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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 KnotVector;
44 
45 /// Abstract class for Finite Elements
46 class FiniteElement
47 {
48 protected:
49  int Dim, ///< Dimension of reference space
50  GeomType, ///< Geometry::Type of the reference element
51  Dof, ///< Number of degrees of freedom
52  Order, ///< Order/degree of the shape functions
53  FuncSpace, RangeType, MapType,
54  DerivType, DerivRangeType, DerivMapType;
55  IntegrationRule Nodes;
56 #ifndef MFEM_THREAD_SAFE
57  mutable DenseMatrix vshape; // Dof x Dim
58 #endif
59 
60 public:
61  /// Enumeration for RangeType and DerivRangeType
62  enum { SCALAR, VECTOR };
63 
64  /** @brief Enumeration for MapType: defines how reference functions are
65  mapped to physical space.
66 
67  A reference function, `uh(xh)`, can be mapped to a function, `u(x)`, on a
68  general physical element in following ways:
69 
70  VALUE u(x) = uh(xh)
71  INTEGRAL u(x) = (1/w) * uh(xh)
72  H_DIV u(x) = (J/w) * uh(xh)
73  H_CURL u(x) = J^{-t} * uh(xh) (square J)
74  H_CURL u(x) = J*(J^t*J)^{-1} * uh(xh) (general J)
75 
76  where
77 
78  x = T(xh) is the image of the reference point xh ("x hat"),
79  J = J(xh) is the Jacobian matrix of the transformation T, and
80  w = w(xh) = / det(J), for square J,
81  \ det(J^t*J)^{1/2}, for general J,
82  is the transformation weight factor.
83  */
84  enum { VALUE, ///< For scalar fields; preserves point values
85  INTEGRAL, ///< For scalar fields; preserves volume integrals
86  H_DIV, /**< For vector fields; preserves surface integrals of the
87  normal component */
88  H_CURL /**< For vector fields; preserves line integrals of the
89  tangential component */
90  };
91 
92  /** @brief Enumeration for DerivType: defines which derivative method
93  is implemented.
94 
95  Each FiniteElement class implements only one type of derivative. The
96  value returned by GetDerivType() indicates which derivative method is
97  implemented.
98  */
99  enum { NONE, ///< No derivatives implemented
100  GRAD, ///< Implements CalcDShape methods
101  DIV, ///< Implements CalcDivShape methods
102  CURL ///< Implements CalcCurlShape methods
103  };
104 
105  /** Construct FiniteElement with given
106  @param D Reference space dimension
107  @param G Geometry type (of type Geometry::Type)
108  @param Do Number of degrees of freedom in the FiniteElement
109  @param O Order/degree of the FiniteElement
110  @param F FunctionSpace type of the FiniteElement
111  */
112  FiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk);
113 
114  /// Returns the reference space dimension for the finite element
115  int GetDim() const { return Dim; }
116 
117  /// Returns the Geometry::Type of the reference element
118  int GetGeomType() const { return GeomType; }
119 
120  /// Returns the number of degrees of freedom in the finite element
121  int GetDof() const { return Dof; }
122 
123  /// Returns the order of the finite element
124  int GetOrder() const { return Order; }
125 
126  /// Returns the type of space on each element
127  int Space() const { return FuncSpace; }
128 
129  int GetRangeType() const { return RangeType; }
130 
131  int GetDerivRangeType() const { return DerivRangeType; }
132 
133  int GetMapType() const { return MapType; }
134 
135  int GetDerivType() const { return DerivType; }
136 
137  int GetDerivMapType() const { return DerivMapType; }
138 
139  /** @brief Evaluate the values of all shape functions of a scalar finite
140  element in reference space at the given point @a ip. */
141  /** The size (#Dof) of the result Vector @a shape must be set in advance. */
142  virtual void CalcShape(const IntegrationPoint &ip,
143  Vector &shape) const = 0;
144 
145  /** @brief Evaluate the values of all shape functions of a scalar finite
146  element in physical space at the point described by @a Trans. */
147  /** The size (#Dof) of the result Vector @a shape must be set in advance. */
148  void CalcPhysShape(ElementTransformation &Trans, Vector &shape) const;
149 
150  /** @brief Evaluate the gradients of all shape functions of a scalar finite
151  element in reference space at the given point @a ip. */
152  /** Each row of the result DenseMatrix @a dshape contains the derivatives of
153  one shape function. The size (#Dof x #Dim) of @a dshape must be set in
154  advance. */
155  virtual void CalcDShape(const IntegrationPoint &ip,
156  DenseMatrix &dshape) const = 0;
157 
158  /** @brief Evaluate the gradients of all shape functions of a scalar finite
159  element in physical space at the point described by @a Trans. */
160  /** Each row of the result DenseMatrix @a dshape contains the derivatives of
161  one shape function. The size (#Dof x SDim) of @a dshape must be set in
162  advance, where SDim >= #Dim is the physical space dimension as described
163  by @a Trans. */
164  void CalcPhysDShape(ElementTransformation &Trans, DenseMatrix &dshape) const;
165 
166  const IntegrationRule & GetNodes() const { return Nodes; }
167 
168  // virtual functions for finite elements on vector spaces
169 
170  /** @brief Evaluate the values of all shape functions of a *vector* finite
171  element in reference space at the given point @a ip. */
172  /** Each row of the result DenseMatrix @a shape contains the components of
173  one vector shape function. The size (#Dof x #Dim) of @a shape must be set
174  in advance. */
175  virtual void CalcVShape(const IntegrationPoint &ip,
176  DenseMatrix &shape) const;
177 
178  /** @brief Evaluate the values of all shape functions of a *vector* finite
179  element in physical space at the point described by @a Trans. */
180  /** Each row of the result DenseMatrix @a shape contains the components of
181  one vector shape function. The size (#Dof x SDim) of @a shape must be set
182  in advance, where SDim >= #Dim is the physical space dimension as
183  described by @a Trans. */
184  virtual void CalcVShape(ElementTransformation &Trans,
185  DenseMatrix &shape) const;
186 
187  /// Equivalent to the CalcVShape() method with the same arguments.
188  void CalcPhysVShape(ElementTransformation &Trans, DenseMatrix &shape) const
189  { CalcVShape(Trans, shape); }
190 
191  /** @brief Evaluate the divergence of all shape functions of a *vector*
192  finite element in reference space at the given point @a ip. */
193  /** The size (#Dof) of the result Vector @a divshape must be set in advance.
194  */
195  virtual void CalcDivShape(const IntegrationPoint &ip,
196  Vector &divshape) const;
197 
198  /** @brief Evaluate the divergence of all shape functions of a *vector*
199  finite element in physical space at the point described by @a Trans. */
200  /** The size (#Dof) of the result Vector @a divshape must be set in advance.
