
mfem::L2Pos_SegmentElement
Definition: fe.hpp:1704
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:2070
mfem::Linear1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:941
mfem::H1_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6685
mfem::H1Pos_TetrahedronElement::H1Pos_TetrahedronElement
H1Pos_TetrahedronElement(const int p)
Definition: fe.cpp:7907
mfem::NURBS1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:10946
mfem::L2_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8304
mfem::RT_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1892
mfem::LagrangeHexFiniteElement::LagrangeHexFiniteElement
LagrangeHexFiniteElement(int degree)
Definition: fe.cpp:3900
mfem::FiniteElement::GetOrder
int GetOrder() const
Returns the order of the finite element.
Definition: fe.hpp:125
mfem::H1_QuadrilateralElement
Definition: fe.hpp:1497
mfem::RT0TriangleFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:2639
mfem::Lagrange1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:3754
mfem::LagrangeHexFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:4062
mfem::ND_QuadrilateralElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:2125
mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition: densemat.hpp:23
mfem::Lagrange1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:3706
mfem::NodalFiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:345
mfem::NURBSFiniteElement::Reset
void Reset() const
Definition: fe.hpp:2298
mfem::RT_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1987
mfem::FunctionSpace::Pk
Polynomials of order k.
Definition: fe.hpp:34
mfem::Quad2DFiniteElement
Class for quadratic FE on triangle.
Definition: fe.hpp:631
mfem::NURBS1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:10960
mfem::PositiveFiniteElement::PositiveFiniteElement
PositiveFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:378
mfem::Quad1DFiniteElement
Class for quadratic FE on interval.
Definition: fe.hpp:602
mfem::RT_QuadrilateralElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1887
mfem::RT_TriangleElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:9710
mfem::ND_TetrahedronElement
Definition: fe.hpp:2151
mfem::Nedelec1TetFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5342
mfem::VectorFiniteElement::ProjectCurl_ND
void ProjectCurl_ND(const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:679
mfem::P0QuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2292
mfem::FiniteElement::Space
int Space() const
Returns the type of space on each element.
Definition: fe.hpp:128
mfem::Cubic1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1950
mfem::FiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:109
mfem::RT_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1951
mfem::RefinedTriLinear3DFiniteElement::RefinedTriLinear3DFiniteElement
RefinedTriLinear3DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:4649
mfem::FiniteElement::vshape
DenseMatrix vshape
Definition: fe.hpp:58
mfem::P0HexFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:3887
mfem::Quadratic3DFiniteElement::Quadratic3DFiniteElement
Quadratic3DFiniteElement()
Construct a quadratic FE on tetrahedron.
Definition: fe.cpp:2362
mfem::FiniteElement::GetMapType
int GetMapType() const
Definition: fe.hpp:134
mfem::L2_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8177
mfem::RT1HexFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:5692
mfem::RT1HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5879
mfem::L2Pos_TetrahedronElement
Definition: fe.hpp:1853
mfem::RT0QuadFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:2738
mfem::H1_HexahedronElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1534
mfem::L2_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8983
mfem::ND_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2101
mfem::Cubic2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2002
mfem::L2Pos_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:9048
mfem::CrouzeixRaviartFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2569
mfem::CrouzeixRaviartFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2561
mfem::L2Pos_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8239
mfem::H1_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:6773
mfem::P0HexFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:1107
mfem::VectorFiniteElement::ProjectCurl_RT
void ProjectCurl_RT(const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:717
mfem::H1Pos_HexahedronElement::H1Pos_HexahedronElement
H1Pos_HexahedronElement(const int p)
Definition: fe.cpp:7295
mfem::FiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:146
mfem::H1Pos_TetrahedronElement::CalcShape
static void CalcShape(const int p, const double x, const double y, const double z, double *shape)
Definition: fe.cpp:8009
mfem::H1Pos_TetrahedronElement::m_dshape
DenseMatrix m_dshape
Definition: fe.hpp:1665
mfem::ND_TriangleElement
Definition: fe.hpp:2197
mfem::H1_SegmentElement::H1_SegmentElement
H1_SegmentElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:6623
mfem::L2_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8925
mfem::BiLinear2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1013
mfem::H1_TetrahedronElement::H1_TetrahedronElement
H1_TetrahedronElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:7592
mfem::NURBSFiniteElement::GetElement
int GetElement() const
Definition: fe.hpp:2302
mfem::H1Pos_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:7267
mfem::Linear2DFiniteElement::Linear2DFiniteElement
Linear2DFiniteElement()
Construct a linear FE on triangle.
Definition: fe.cpp:955
mfem::RT_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1896
mfem::Quadratic3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2419
mfem::ND_TriangleElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:2226
mfem::RefinedBiLinear2DFiniteElement
Class for refined bi-linear FE on quadrilateral.
Definition: fe.hpp:1186
mfem::RT0TetFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:6014
mfem::RefinedTriLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4838
mfem::L2_QuadrilateralElement::L2_QuadrilateralElement
L2_QuadrilateralElement(const int p, const int _type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8263
mfem::ND_TriangleElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:10842
mfem::PointFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:922
mfem::Cubic2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2022
mfem::FiniteElement::CalcPhysCurlShape
void CalcPhysCurlShape(ElementTransformation &Trans, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in physical space at the point de...
Definition: fe.cpp:73
mfem::L2Pos_HexahedronElement::L2Pos_HexahedronElement
L2Pos_HexahedronElement(const int p)
Definition: fe.cpp:8607
mfem::ND_TriangleElement::ND_TriangleElement
ND_TriangleElement(const int p)
Definition: fe.cpp:10761
mfem::RT_QuadrilateralElement::RT_QuadrilateralElement
RT_QuadrilateralElement(const int p, const int cp_type=Quadrature1D::GaussLobatto, const int op_type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:9075
mfem::L2_TriangleElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1810
mfem::Poly_1D::GetPoints
const double * GetPoints(const int p, const int type)
Get the coordinates of the points of the given Quadrature1D type.
Definition: fe.cpp:6552
mfem::RT_TetrahedronElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:9890
mfem::FiniteElement::DIV
Implements CalcDivShape methods.
Definition: fe.hpp:102
mfem::H1Pos_TetrahedronElement::CalcDShape
static void CalcDShape(const int p, const double x, const double y, const double z, double *dshape_1d, double *dshape)
Definition: fe.cpp:8042
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u)
Definition: fe.hpp:1434
mfem::H1_HexahedronElement::H1_HexahedronElement
H1_HexahedronElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:6863
mfem::RT0QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:929
mfem::P0TriangleFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
evaluate shape function - constant 1
Definition: fe.cpp:2271
mfem::Cubic2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:2050
mfem::Poly_1D::CalcBinomTerms
static void CalcBinomTerms(const int p, const double x, const double y, double *u)
Compute the terms in the expansion of the binomial (x + y)^p.
Definition: fe.cpp:6387
mfem::FiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:103
mfem::H1Pos_TriangleElement::H1Pos_TriangleElement
H1Pos_TriangleElement(const int p)
Definition: fe.cpp:7762
mfem::RT2QuadFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:3343
mfem::ScalarFiniteElement::SetMapType
void SetMapType(int M)
Definition: fe.hpp:311
mfem::FiniteElement::VerifyOpen
static int VerifyOpen(int pt_type)
Definition: fe.hpp:295
mfem::Cubic3DFiniteElement::Cubic3DFiniteElement
Cubic3DFiniteElement()
Construct a cubic FE on tetrahedron.
Definition: fe.cpp:2097
mfem::Linear1DFiniteElement::Linear1DFiniteElement
Linear1DFiniteElement()
Construct a linear FE on interval.
Definition: fe.cpp:934
mfem::RefinedLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4211
mfem::RT0TetFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:6002
mfem::BiQuadPos2DFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:1570
mfem::FiniteElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:154
mfem::QuadPos1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1188
mfem::RT_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1941
mfem::H1Pos_TriangleElement::CalcShape
static void CalcShape(const int p, const double x, const double y, double *shape)
Definition: fe.cpp:7817
mfem::CrouzeixRaviartQuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2592
mfem::H1Pos_TriangleElement::dshape_1d
Vector dshape_1d
Definition: fe.hpp:1638
mfem::Cubic3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2190
mfem::P2SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:3649
mfem::P1OnQuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:597
mfem::L2Pos_QuadrilateralElement
Definition: fe.hpp:1743
mfem::FiniteElement::Dof
int Dof
Number of degrees of freedom.