201  */
202  void CalcPhysDivShape(ElementTransformation &Trans, Vector &divshape) const;
203 
204  /** @brief Evaluate the curl of all shape functions of a *vector* finite
205  element in reference space at the given point @a ip. */
206  /** Each row of the result DenseMatrix @a curl_shape contains the components
207  of the curl of one vector shape function. The size (#Dof x CDim) of
208  @a curl_shape must be set in advance, where CDim = 3 for #Dim = 3 and
209  CDim = 1 for #Dim = 2. */
210  virtual void CalcCurlShape(const IntegrationPoint &ip,
211  DenseMatrix &curl_shape) const;
212 
213  /** @brief Evaluate the curl of all shape functions of a *vector* finite
214  element in physical space at the point described by @a Trans. */
215  /** Each row of the result DenseMatrix @a curl_shape contains the components
216  of the curl of one vector shape function. The size (#Dof x CDim) of
217  @a curl_shape must be set in advance, where CDim = 3 for #Dim = 3 and
218  CDim = 1 for #Dim = 2. */
219  void CalcPhysCurlShape(ElementTransformation &Trans,
220  DenseMatrix &curl_shape) const;
221 
222  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
223 
224  /** each row of h contains the upper triangular part of the hessian
225  of one shape function; the order in 2D is {u_xx, u_xy, u_yy} */
226  virtual void CalcHessian (const IntegrationPoint &ip,
227  DenseMatrix &h) const;
228 
229  /** Return the local interpolation matrix I (Dof x Dof) where the
230  fine element is the image of the base geometry under the given
231  transformation. */
232  virtual void GetLocalInterpolation (ElementTransformation &Trans,
233  DenseMatrix &I) const;
234 
235  /** Given a coefficient and a transformation, compute its projection
236  (approximation) in the local finite dimensional space in terms
237  of the degrees of freedom. */
238  virtual void Project (Coefficient &coeff,
239  ElementTransformation &Trans, Vector &dofs) const;
240 
241  /** Given a vector coefficient and a transformation, compute its
242  projection (approximation) in the local finite dimensional space
243  in terms of the degrees of freedom. (VectorFiniteElements) */
244  virtual void Project (VectorCoefficient &vc,
245  ElementTransformation &Trans, Vector &dofs) const;
246 
247  /** Compute a representation (up to multiplicative constant) for
248  the delta function at the vertex with the given index. */
249  virtual void ProjectDelta(int vertex, Vector &dofs) const;
250 
251  /** Compute the embedding/projection matrix from the given FiniteElement
252  onto 'this' FiniteElement. The ElementTransformation is included to
253  support cases when the projection depends on it. */
254  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
255  DenseMatrix &I) const;
256 
257  /** Compute the discrete gradient matrix from the given FiniteElement onto
258  'this' FiniteElement. The ElementTransformation is included to support
259  cases when the matrix depends on it. */
260  virtual void ProjectGrad(const FiniteElement &fe,
261  ElementTransformation &Trans,
262  DenseMatrix &grad) const;
263 
264  /** Compute the discrete curl matrix from the given FiniteElement onto
265  'this' FiniteElement. The ElementTransformation is included to support
266  cases when the matrix depends on it. */
267  virtual void ProjectCurl(const FiniteElement &fe,
268  ElementTransformation &Trans,
269  DenseMatrix &curl) const;
270 
271  /** Compute the discrete divergence matrix from the given FiniteElement onto
272  'this' FiniteElement. The ElementTransformation is included to support
273  cases when the matrix depends on it. */
274  virtual void ProjectDiv(const FiniteElement &fe,
275  ElementTransformation &Trans,
276  DenseMatrix &div) const;
277 
278  virtual ~FiniteElement () { }
279 
280  static int VerifyClosed(int pt_type)
281  {
282  int cp_type = Quadrature1D::CheckClosed(pt_type);
283  MFEM_VERIFY(cp_type != Quadrature1D::Invalid,
284  "invalid closed point type: " << pt_type);
285  return cp_type;
286  }
287  static int VerifyOpen(int pt_type)
288  {
289  int op_type = Quadrature1D::CheckOpen(pt_type);
290  MFEM_VERIFY(op_type != Quadrature1D::Invalid,
291  "invalid open point type: " << pt_type);
292  return op_type;
293  }
294 };
295 
296 class ScalarFiniteElement : public FiniteElement
297 {
298 public:
299  ScalarFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
300  : FiniteElement(D, G, Do, O, F)
301  { DerivType = GRAD; DerivRangeType = VECTOR; DerivMapType = H_CURL; }
302 
303  void SetMapType(int M)
304  {
305  MFEM_VERIFY(M == VALUE || M == INTEGRAL, "unknown MapType");
306  MapType = M;
307  DerivType = (M == VALUE) ? GRAD : NONE;
308  }
309 };
310 
311 class NodalFiniteElement : public ScalarFiniteElement
312 {
313 protected:
314  void NodalLocalInterpolation (ElementTransformation &Trans,
315  DenseMatrix &I,
316  const NodalFiniteElement &fine_fe) const;
317 
318  void ProjectCurl_2D(const FiniteElement &fe,
319  ElementTransformation &Trans,
320  DenseMatrix &curl) const;
321 
322 #ifndef MFEM_THREAD_SAFE
323  mutable Vector c_shape;
324 #endif
325 
326 public:
327 #ifdef MFEM_THREAD_SAFE
328  NodalFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
329  : ScalarFiniteElement(D, G, Do, O, F) { }
330 #else
331  NodalFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
332  : ScalarFiniteElement(D, G, Do, O, F), c_shape(Do) { }
333 #endif
334 
335  virtual void GetLocalInterpolation (ElementTransformation &Trans,
336  DenseMatrix &I) const
337  { NodalLocalInterpolation (Trans, I, *this); }
338 
339  virtual void Project (Coefficient &coeff,
340  ElementTransformation &Trans, Vector &dofs) const;
341 
342  virtual void Project (VectorCoefficient &vc,
343  ElementTransformation &Trans, Vector &dofs) const;
344 
345  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
346  DenseMatrix &I) const;
347 
348  virtual void ProjectGrad(const FiniteElement &fe,
349  ElementTransformation &Trans,
350  DenseMatrix &grad) const;
351 
352  virtual void ProjectDiv(const FiniteElement &fe,
353  ElementTransformation &Trans,
354  DenseMatrix &div) const;
355 };
356 
357 
358 class PositiveFiniteElement : public ScalarFiniteElement
359 {
360 protected:
361  void PositiveLocalInterpolation(ElementTransformation &Trans,
362  DenseMatrix &I,
363  const PositiveFiniteElement &fine_fe) const;
364 
365 public:
366  PositiveFiniteElement(int D, int G, int Do, int O,
367  int F = FunctionSpace::Pk) :
368  ScalarFiniteElement(D, G, Do, O, F)
369  { }
370 
371  virtual void GetLocalInterpolation(ElementTransformation &Trans,
372  DenseMatrix &I) const
373  { PositiveLocalInterpolation(Trans, I, *this); }
374 
375  using FiniteElement::Project;
376 
377  // Low-order monotone "projection" (actually it is not a projection): the
378  // dofs are set to be the Coefficient values at the nodes.
379  virtual void Project(Coefficient &coeff,
380  ElementTransformation &Trans, Vector &dofs) const;
381 
382  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
383  DenseMatrix &I) const;
384 };
385 
386 class VectorFiniteElement : public FiniteElement
387 {
388  // Hide the scalar functions CalcShape and CalcDShape.
389 private:
390  /// Overrides the scalar CalcShape function to print an error.
391  virtual void CalcShape(const IntegrationPoint &ip,
392  Vector &shape) const;
393 
394  /// Overrides the scalar CalcDShape function to print an error.