Definition: fe.hpp:50
mfem::GaussBiLinear2DFiniteElement
Class for bilinear FE on quad with nodes at the 4 Gaussian points.
Definition: fe.hpp:577
mfem::RefinedLinear1DFiniteElement
Class for refined linear FE on interval.
Definition: fe.hpp:1133
mfem::L2_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8183
mfem::RefinedLinear2DFiniteElement
Class for refined linear FE on triangle.
Definition: fe.hpp:1153
mfem::RefinedLinear3DFiniteElement
Class for refined linear FE on tetrahedron.
Definition: fe.hpp:1173
mfem::L2_SegmentElement
Definition: fe.hpp:1686
mfem::NURBSFiniteElement::SetPatch
void SetPatch(int p) const
Definition: fe.hpp:2301
mfem::Quad1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1148
mfem::Quad1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1159
mfem::BiQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1407
mfem::P0TriangleFiniteElement
Class for constant FE on triangle.
Definition: fe.hpp:770
mfem::ND_SegmentElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2273
mfem::RefinedLinear1DFiniteElement::RefinedLinear1DFiniteElement
RefinedLinear1DFiniteElement()
Construct a quadratic FE on interval.
Definition: fe.cpp:4100
mfem::H1_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7038
mfem::H1Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7288
mfem::RT_HexahedronElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:1948
mfem::GaussBiQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1674
mfem::L2_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8766
mfem::H1_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:7540
mfem::RT_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1954
mfem::RefinedLinear1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4127
mfem::VectorFiniteElement::VectorFiniteElement
VectorFiniteElement(int D, int G, int Do, int O, int M, int F=FunctionSpace::Pk)
Definition: fe.hpp:477
mfem::VectorFiniteElement::LocalInterpolation_RT
void LocalInterpolation_RT(const double *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:847
mfem::RT2TriangleFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:3282
mfem::Poly_1D::ChebyshevPoints
static void ChebyshevPoints(const int p, double *x)
Definition: fe.cpp:6355
mfem::NURBSFiniteElement::NURBSFiniteElement
NURBSFiniteElement(int D, int G, int Do, int O, int F)
Definition: fe.hpp:2288
mfem::FiniteElement::GRAD
Implements CalcDShape methods.
Definition: fe.hpp:101
mfem::RotTriLinearHexFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:6139
mfem::H1_QuadrilateralElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1514
mfem::P0TetFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:3872
mfem::RT0TetFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:5980
mfem::RefinedTriLinear3DFiniteElement
Class for refined trilinear FE on a hexahedron.
Definition: fe.hpp:1206
mfem::ND_TetrahedronElement::ND_TetrahedronElement
ND_TetrahedronElement(const int p)
Definition: fe.cpp:10499
mfem::L2Pos_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8852
mfem::Poly_1D
Definition: fe.hpp:1364
mfem::FiniteElement::DerivMapType
int DerivMapType
Definition: fe.hpp:50
mfem::Quadratic3DFiniteElement
Class for quadratic FE on tetrahedron.
Definition: fe.hpp:825
mfem::FiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const =0
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
mfem::ND_TetrahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:2167
mfem::PointFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:928
mfem::RT_TetrahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:2026
mfem::FiniteElement::VALUE
For scalar fields; preserves point values.
Definition: fe.hpp:85
mfem::FiniteElement::GeomType
int GeomType
Geometry::Type of the reference element.
Definition: fe.hpp:50
mfem::Cubic1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1965
mfem::ND_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2172
mfem::FiniteElement::GetNodes
const IntegrationRule & GetNodes() const
Definition: fe.hpp:167
mfem::FiniteElement::INTEGRAL
For scalar fields; preserves volume integrals.
Definition: fe.hpp:86
mfem::FunctionSpace::rQk
Refined tensor products of polynomials of order k.