395  virtual void CalcDShape(const IntegrationPoint &ip,
396  DenseMatrix &dshape) const;
397 
398 protected:
399 #ifndef MFEM_THREAD_SAFE
400  mutable DenseMatrix J, Jinv;
401  mutable DenseMatrix curlshape, curlshape_J;
402 #endif
403  void SetDerivMembers();
404 
405  void CalcVShape_RT(ElementTransformation &Trans,
406  DenseMatrix &shape) const;
407 
408  void CalcVShape_ND(ElementTransformation &Trans,
409  DenseMatrix &shape) const;
410 
411  void Project_RT(const double *nk, const Array<int> &d2n,
412  VectorCoefficient &vc, ElementTransformation &Trans,
413  Vector &dofs) const;
414 
415  void Project_RT(const double *nk, const Array<int> &d2n,
416  const FiniteElement &fe, ElementTransformation &Trans,
417  DenseMatrix &I) const;
418 
419  // rotated gradient in 2D
420  void ProjectGrad_RT(const double *nk, const Array<int> &d2n,
421  const FiniteElement &fe, ElementTransformation &Trans,
422  DenseMatrix &grad) const;
423 
424  // Compute the curl as a discrete operator from ND FE (fe) to ND FE (this).
425  // The natural FE for the range is RT, so this is an approximation.
426  void ProjectCurl_ND(const double *tk, const Array<int> &d2t,
427  const FiniteElement &fe, ElementTransformation &Trans,
428  DenseMatrix &curl) const;
429 
430  void ProjectCurl_RT(const double *nk, const Array<int> &d2n,
431  const FiniteElement &fe, ElementTransformation &Trans,
432  DenseMatrix &curl) const;
433 
434  void Project_ND(const double *tk, const Array<int> &d2t,
435  VectorCoefficient &vc, ElementTransformation &Trans,
436  Vector &dofs) const;
437 
438  void Project_ND(const double *tk, const Array<int> &d2t,
439  const FiniteElement &fe, ElementTransformation &Trans,
440  DenseMatrix &I) const;
441 
442  void ProjectGrad_ND(const double *tk, const Array<int> &d2t,
443  const FiniteElement &fe, ElementTransformation &Trans,
444  DenseMatrix &grad) const;
445 
446  void LocalInterpolation_RT(const double *nk, const Array<int> &d2n,
447  ElementTransformation &Trans,
448  DenseMatrix &I) const;
449 
450  void LocalInterpolation_ND(const double *tk, const Array<int> &d2t,
451  ElementTransformation &Trans,
452  DenseMatrix &I) const;
453 
454 public:
455  VectorFiniteElement (int D, int G, int Do, int O, int M,
456  int F = FunctionSpace::Pk) :
457 #ifdef MFEM_THREAD_SAFE
458  FiniteElement(D, G, Do, O, F)
459  { RangeType = VECTOR; MapType = M; SetDerivMembers(); }
460 #else
461  FiniteElement(D, G, Do, O, F), Jinv(D)
462  { RangeType = VECTOR; MapType = M; SetDerivMembers(); }
463 #endif
464 };
465 
466 class PointFiniteElement : public NodalFiniteElement
467 {
468 public:
469  PointFiniteElement();
470 
471  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
472 
473  virtual void CalcDShape(const IntegrationPoint &ip,
474  DenseMatrix &dshape) const;
475 };
476 
477 /// Class for linear FE on interval
478 class Linear1DFiniteElement : public NodalFiniteElement
479 {
480 public:
481  /// Construct a linear FE on interval
482  Linear1DFiniteElement();
483 
484  /** virtual function which evaluates the values of all
485  shape functions at a given point ip and stores
486  them in the vector shape of dimension Dof (2) */
487  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
488 
489  /** virtual function which evaluates the derivatives of all
490  shape functions at a given point ip and stores them in
491  the matrix dshape (Dof x Dim) (2 x 1) so that each row
492  contains the derivative of one shape function */
493  virtual void CalcDShape(const IntegrationPoint &ip,
494  DenseMatrix &dshape) const;
495 };
496 
497 /// Class for linear FE on triangle
498 class Linear2DFiniteElement : public NodalFiniteElement
499 {
500 public:
501  /// Construct a linear FE on triangle
502  Linear2DFiniteElement();
503 
504  /** virtual function which evaluates the values of all
505  shape functions at a given point ip and stores
506  them in the vector shape of dimension Dof (3) */
507  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
508 
509  /** virtual function which evaluates the values of all
510  partial derivatives of all shape functions at a given
511  point ip and stores them in the matrix dshape (Dof x Dim) (3 x 2)
512  so that each row contains the derivatives of one shape function */
513  virtual void CalcDShape(const IntegrationPoint &ip,
514  DenseMatrix &dshape) const;
515  virtual void ProjectDelta(int vertex, Vector &dofs) const
516  { dofs = 0.0; dofs(vertex) = 1.0; }
517 };
518 
519 /// Class for bilinear FE on quadrilateral
520 class BiLinear2DFiniteElement : public NodalFiniteElement
521 {
522 public:
523  /// Construct a bilinear FE on quadrilateral
524  BiLinear2DFiniteElement();
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 (4) */
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) (4 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 CalcHessian (const IntegrationPoint &ip,
538  DenseMatrix &h) const;
539  virtual void ProjectDelta(int vertex, Vector &dofs) const
540  { dofs = 0.0; dofs(vertex) = 1.0; } // { dofs = 1.0; }
541 };
542 
543 /// Class for linear FE on triangle with nodes at the 3 "Gaussian" points
544 class GaussLinear2DFiniteElement : public NodalFiniteElement
545 {
546 public:
547  GaussLinear2DFiniteElement();
548  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
549  virtual void CalcDShape(const IntegrationPoint &ip,
550  DenseMatrix &dshape) const;
551  virtual void ProjectDelta(int vertex, Vector &dofs) const;
552 };
553 
554 /// Class for bilinear FE on quad with nodes at the 4 Gaussian points
555 class GaussBiLinear2DFiniteElement : public NodalFiniteElement
556 {
557 private:
558  static const double p[2];
559 
560 public:
561  GaussBiLinear2DFiniteElement();
562  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
563  virtual void CalcDShape(const IntegrationPoint &ip,
564  DenseMatrix &dshape) const;
565  virtual void ProjectDelta(int vertex, Vector &dofs) const;
566 };
567 
568 class P1OnQuadFiniteElement : public NodalFiniteElement
569 {
570 public:
571  P1OnQuadFiniteElement();
572  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
573  virtual void CalcDShape(const IntegrationPoint &ip,
574  DenseMatrix &dshape) const;
575  virtual void ProjectDelta(int vertex, Vector &dofs) const
576  { dofs = 1.0; }
577 };
578 
579 /// Class for quadratic FE on interval
580 class Quad1DFiniteElement : public NodalFiniteElement
581 {
582 public:
583  /// Construct a quadratic FE on interval
584  Quad1DFiniteElement();
585 
586  /** virtual function which evaluates the values of all
587  shape functions at a given point ip and stores
588  them in the vector shape of dimension Dof (3) */
589  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
590 
591  /** virtual function which evaluates the derivatives of all
592  shape functions at a given point ip and stores them in
593  the matrix dshape (Dof x Dim) (3 x 1) so that each row
594  contains the derivative of one shape function */
595  virtual void CalcDShape(const IntegrationPoint &ip,
596  DenseMatrix &dshape) const;
597 };
598 
599 class QuadPos1DFiniteElement : public PositiveFiniteElement
600 {
601 public:
602  QuadPos1DFiniteElement();
603  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
604  virtual void CalcDShape(const IntegrationPoint &ip,
605  DenseMatrix &dshape) const;
606 };
607 
608 /// Class for quadratic FE on triangle
609 class Quad2DFiniteElement : public NodalFiniteElement
610 {
611 public:
612  /// Construct a quadratic FE on triangle
613  Quad2DFiniteElement();
614 
615  /** virtual function which evaluates the values of all
616  shape functions at a given point ip and stores
617  them in the vector shape of dimension Dof (6) */
618  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
619 
620  /** virtual function which evaluates the values of all
621  partial derivatives of all shape functions at a given
622  point ip and stores them in the matrix dshape (Dof x Dim) (6 x 2)
623  so that each row contains the derivatives of one shape function */
624  virtual void CalcDShape(const IntegrationPoint &ip,
625  DenseMatrix &dshape) const;
626 
627  virtual void CalcHessian (const IntegrationPoint &ip,
628  DenseMatrix &h) const;
629  virtual void ProjectDelta(int vertex, Vector &dofs) const;
630 };
631 
632 /// Class for quadratic FE on triangle with nodes at the "Gaussian" points
633 class GaussQuad2DFiniteElement : public NodalFiniteElement
634 {
635 private:
636  static const double p[2];
637  DenseMatrix A;
638  mutable DenseMatrix D;
639  mutable Vector pol;
640 public:
641  GaussQuad2DFiniteElement();
642  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
643  virtual void CalcDShape(const IntegrationPoint &ip,
644  DenseMatrix &dshape) const;
645  // virtual void ProjectDelta(int vertex, Vector &dofs) const;
646 };
647 
648 /// Class for bi-quadratic FE on quadrilateral
649 class BiQuad2DFiniteElement : public NodalFiniteElement
650 {
651 public:
652  /// Construct a biquadratic FE on quadrilateral
653  BiQuad2DFiniteElement();
654 
655  /** virtual function which evaluates the values of all
656  shape functions at a given point ip and stores
657  them in the vector shape of dimension Dof (9) */
658  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
659 
660  /** virtual function which evaluates the values of all
661  partial derivatives of all shape functions at a given
662  point ip and stores them in the matrix dshape (Dof x Dim) (9 x 2)
663  so that each row contains the derivatives of one shape function */
664  virtual void CalcDShape(const IntegrationPoint &ip,
665  DenseMatrix &dshape) const;
666  virtual void ProjectDelta(int vertex, Vector &dofs) const;
667 };
668 
669 class BiQuadPos2DFiniteElement : public PositiveFiniteElement
670 {
671 public:
672  BiQuadPos2DFiniteElement();
673  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
674  virtual void CalcDShape(const IntegrationPoint &ip,
675  DenseMatrix &dshape) const;
676  virtual void GetLocalInterpolation(ElementTransformation &Trans,
677  DenseMatrix &I) const;
678  using FiniteElement::Project;
679  virtual void Project(Coefficient &coeff, ElementTransformation &Trans,
680  Vector &dofs) const;
681  virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans,
682  Vector &dofs) const;
683  virtual void ProjectDelta(int vertex, Vector &dofs) const
684  { dofs = 0.; dofs(vertex) = 1.; }
685 };
686 
687 /// Bi-quadratic element on quad with nodes at the 9 Gaussian points
688 class GaussBiQuad2DFiniteElement : public NodalFiniteElement
689 {
690 public:
691  GaussBiQuad2DFiniteElement();
692  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
693  virtual void CalcDShape(const IntegrationPoint &ip,
694  DenseMatrix &dshape) const;
695  // virtual void ProjectDelta(int vertex, Vector &dofs) const { dofs = 1.; }
696 };
697 
698 class BiCubic2DFiniteElement : public NodalFiniteElement
699 {
700 public:
701  BiCubic2DFiniteElement();
702  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
703  virtual void CalcDShape(const IntegrationPoint &ip,
704  DenseMatrix &dshape) const;
705  virtual void CalcHessian (const IntegrationPoint &ip,
706  DenseMatrix &h) const;
707 };
708 
709 class Cubic1DFiniteElement : public NodalFiniteElement
710 {
711 public:
712  Cubic1DFiniteElement();
713 
714  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
715 
716  virtual void CalcDShape(const IntegrationPoint &ip,
717  DenseMatrix &dshape) const;
718 };
719 
720 class Cubic2DFiniteElement : public NodalFiniteElement
721 {
722 public:
723  Cubic2DFiniteElement();
724 
725  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
726 
727  virtual void CalcDShape(const IntegrationPoint &ip,
728  DenseMatrix &dshape) const;
729 
730  virtual void CalcHessian (const IntegrationPoint &ip,
731  DenseMatrix &h) const;
732 };
733 
734 /// Class for cubic FE on tetrahedron
735 class Cubic3DFiniteElement : public NodalFiniteElement
736 {
737 public:
738  /// Construct a cubic FE on tetrahedron
739  Cubic3DFiniteElement();
740 
741  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
742 
743  virtual void CalcDShape(const IntegrationPoint &ip,
744  DenseMatrix &dshape) const;
745 };
746 
747 /// Class for constant FE on triangle
748 class P0TriangleFiniteElement : public NodalFiniteElement
749 {
750 public:
751  /// Construct P0 triangle finite element
752  P0TriangleFiniteElement();
753 
754  /// evaluate shape function - constant 1
755  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
756 
757  /// evaluate derivatives of shape function - constant 0
758  virtual void CalcDShape(const IntegrationPoint &ip,
759  DenseMatrix &dshape) const;
760  virtual void ProjectDelta(int vertex, Vector &dofs) const
761  { dofs(0) = 1.0; }
762 };
763 
764 
765 class P0QuadFiniteElement : public NodalFiniteElement
766 {
767 public:
768  P0QuadFiniteElement();
769  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
770  virtual void CalcDShape(const IntegrationPoint &ip,
771  DenseMatrix &dshape) const;
772  virtual void ProjectDelta(int vertex, Vector &dofs) const
773  { dofs(0) = 1.0; }
774 };
775 
776 
777 /// Class for linear FE on tetrahedron
778 class Linear3DFiniteElement : public NodalFiniteElement