Definition: fe.hpp:36
mfem::Nedelec1HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5229
mfem::Quad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1229
mfem::L2_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8522
mfem::Quadratic3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2397
mfem::RT_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1906
mfem::L2Pos_QuadrilateralElement::L2Pos_QuadrilateralElement
L2Pos_QuadrilateralElement(const int p)
Definition: fe.cpp:8373
mfem::P0SegmentFiniteElement::P0SegmentFiniteElement
P0SegmentFiniteElement(int Ord=0)
Definition: fe.cpp:2532
mfem::H1_TetrahedronElement
Definition: fe.hpp:1615
mfem::H1Pos_TriangleElement::CalcDShape
static void CalcDShape(const int p, const double x, const double y, double *dshape_1d, double *dshape)
Definition: fe.cpp:7843
mfem::FiniteElement::GetDerivRangeType
int GetDerivRangeType() const
Definition: fe.hpp:132
mfem::RT1TriangleFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:2884
mfem::NURBS3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:11033
mfem::FiniteElement::CURL
Implements CalcCurlShape methods.
Definition: fe.hpp:103
mfem::VectorFiniteElement::curlshape
DenseMatrix curlshape
Definition: fe.hpp:413
mfem::ND_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2176
mfem::RT2TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1009
mfem::Linear3DFiniteElement
Class for linear FE on tetrahedron.
Definition: fe.hpp:800
mfem::Linear1DFiniteElement
Class for linear FE on interval.
Definition: fe.hpp:500
mfem::RT_HexahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:9450
mfem::Nedelec1TetFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:5280
mfem::FiniteElement::CalcPhysDShape
void CalcPhysDShape(ElementTransformation &Trans, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in physical space at the poi...
Definition: fe.cpp:180
mfem::CrouzeixRaviartQuadFiniteElement
Crouzeix-Raviart finite element on quadrilateral.
Definition: fe.hpp:873
mfem::Linear2DFiniteElement
Class for linear FE on triangle.
Definition: fe.hpp:520
mfem::GaussQuad2DFiniteElement
Class for quadratic FE on triangle with nodes at the &quot;Gaussian&quot; points.
Definition: fe.hpp:655
mfem::L2_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8744
mfem::RT_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:9189
mfem::ND_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2219
mfem::BiCubic2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1829
mfem::RT2QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:3541
mfem::ND_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2130
mfem::BiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1004
mfem::Linear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2332
mfem::RT_HexahedronElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:9524
mfem::H1_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:7703
mfem::RT_TriangleElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:1990
mfem::Quad2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1253
mfem::NURBSFiniteElement::SetElement
void SetElement(int e) const
Definition: fe.hpp:2303
mfem::GaussQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1331
mfem::VectorFiniteElement::ProjectGrad_ND
void ProjectGrad_ND(const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:826
mfem::ScalarFiniteElement::ScalarFiniteElement
ScalarFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:307
mfem::FiniteElement::CalcPhysVShape
void CalcPhysVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Equivalent to the CalcVShape() method with the same arguments.
Definition: fe.hpp:189
mfem::L2Pos_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8846
mfem::RT_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2041
mfem::RT1TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:956
mfem::L2_QuadrilateralElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1736
mfem::NURBS3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:11057
mfem::GaussQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1345
mfem::FiniteElement::GetGeomType
int GetGeomType() const
Returns the Geometry::Type of the reference element.
Definition: fe.hpp:119
mfem::H1Pos_TriangleElement::m_dshape
DenseMatrix m_dshape
Definition: fe.hpp:1639
mfem::FiniteElement::Dim
int Dim
Dimension of reference space.
Definition: fe.hpp:50
mfem::ND_QuadrilateralElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:10445
mfem::L2Pos_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8398
mfem::FiniteElement::Nodes
IntegrationRule Nodes
Definition: fe.hpp:56
mfem::H1Pos_HexahedronElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1594
mfem::ND_SegmentElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2269
mfem::L2_TetrahedronElement
Definition: fe.hpp:1833
mfem::Quad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1215
mfem::L2Pos_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8635
mfem::H1Pos_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:7145
mfem::H1Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7466
mfem::RT2QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:3593
mfem::ND_TriangleElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:10876
mfem::RT0QuadFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:2753
mfem::RefinedBiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4525
mfem::Quadrature1D::CheckClosed
static int CheckClosed(int type)
If the Quadrature1D type is not closed return Invalid; otherwise return type.