779 {
780 public:
781  /// Construct a linear FE on tetrahedron
782  Linear3DFiniteElement();
783 
784  /** virtual function which evaluates the values of all
785  shape functions at a given point ip and stores
786  them in the vector shape of dimension Dof (4) */
787  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
788 
789  /** virtual function which evaluates the values of all
790  partial derivatives of all shape functions at a given
791  point ip and stores them in the matrix dshape (Dof x Dim) (4 x 3)
792  so that each row contains the derivatives of one shape function */
793  virtual void CalcDShape(const IntegrationPoint &ip,
794  DenseMatrix &dshape) const;
795 
796  virtual void ProjectDelta(int vertex, Vector &dofs) const
797  { dofs = 0.0; dofs(vertex) = 1.0; }
798 
799  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
800 };
801 
802 /// Class for quadratic FE on tetrahedron
803 class Quadratic3DFiniteElement : public NodalFiniteElement
804 {
805 public:
806  /// Construct a quadratic FE on tetrahedron
807  Quadratic3DFiniteElement();
808 
809  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
810 
811  virtual void CalcDShape(const IntegrationPoint &ip,
812  DenseMatrix &dshape) const;
813 };
814 
815 /// Class for tri-linear FE on cube
816 class TriLinear3DFiniteElement : public NodalFiniteElement
817 {
818 public:
819  /// Construct a tri-linear FE on cube
820  TriLinear3DFiniteElement();
821 
822  /** virtual function which evaluates the values of all
823  shape functions at a given point ip and stores
824  them in the vector shape of dimension Dof (8) */
825  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
826 
827  /** virtual function which evaluates the values of all
828  partial derivatives of all shape functions at a given
829  point ip and stores them in the matrix dshape (Dof x Dim) (8 x 3)
830  so that each row contains the derivatives of one shape function */
831  virtual void CalcDShape(const IntegrationPoint &ip,
832  DenseMatrix &dshape) const;
833 
834  virtual void ProjectDelta(int vertex, Vector &dofs) const
835  { dofs = 0.0; dofs(vertex) = 1.0; }
836 };
837 
838 /// Crouzeix-Raviart finite element on triangle
839 class CrouzeixRaviartFiniteElement : public NodalFiniteElement
840 {
841 public:
842  CrouzeixRaviartFiniteElement();
843  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
844  virtual void CalcDShape(const IntegrationPoint &ip,
845  DenseMatrix &dshape) const;
846  virtual void ProjectDelta(int vertex, Vector &dofs) const
847  { dofs = 1.0; }
848 };
849 
850 /// Crouzeix-Raviart finite element on quadrilateral
851 class CrouzeixRaviartQuadFiniteElement : public NodalFiniteElement
852 {
853 public:
854  CrouzeixRaviartQuadFiniteElement();
855  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
856  virtual void CalcDShape(const IntegrationPoint &ip,
857  DenseMatrix &dshape) const;
858 };
859 
860 class P0SegmentFiniteElement : public NodalFiniteElement
861 {
862 public:
863  P0SegmentFiniteElement(int Ord = 0);
864  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
865  virtual void CalcDShape(const IntegrationPoint &ip,
866  DenseMatrix &dshape) const;
867 };
868 
869 class RT0TriangleFiniteElement : public VectorFiniteElement
870 {
871 private:
872  static const double nk[3][2];
873 
874 public:
875  RT0TriangleFiniteElement();
876 
877  virtual void CalcVShape(const IntegrationPoint &ip,
878  DenseMatrix &shape) const;
879 
880  virtual void CalcVShape(ElementTransformation &Trans,
881  DenseMatrix &shape) const
882  { CalcVShape_RT(Trans, shape); }
883 
884  virtual void CalcDivShape(const IntegrationPoint &ip,
885  Vector &divshape) const;
886 
887  virtual void GetLocalInterpolation (ElementTransformation &Trans,
888  DenseMatrix &I) const;
889 
890  using FiniteElement::Project;
891 
892  virtual void Project (VectorCoefficient &vc,
893  ElementTransformation &Trans, Vector &dofs) const;
894 };
895 
896 class RT0QuadFiniteElement : public VectorFiniteElement
897 {
898 private:
899  static const double nk[4][2];
900 
901 public:
902  RT0QuadFiniteElement();
903 
904  virtual void CalcVShape(const IntegrationPoint &ip,
905  DenseMatrix &shape) const;
906 
907  virtual void CalcVShape(ElementTransformation &Trans,
908  DenseMatrix &shape) const
909  { CalcVShape_RT(Trans, shape); }
910 
911  virtual void CalcDivShape(const IntegrationPoint &ip,
912  Vector &divshape) const;
913 
914  virtual void GetLocalInterpolation (ElementTransformation &Trans,
915  DenseMatrix &I) const;
916 
917  using FiniteElement::Project;
918 
919  virtual void Project (VectorCoefficient &vc,
920  ElementTransformation &Trans, Vector &dofs) const;
921 };
922 
923 class RT1TriangleFiniteElement : public VectorFiniteElement
924 {
925 private:
926  static const double nk[8][2];
927 
928 public:
929  RT1TriangleFiniteElement();
930 
931  virtual void CalcVShape(const IntegrationPoint &ip,
932  DenseMatrix &shape) const;
933 
934  virtual void CalcVShape(ElementTransformation &Trans,
935  DenseMatrix &shape) const
936  { CalcVShape_RT(Trans, shape); }
937 
938  virtual void CalcDivShape(const IntegrationPoint &ip,
939  Vector &divshape) const;
940 
941  virtual void GetLocalInterpolation (ElementTransformation &Trans,
942  DenseMatrix &I) const;
943 
944  using FiniteElement::Project;
945 
946  virtual void Project (VectorCoefficient &vc,
947  ElementTransformation &Trans, Vector &dofs) const;
948 };
949 
950 class RT1QuadFiniteElement : public VectorFiniteElement
951 {
952 private:
953  static const double nk[12][2];
954 
955 public:
956  RT1QuadFiniteElement();
957 
958  virtual void CalcVShape(const IntegrationPoint &ip,
959  DenseMatrix &shape) const;
960 
961  virtual void CalcVShape(ElementTransformation &Trans,
962  DenseMatrix &shape) const
963  { CalcVShape_RT(Trans, shape); }
964 
965  virtual void CalcDivShape(const IntegrationPoint &ip,
966  Vector &divshape) const;
967 
968  virtual void GetLocalInterpolation (ElementTransformation &Trans,
969  DenseMatrix &I) const;
970 
971  using FiniteElement::Project;
972 
973  virtual void Project (VectorCoefficient &vc,
974  ElementTransformation &Trans, Vector &dofs) const;
975 };
976 
977 class RT2TriangleFiniteElement : public VectorFiniteElement
978 {
979 private:
980  static const double M[15][15];
981 public:
982  RT2TriangleFiniteElement();
983 
984  virtual void CalcVShape(const IntegrationPoint &ip,
985  DenseMatrix &shape) const;
986 
987  virtual void CalcVShape(ElementTransformation &Trans,
988  DenseMatrix &shape) const
989  { CalcVShape_RT(Trans, shape); }