Definition: intrules.cpp:799
mfem::RT_TetrahedronElement
Definition: fe.hpp:2009
mfem::FiniteElement::~FiniteElement
virtual ~FiniteElement()
Definition: fe.hpp:286
mfem::RT0TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2650
mfem::H1Pos_QuadrilateralElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1575
mfem::ND_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Overrides the scalar CalcShape function to print an error.
Definition: fe.hpp:2250
mfem::VectorFiniteElement::CalcVShape_ND
void CalcVShape_ND(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:546
mfem::VectorFiniteElement::Jinv
DenseMatrix Jinv
Definition: fe.hpp:412
mfem::RT0HexFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1281
mfem::FiniteElement::NONE
No derivatives implemented.
Definition: fe.hpp:100
mfem::ND_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2263
mfem::L2_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8194
mfem::FiniteElement::GetDof
int GetDof() const
Returns the number of degrees of freedom in the finite element.
Definition: fe.hpp:122
mfem::H1_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:7728
mfem::BiQuad2DFiniteElement
Class for bi-quadratic FE on quadrilateral.
Definition: fe.hpp:671
mfem::H1Pos_HexahedronElement
Definition: fe.hpp:1579
mfem::TriLinear3DFiniteElement
Class for tri-linear FE on cube.
Definition: fe.hpp:838
mfem::Coefficient
Base class Coefficient that may optionally depend on time.
Definition: coefficient.hpp:31
mfem::ND_SegmentElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:2266
mfem::H1Pos_TetrahedronElement::m_shape
Vector m_shape
Definition: fe.hpp:1664
mfem::GaussBiLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1099
mfem::P0TetFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:1096
mfem::Nedelec1TetFiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:5310
mfem::H1Pos_TetrahedronElement::dof_map
Array< int > dof_map
Definition: fe.hpp:1667
mfem::L2Pos_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:9041
mfem::FiniteElement::CalcPhysShape
void CalcPhysShape(ElementTransformation &Trans, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in physical space at the point ...
Definition: fe.cpp:170
mfem::Poly_1D::OpenBasis
Basis & OpenBasis(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.hpp:1425
mfem::CrouzeixRaviartFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:868
mfem::Linear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:966
mfem::RefinedTriLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4695
mfem::RefinedLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:4392
mfem::P0TriangleFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:782
mfem::Poly_1D::Binom
static const int * Binom(const int p)
Get a poiner to an array containing the binomial coefficients &quot;p choose k&quot; for k=0,...,p for the given p.
Definition: fe.cpp:6338
mfem::RT2QuadFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:3443
mfem::H1_HexahedronElement
Definition: fe.hpp:1518
mfem::H1Pos_TetrahedronElement
Definition: fe.hpp:1660
mfem::H1Pos_TetrahedronElement::dshape_1d
Vector dshape_1d
Definition: fe.hpp:1664
mfem::FiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:52
mfem::GaussLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1034
mfem::RT_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1902
mfem::Nedelec1HexFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1235
mfem::L2_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8950
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:10154
mfem::RT_TriangleElement
Definition: fe.hpp:1961
mfem::RT0QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2817
mfem::FiniteElement::FiniteElement
FiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.cpp:24
mfem::BiQuad2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1456
mfem::TriLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2477
mfem::BiLinear2DFiniteElement
Class for bilinear FE on quadrilateral.
Definition: fe.hpp:542
mfem::Quadrature1D::CheckOpen
static int CheckOpen(int type)
If the Quadrature1D type is not open return Invalid; otherwise return type.
Definition: intrules.cpp:811
mfem::PositiveFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:383
mfem::RT_QuadrilateralElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:1899
mfem::ND_HexahedronElement::ND_HexahedronElement
ND_HexahedronElement(const int p, const int cp_type=Quadrature1D::GaussLobatto, const int op_type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:9936
mfem::Quad1DFiniteElement::Quad1DFiniteElement
Quad1DFiniteElement()
Construct a quadratic FE on interval.
Definition: fe.cpp:1140
mfem::RT_HexahedronElement::RT_HexahedronElement
RT_HexahedronElement(const int p, const int cp_type=Quadrature1D::GaussLobatto, const int op_type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:9286
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:2254
mfem::H1Pos_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:7421
mfem::FiniteElement::GetFaceDofs
virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const
Definition: fe.cpp:98
mfem::GaussLinear2DFiniteElement
Class for linear FE on triangle with nodes at the 3 &quot;Gaussian&quot; points.
Definition: fe.hpp:566
mfem::H1Pos_TriangleElement::m_shape
Vector m_shape
Definition: fe.hpp:1638
mfem::GaussBiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1088
mfem::ND_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2077
mfem::RT2QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1030
mfem::BiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:995
mfem::Poly_1D::ClosedBasis
Basis & ClosedBasis(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.hpp:1428
mfem::FiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:66
mfem::H1Pos_QuadrilateralElement::H1Pos_QuadrilateralElement
H1Pos_QuadrilateralElement(const int p)
Definition: fe.cpp:7192
mfem::ND_QuadrilateralElement
Definition: fe.hpp:2108
mfem::ND_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2223
mfem::NURBSFiniteElement::KnotVectors
Array< KnotVector * > & KnotVectors() const
Definition: fe.hpp:2304
mfem::ND_TetrahedronElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:2179
mfem::IntegrationPoint
Class for integration point with weight.
Definition: intrules.hpp:25
mfem::Linear1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:948
mfem::L2_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8795
mfem::FiniteElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.cpp:127
mfem::Poly_1D::GetBasis
Basis & GetBasis(const int p, const int type)
Get a Poly_1D::Basis object of the given degree and Quadrature1D type.
Definition: fe.cpp:6573
mfem::H1Pos_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:7442
mfem::L2Pos_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8245
mfem::NodalFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:343
mfem::P0QuadFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2298
mfem::RT_QuadrilateralElement
Definition: fe.hpp:1869
mfem::GaussBiQuad2DFiniteElement
Bi-quadratic element on quad with nodes at the 9 Gaussian points.
Definition: fe.hpp:710
mfem::RT1QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:983
mfem::L2Pos_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8656
mfem::VectorFiniteElement::Project_RT
void Project_RT(const double *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:557
mfem::H1_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:6993
mfem::P1OnQuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1123
mfem::RT_TetrahedronElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:2038
mfem::RT2TriangleFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:3257
mfem::ND_TetrahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:10647
mfem::RT1QuadFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:3017
mfem::ND_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:10396
mfem::Linear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:537
mfem::ND_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2233
mfem::NodalFiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:374
mfem::FiniteElement::VerifyClosed
static int VerifyClosed(int pt_type)
Definition: fe.hpp:288
mfem::FiniteElement::DerivRangeType
int DerivRangeType
Definition: fe.hpp:50
mfem::H1_TriangleElement
Definition: fe.hpp:1598
mfem::RT0QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2765
mfem::ND_QuadrilateralElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:2137
mfem::L2Pos_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8256
mfem::RefinedLinear2DFiniteElement::RefinedLinear2DFiniteElement
RefinedLinear2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:4146
mfem::L2_QuadrilateralElement
Definition: fe.hpp:1720