990 
991  virtual void CalcDivShape(const IntegrationPoint &ip,
992  Vector &divshape) const;
993 };
994 
995 class RT2QuadFiniteElement : public VectorFiniteElement
996 {
997 private:
998  static const double nk[24][2];
999  static const double pt[4];
1000  static const double dpt[3];
1001 
1002 public:
1003  RT2QuadFiniteElement();
1004 
1005  virtual void CalcVShape(const IntegrationPoint &ip,
1006  DenseMatrix &shape) const;
1007 
1008  virtual void CalcVShape(ElementTransformation &Trans,
1009  DenseMatrix &shape) const
1010  { CalcVShape_RT(Trans, shape); }
1011 
1012  virtual void CalcDivShape(const IntegrationPoint &ip,
1013  Vector &divshape) const;
1014 
1015  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1016  DenseMatrix &I) const;
1017 
1018  using FiniteElement::Project;
1019 
1020  virtual void Project (VectorCoefficient &vc,
1021  ElementTransformation &Trans, Vector &dofs) const;
1022 };
1023 
1024 /// Linear 1D element with nodes 1/3 and 2/3 (trace of RT1)
1025 class P1SegmentFiniteElement : public NodalFiniteElement
1026 {
1027 public:
1028  P1SegmentFiniteElement();
1029  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1030  virtual void CalcDShape(const IntegrationPoint &ip,
1031  DenseMatrix &dshape) const;
1032 };
1033 
1034 /// Quadratic 1D element with nodes the Gaussian points in [0,1] (trace of RT2)
1035 class P2SegmentFiniteElement : public NodalFiniteElement
1036 {
1037 public:
1038  P2SegmentFiniteElement();
1039  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1040  virtual void CalcDShape(const IntegrationPoint &ip,
1041  DenseMatrix &dshape) const;
1042 };
1043 
1044 class Lagrange1DFiniteElement : public NodalFiniteElement
1045 {
1046 private:
1047  Vector rwk;
1048 #ifndef MFEM_THREAD_SAFE
1049  mutable Vector rxxk;
1050 #endif
1051 public:
1052  Lagrange1DFiniteElement (int degree);
1053  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1054  virtual void CalcDShape(const IntegrationPoint &ip,
1055  DenseMatrix &dshape) const;
1056 };
1057 
1058 class P1TetNonConfFiniteElement : public NodalFiniteElement
1059 {
1060 public:
1061  P1TetNonConfFiniteElement();
1062  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1063  virtual void CalcDShape(const IntegrationPoint &ip,
1064  DenseMatrix &dshape) const;
1065 };
1066 
1067 class P0TetFiniteElement : public NodalFiniteElement
1068 {
1069 public:
1070  P0TetFiniteElement ();
1071  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1072  virtual void CalcDShape(const IntegrationPoint &ip,
1073  DenseMatrix &dshape) const;
1074  virtual void ProjectDelta(int vertex, Vector &dofs) const
1075  { dofs(0) = 1.0; }
1076 };
1077 
1078 class P0HexFiniteElement : public NodalFiniteElement
1079 {
1080 public:
1081  P0HexFiniteElement ();
1082  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1083  virtual void CalcDShape(const IntegrationPoint &ip,
1084  DenseMatrix &dshape) const;
1085  virtual void ProjectDelta(int vertex, Vector &dofs) const
1086  { dofs(0) = 1.0; }
1087 };
1088 
1089 /// Tensor products of 1D FEs (only degree 2 is functional)
1090 class LagrangeHexFiniteElement : public NodalFiniteElement
1091 {
1092 private:
1093  Lagrange1DFiniteElement * fe1d;
1094  int dof1d;
1095  int *I, *J, *K;
1096 #ifndef MFEM_THREAD_SAFE
1097  mutable Vector shape1dx, shape1dy, shape1dz;
1098  mutable DenseMatrix dshape1dx, dshape1dy, dshape1dz;
1099 #endif
1100 
1101 public:
1102  LagrangeHexFiniteElement (int degree);
1103  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1104  virtual void CalcDShape(const IntegrationPoint &ip,
1105  DenseMatrix &dshape) const;
1106  ~LagrangeHexFiniteElement ();
1107 };
1108 
1109 
1110 /// Class for refined linear FE on interval
1111 class RefinedLinear1DFiniteElement : public NodalFiniteElement
1112 {
1113 public:
1114  /// Construct a quadratic FE on interval
1115  RefinedLinear1DFiniteElement();
1116 
1117  /** virtual function which evaluates the values of all
1118  shape functions at a given point ip and stores
1119  them in the vector shape of dimension Dof (3) */
1120  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1121 
1122  /** virtual function which evaluates the derivatives of all
1123  shape functions at a given point ip and stores them in
1124  the matrix dshape (Dof x Dim) (3 x 1) so that each row
1125  contains the derivative of one shape function */
1126  virtual void CalcDShape(const IntegrationPoint &ip,
1127  DenseMatrix &dshape) const;
1128 };
1129 
1130 /// Class for refined linear FE on triangle
1131 class RefinedLinear2DFiniteElement : public NodalFiniteElement
1132 {
1133 public:
1134  /// Construct a quadratic FE on triangle
1135  RefinedLinear2DFiniteElement();
1136 
1137  /** virtual function which evaluates the values of all
1138  shape functions at a given point ip and stores
1139  them in the vector shape of dimension Dof (6) */
1140  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1141 
1142  /** virtual function which evaluates the values of all
1143  partial derivatives of all shape functions at a given
1144  point ip and stores them in the matrix dshape (Dof x Dim) (6 x 2)
1145  so that each row contains the derivatives of one shape function */
1146  virtual void CalcDShape(const IntegrationPoint &ip,
1147  DenseMatrix &dshape) const;
1148 };
1149 
1150 /// Class for refined linear FE on tetrahedron
1151 class RefinedLinear3DFiniteElement : public NodalFiniteElement
1152 {
1153 public:
1154  /// Construct a quadratic FE on tetrahedron
1155  RefinedLinear3DFiniteElement();
1156 
1157  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1158 
1159  virtual void CalcDShape(const IntegrationPoint &ip,
1160  DenseMatrix &dshape) const;
1161 };
1162 
1163 /// Class for refined bi-linear FE on quadrilateral
1164 class RefinedBiLinear2DFiniteElement : public NodalFiniteElement
1165 {
1166 public:
1167  /// Construct a biquadratic FE on quadrilateral
1168  RefinedBiLinear2DFiniteElement();
1169 
1170  /** virtual function which evaluates the values of all
1171  shape functions at a given point ip and stores
1172  them in the vector shape of dimension Dof (9) */
1173  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1174 
1175  /** virtual function which evaluates the values of all
1176  partial derivatives of all shape functions at a given
1177  point ip and stores them in the matrix dshape (Dof x Dim) (9 x 2)
1178  so that each row contains the derivatives of one shape function */
1179  virtual void CalcDShape(const IntegrationPoint &ip,
1180  DenseMatrix &dshape) const;
1181 };
1182 