mfem::NodalFiniteElement::NodalLocalInterpolation
void NodalLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I, const NodalFiniteElement &fine_fe) const
Definition: fe.cpp:191
mfem::H1_SegmentElement
Definition: fe.hpp:1477
mfem::RT1HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5934
mfem::NodalFiniteElement::ProjectCurl_2D
void ProjectCurl_2D(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:224
mfem::NURBSFiniteElement::SetIJK
void SetIJK(int *IJK) const
Definition: fe.hpp:2299
mfem::ND_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2134
mfem::ND_HexahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2096
mfem::RefinedLinear1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4108
mfem::P1TetNonConfFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:3836
mfem::H1Pos_TriangleElement::dof_map
Array< int > dof_map
Definition: fe.hpp:1641
mfem::RT_TetrahedronElement::RT_TetrahedronElement
RT_TetrahedronElement(const int p)
Definition: fe.cpp:9752
mfem::ND_QuadrilateralElement::ND_QuadrilateralElement
ND_QuadrilateralElement(const int p, const int cp_type=Quadrature1D::GaussLobatto, const int op_type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:10307
mfem::Poly_1D::Basis
Definition: fe.hpp:1367
mfem::RT0HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5490
mfem::L2_TetrahedronElement::L2_TetrahedronElement
L2_TetrahedronElement(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8875
mfem::H1Pos_SegmentElement
Definition: fe.hpp:1537
mfem::LagrangeHexFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:4041
mfem::NURBSFiniteElement::Weights
Vector & Weights() const
Definition: fe.hpp:2305
mfem::H1_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:6666
mfem::BiQuad2DFiniteElement::BiQuad2DFiniteElement
BiQuad2DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:1360
mfem::Linear3DFiniteElement::GetFaceDofs
virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const
Definition: fe.cpp:2352
mfem::LagrangeHexFiniteElement
Tensor products of 1D FEs (only degree 2 is functional)
Definition: fe.hpp:1112
mfem::RT1QuadFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:3054
mfem::P0TriangleFiniteElement::P0TriangleFiniteElement
P0TriangleFiniteElement()
Construct P0 triangle finite element.
Definition: fe.cpp:2264
mfem::ND_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2229
mfem::Poly_1D::ClosedPoints
const double * ClosedPoints(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.hpp:1414
mfem::ND_HexahedronElement
Definition: fe.hpp:2051
mfem::H1Pos_QuadrilateralElement
Definition: fe.hpp:1560
mfem::P0SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2538
mfem::L2Pos_HexahedronElement
Definition: fe.hpp:1778
mfem::RT_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1993
mfem::RT_TriangleElement::RT_TriangleElement
RT_TriangleElement(const int p)
Definition: fe.cpp:9599
mfem::H1_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:6647
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:10937
mfem::ND_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2083
mfem::ND_HexahedronElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Definition: fe.hpp:2087
mfem::ND_HexahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:10228
mfem::Poly_1D::Basis::Eval
void Eval(const double x, Vector &u) const
Definition: fe.cpp:6224
mfem::L2Pos_SegmentElement::L2Pos_SegmentElement
L2Pos_SegmentElement(const int p)
Definition: fe.cpp:8218
mfem::RefinedLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:4305
mfem::RT0HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5545
mfem::Cubic3DFiniteElement
Class for cubic FE on tetrahedron.
Definition: fe.hpp:757
mfem::Vector
Vector data type.
Definition: vector.hpp:41
mfem::RT0HexFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:5476
mfem::Poly_1D::CalcBernstein
static void CalcBernstein(const int p, const double x, double *u)
Definition: fe.hpp:1466
mfem::ND_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2091
mfem::FiniteElement::GetDerivType
int GetDerivType() const
Definition: fe.hpp:136
mfem::H1Pos_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:7247
mfem::L2_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8498
mfem::Quad2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1281
mfem::RT_TriangleElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:9677
mfem::Quad2DFiniteElement::Quad2DFiniteElement
Quad2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:1198
mfem::ND_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2140
mfem::RT_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2035
mfem::FunctionSpace
Describes the space on each element.