1183 /// Class for refined trilinear FE on a hexahedron
1184 class RefinedTriLinear3DFiniteElement : public NodalFiniteElement
1185 {
1186 public:
1187  /// Construct a biquadratic FE on quadrilateral
1188  RefinedTriLinear3DFiniteElement();
1189 
1190  /** virtual function which evaluates the values of all
1191  shape functions at a given point ip and stores
1192  them in the vector shape of dimension Dof (9) */
1193  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1194 
1195  /** virtual function which evaluates the values of all
1196  partial derivatives of all shape functions at a given
1197  point ip and stores them in the matrix dshape (Dof x Dim) (9 x 2)
1198  so that each row contains the derivatives of one shape function */
1199  virtual void CalcDShape(const IntegrationPoint &ip,
1200  DenseMatrix &dshape) const;
1201 };
1202 
1203 
1204 class Nedelec1HexFiniteElement : public VectorFiniteElement
1205 {
1206 private:
1207  static const double tk[12][3];
1208 
1209 public:
1210  Nedelec1HexFiniteElement();
1211  virtual void CalcVShape(const IntegrationPoint &ip,
1212  DenseMatrix &shape) const;
1213  virtual void CalcVShape(ElementTransformation &Trans,
1214  DenseMatrix &shape) const
1215  { CalcVShape_ND(Trans, shape); }
1216  virtual void CalcCurlShape(const IntegrationPoint &ip,
1217  DenseMatrix &curl_shape) const;
1218  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1219  DenseMatrix &I) const;
1220  using FiniteElement::Project;
1221  virtual void Project (VectorCoefficient &vc,
1222  ElementTransformation &Trans, Vector &dofs) const;
1223 };
1224 
1225 
1226 class Nedelec1TetFiniteElement : public VectorFiniteElement
1227 {
1228 private:
1229  static const double tk[6][3];
1230 
1231 public:
1232  Nedelec1TetFiniteElement();
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 RT0HexFiniteElement : public VectorFiniteElement
1249 {
1250 private:
1251  static const double nk[6][3];
1252 
1253 public:
1254  RT0HexFiniteElement();
1255 
1256  virtual void CalcVShape(const IntegrationPoint &ip,
1257  DenseMatrix &shape) const;
1258 
1259  virtual void CalcVShape(ElementTransformation &Trans,
1260  DenseMatrix &shape) const
1261  { CalcVShape_RT(Trans, shape); }
1262 
1263  virtual void CalcDivShape(const IntegrationPoint &ip,
1264  Vector &divshape) const;
1265 
1266  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1267  DenseMatrix &I) const;
1268 
1269  using FiniteElement::Project;
1270 
1271  virtual void Project (VectorCoefficient &vc,
1272  ElementTransformation &Trans, Vector &dofs) const;
1273 };
1274 
1275 
1276 class RT1HexFiniteElement : public VectorFiniteElement
1277 {
1278 private:
1279  static const double nk[36][3];
1280 
1281 public:
1282  RT1HexFiniteElement();
1283 
1284  virtual void CalcVShape(const IntegrationPoint &ip,
1285  DenseMatrix &shape) const;
1286 
1287  virtual void CalcVShape(ElementTransformation &Trans,
1288  DenseMatrix &shape) const
1289  { CalcVShape_RT(Trans, shape); }
1290 
1291  virtual void CalcDivShape(const IntegrationPoint &ip,
1292  Vector &divshape) const;
1293 
1294  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1295  DenseMatrix &I) const;
1296 
1297  using FiniteElement::Project;
1298 
1299  virtual void Project (VectorCoefficient &vc,
1300  ElementTransformation &Trans, Vector &dofs) const;
1301 };
1302 
1303 
1304 class RT0TetFiniteElement : public VectorFiniteElement
1305 {
1306 private:
1307  static const double nk[4][3];
1308 
1309 public:
1310  RT0TetFiniteElement();
1311 
1312  virtual void CalcVShape(const IntegrationPoint &ip,
1313  DenseMatrix &shape) const;
1314 
1315  virtual void CalcVShape(ElementTransformation &Trans,
1316  DenseMatrix &shape) const
1317  { CalcVShape_RT(Trans, shape); }
1318 
1319  virtual void CalcDivShape(const IntegrationPoint &ip,
1320  Vector &divshape) const;
1321 
1322  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1323  DenseMatrix &I) const;
1324 
1325  using FiniteElement::Project;
1326 
1327  virtual void Project (VectorCoefficient &vc,
1328  ElementTransformation &Trans, Vector &dofs) const;
1329 };
1330 
1331 
1332 class RotTriLinearHexFiniteElement : public NodalFiniteElement
1333 {
1334 public:
1335  RotTriLinearHexFiniteElement();
1336  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1337  virtual void CalcDShape(const IntegrationPoint &ip,
1338  DenseMatrix &dshape) const;
1339 };
1340 
1341 
1342 class Poly_1D
1343 {
1344 public:
1345  class Basis
1346  {
1347  private:
1348  int mode; /* 0 - use change of basis, O(p^2) Evals
1349  1 - use barycentric Lagrangian interpolation, O(p) Evals */
1350  DenseMatrixInverse Ai;
1351  mutable Vector x, w;
1352 
1353  public:
1354  Basis(const int p, const double *nodes, const int _mode = 1);
1355  void Eval(const double x, Vector &u) const;
1356  void Eval(const double x, Vector &u, Vector &d) const;
1357  };
1358 
1359 private:
1360  std::map< int, Array<double*>* > points_container;
1361  std::map< int, Array<Basis*>* > bases_container;
1362 
1363  static Array2D<int> binom;
1364 
1365  static void CalcMono(const int p, const double x, double *u);
1366  static void CalcMono(const int p, const double x, double *u, double *d);
1367 
1368  static void CalcLegendre(const int p, const double x, double *u);
1369  static void CalcLegendre(const int p, const double x, double *u, double *d);
1370 
1371  static void CalcChebyshev(const int p, const double x, double *u);
1372  static void CalcChebyshev(const int p, const double x, double *u, double *d);
1373 
1374  QuadratureFunctions1D quad_func;
1375 
1376 public:
1377  Poly_1D() { }
1378 
1379  /** @brief Get a poiner to an array containing the binomial coefficients "p
1380  choose k" for k=0,...,p for the given p. */
1381  static const int *Binom(const int p);
1382 
1383  /** @brief Get the coordinates of the points of the given Quadrature1D type.
1384  @param p the polynomial degree; the number of points is `p+1`.
1385  @param type the Quadrature1D type.
1386  @return a pointer to an array containing the `p+1` coordiantes of the
1387  quadrature points. */
1388  const double *GetPoints(const int p, const int type);
1389  const double *OpenPoints(const int p,
1390  const int type = Quadrature1D::GaussLegendre)
1391  { return GetPoints(p, type); }
1392  const double *ClosedPoints(const int p,
1393  const int type = Quadrature1D::GaussLobatto)
1394  { return GetPoints(p, type); }
1395 
1396  /** @brief Get a Poly_1D::Basis object of the given degree and Quadrature1D
1397  type.
1398  @param p the polynomial degree of the basis.
1399  @param type the Quadrature1D type.