Definition: fe.hpp:29
mfem::H1_QuadrilateralElement::H1_QuadrilateralElement
H1_QuadrilateralElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:6713
mfem::TriLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2493
mfem::ND_SegmentElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2259
mfem::Nedelec1TetFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5395
mfem::L2Pos_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:8417
mfem::PositiveFiniteElement::PositiveLocalInterpolation
void PositiveLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I, const PositiveFiniteElement &fine_fe) const
Definition: fe.cpp:405
mfem::ND_TetrahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe.cpp:10689
mfem::P0HexFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:3893
mfem::BiQuadPos2DFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:1599
mfem::Linear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:974
mfem::Cubic3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:2162
mfem::NodalFiniteElement::NodalFiniteElement
NodalFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:336
mfem::CrouzeixRaviartQuadFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:2603
mfem::H1_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6814
mfem::TriLinear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:856
mfem::RT0HexFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:5446
mfem::P2SegmentFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:3661
mfem::BiLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:561
mfem::RefinedBiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4576
mfem::FiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const =0
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
mfem::RT_HexahedronElement
Definition: fe.hpp:1918
mfem::NURBS2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:10979
mfem::RT_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1983
mfem::ND_TetrahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2186
mfem::VectorFiniteElement::Project_ND
void Project_ND(const double *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:736
mfem::FiniteElement::GetRangeType
int GetRangeType() const
Definition: fe.hpp:130
mfem::GaussBiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1077
mfem::FiniteElement::Order
int Order
Order/degree of the shape functions.
Definition: fe.hpp:50
mfem::RT1TriangleFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2959
mfem::H1_TriangleElement::H1_TriangleElement
H1_TriangleElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:7473
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u, double *d)
Definition: fe.hpp:1443
mfem::QuadratureFunctions1D
A Class that defines 1-D numerical quadrature rules on [0,1].
Definition: intrules.hpp:235
mfem::ND_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2182
mfem::P0TetFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:3866
mfem::H1_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:7014
mfem::RT_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1997
mfem::H1_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:6792
mfem::Poly_1D::Basis::Basis
Basis(const int p, const double *nodes, const int _mode=1)
Definition: fe.cpp:6174
mfem::Poly_1D::CalcDBinomTerms
static void CalcDBinomTerms(const int p, const double x, const double y, double *d)
Definition: fe.cpp:6451
mfem::Nedelec1HexFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe.cpp:5059
mfem::FunctionSpace::Qk
Tensor products of polynomials of order k.
Definition: fe.hpp:35
mfem::TriLinear3DFiniteElement::TriLinear3DFiniteElement
TriLinear3DFiniteElement()
Construct a tri-linear FE on cube.
Definition: fe.cpp:2441
mfem::ND_SegmentElement::ND_SegmentElement
ND_SegmentElement(const int p, const int op_type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:10921
mfem::FiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:133
mfem::QuadPos1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:1178
mfem::L2_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:8477
mfem::RT_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:1936
mfem::RefinedLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4163
mfem::H1Pos_TriangleElement
Definition: fe.hpp:1634
mfem::P1SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:3622
mfem::BiLinear2DFiniteElement::BiLinear2DFiniteElement
BiLinear2DFiniteElement()
Construct a bilinear FE on quadrilateral.
Definition: fe.cpp:982
mfem::ND_TriangleElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe.hpp:2214
mfem::L2_HexahedronElement::L2_HexahedronElement
L2_HexahedronElement(const int p, const int _type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8452
mfem::poly1d
Poly_1D poly1d
Definition: fe.cpp:6619
mfem::CrouzeixRaviartFiniteElement
Crouzeix-Raviart finite element on triangle.
Definition: fe.hpp:861
mfem::RotTriLinearHexFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Evaluate the values of all shape functions of a scalar finite element in reference space at the given...
Definition: fe.cpp:6122
mfem::Lagrange1DFiniteElement::Lagrange1DFiniteElement
Lagrange1DFiniteElement(int degree)
Definition: fe.cpp:3674
mfem::Poly_1D::~Poly_1D
~Poly_1D()
Definition: fe.cpp:6594
mfem::RT0TriangleFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2702
mfem::RT1HexFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Evaluate the divergence of all shape functions of a vector finite element in reference space at the g...
Definition: fe.cpp:5815
mfem::H1_SegmentElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1493
mfem::L2Pos_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:9059
mfem::L2_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8324
mfem::GaussLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:1044
mfem::Linear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:818
mfem::H1_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Evaluate the gradients of all shape functions of a scalar finite element in reference space at the gi...
Definition: fe.cpp:7562
mfem::VectorFiniteElement::ProjectGrad_RT
void ProjectGrad_RT(const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:652
mfem::PositiveFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:445
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