1400  @return a reference to an object of type Poly_1D::Basis that represents
1401  the requested nodal basis. */
1402  Basis &GetBasis(const int p, const int type);
1403  Basis &OpenBasis(const int p,
1404  const int type = Quadrature1D::GaussLegendre)
1405  { return GetBasis(p, type); }
1406  Basis &ClosedBasis(const int p,
1407  const int type = Quadrature1D::GaussLobatto)
1408  { return GetBasis(p, type); }
1409 
1410  // Evaluate the values of a hierarchical 1D basis at point x
1411  // hierarchical = k-th basis function is degree k polynomial
1412  static void CalcBasis(const int p, const double x, double *u)
1413  // { CalcMono(p, x, u); }
1414  // Bernstein basis is not hierarchical --> does not work for triangles
1415  // and tetrahedra
1416  // { CalcBernstein(p, x, u); }
1417  // { CalcLegendre(p, x, u); }
1418  { CalcChebyshev(p, x, u); }
1419 
1420  // Evaluate the values and derivatives of a hierarchical 1D basis at point x
1421  static void CalcBasis(const int p, const double x, double *u, double *d)
1422  // { CalcMono(p, x, u, d); }
1423  // { CalcBernstein(p, x, u, d); }
1424  // { CalcLegendre(p, x, u, d); }
1425  { CalcChebyshev(p, x, u, d); }
1426 
1427  // Evaluate a representation of a Delta function at point x
1428  static double CalcDelta(const int p, const double x)
1429  { return pow(x, (double) p); }
1430 
1431  static void ChebyshevPoints(const int p, double *x);
1432 
1433  /// Compute the terms in the expansion of the binomial (x + y)^p
1434  static void CalcBinomTerms(const int p, const double x, const double y,
1435  double *u);
1436  /** Compute the terms in the expansion of the binomial (x + y)^p and their
1437  derivatives with respect to x assuming that dy/dx = -1. */
1438  static void CalcBinomTerms(const int p, const double x, const double y,
1439  double *u, double *d);
1440  /** Compute the derivatives (w.r.t. x) of the terms in the expansion of the
1441  binomial (x + y)^p assuming that dy/dx = -1. */
1442  static void CalcDBinomTerms(const int p, const double x, const double y,
1443  double *d);
1444  static void CalcBernstein(const int p, const double x, double *u)
1445  { CalcBinomTerms(p, x, 1. - x, u); }
1446  static void CalcBernstein(const int p, const double x, double *u, double *d)
1447  { CalcBinomTerms(p, x, 1. - x, u, d); }
1448 
1449  ~Poly_1D();
1450 };
1451 
1452 extern Poly_1D poly1d;
1453 
1454 
1455 class H1_SegmentElement : public NodalFiniteElement
1456 {
1457 private:
1458  int pt_type;
1459  Poly_1D::Basis &basis1d;
1460 #ifndef MFEM_THREAD_SAFE
1461  mutable Vector shape_x, dshape_x;
1462 #endif
1463  Array<int> dof_map;
1464 
1465 public:
1466  H1_SegmentElement(const int p, const int type = Quadrature1D::GaussLobatto);
1467  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1468  virtual void CalcDShape(const IntegrationPoint &ip,
1469  DenseMatrix &dshape) const;
1470  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1471  const Array<int> &GetDofMap() const { return dof_map; }
1472 };
1473 
1474 
1475 class H1_QuadrilateralElement : public NodalFiniteElement
1476 {
1477 private:
1478  int pt_type;
1479  Poly_1D::Basis &basis1d;
1480 #ifndef MFEM_THREAD_SAFE
1481  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1482 #endif
1483  Array<int> dof_map;
1484 
1485 public:
1486  H1_QuadrilateralElement(const int p,
1487  const int type = Quadrature1D::GaussLobatto);
1488  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1489  virtual void CalcDShape(const IntegrationPoint &ip,
1490  DenseMatrix &dshape) const;
1491  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1492  const Array<int> &GetDofMap() const { return dof_map; }
1493 };
1494 
1495 
1496 class H1_HexahedronElement : public NodalFiniteElement
1497 {
1498 private:
1499  int pt_type;
1500  Poly_1D::Basis &basis1d;
1501 #ifndef MFEM_THREAD_SAFE
1502  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1503 #endif
1504  Array<int> dof_map;
1505 
1506 public:
1507  H1_HexahedronElement(const int p, const int type = Quadrature1D::GaussLobatto);
1508  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1509  virtual void CalcDShape(const IntegrationPoint &ip,
1510  DenseMatrix &dshape) const;
1511  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1512  const Array<int> &GetDofMap() const { return dof_map; }
1513 };
1514 
1515 class H1Pos_SegmentElement : public PositiveFiniteElement
1516 {
1517 private:
1518 #ifndef MFEM_THREAD_SAFE
1519  // This is to share scratch space between invocations, which helps
1520  // speed things up, but with OpenMP, we need one copy per thread.
1521  // Right now, we solve this by allocating this space within each function
1522  // call every time we call it. Alternatively, we should do some sort
1523  // thread private thing. Brunner, Jan 2014
1524  mutable Vector shape_x, dshape_x;
1525 #endif
1526  Array<int> dof_map;
1527 
1528 public:
1529  H1Pos_SegmentElement(const int p);
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 
1538 class H1Pos_QuadrilateralElement : public PositiveFiniteElement
1539 {
1540 private:
1541 #ifndef MFEM_THREAD_SAFE
1542  // See comment in H1Pos_SegmentElement
1543  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1544 #endif
1545  Array<int> dof_map;
1546 
1547 public:
1548  H1Pos_QuadrilateralElement(const int p);
1549  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1550  virtual void CalcDShape(const IntegrationPoint &ip,
1551  DenseMatrix &dshape) const;
1552  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1553  const Array<int> &GetDofMap() const { return dof_map; }
1554 };
1555 
1556 
1557 class H1Pos_HexahedronElement : public PositiveFiniteElement
1558 {
1559 private:
1560 #ifndef MFEM_THREAD_SAFE
1561  // See comment in H1Pos_SegementElement.
1562  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1563 #endif
1564  Array<int> dof_map;
1565 
1566 public:
1567  H1Pos_HexahedronElement(const int p);
1568  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1569  virtual void CalcDShape(const IntegrationPoint &ip,
1570  DenseMatrix &dshape) const;
1571  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1572  const Array<int> &GetDofMap() const { return dof_map; }
1573 };
1574 
1575 
1576 class H1_TriangleElement : public NodalFiniteElement
1577 {
1578 private:
1579 #ifndef MFEM_THREAD_SAFE
1580  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1581  mutable DenseMatrix du;
1582 #endif
1583  DenseMatrixInverse Ti;
1584 
1585 public:
1586  H1_TriangleElement(const int p, const int type = Quadrature1D::GaussLobatto);
1587  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1588  virtual void CalcDShape(const IntegrationPoint &ip,
1589  DenseMatrix &dshape) const;
1590 };
1591 
1592 
1593 class H1_TetrahedronElement : public NodalFiniteElement
1594 {
1595 private:
1596 #ifndef MFEM_THREAD_SAFE
1597  mutable Vector shape_x, shape_y, shape_z, shape_l;
1598  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1599  mutable DenseMatrix du;
1600 #endif
1601  DenseMatrixInverse Ti;
1602 
1603 public:
1604  H1_TetrahedronElement(const int p,
1605  const int type = Quadrature1D::GaussLobatto);
1606  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1607  virtual void CalcDShape(const IntegrationPoint &ip,
1608  DenseMatrix &dshape) const;
1609 };
1610 
1611 
1612 class H1Pos_TriangleElement : public PositiveFiniteElement
1613 {
1614 protected:
1615 #ifndef MFEM_THREAD_SAFE
1616  mutable Vector m_shape, dshape_1d;
1617  mutable DenseMatrix m_dshape;
1618 #endif
1619  Array<int> dof_map;
1620 
1621 public:
1622  H1Pos_TriangleElement(const int p);
1623 
1624  // The size of shape is (p+1)(p+2)/2 (dof).
1625  static void CalcShape(const int p, const double x, const double y,
1626  double *shape);
1627 
1628  // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
1629  static void CalcDShape(const int p, const double x, const double y,
1630  double *dshape_1d, double *dshape);
1631 
1632  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1633  virtual void CalcDShape(const IntegrationPoint &ip,
1634  DenseMatrix &dshape) const;
1635 };
1636 
1637 
1638 class H1Pos_TetrahedronElement : public PositiveFiniteElement
1639 {
1640 protected:
1641 #ifndef MFEM_THREAD_SAFE
1642  mutable Vector m_shape, dshape_1d;
1643  mutable DenseMatrix m_dshape;
1644 #endif
1645  Array<int> dof_map;
1646 
1647 public:
1648  H1Pos_TetrahedronElement(const int p);
1649 
1650  // The size of shape is (p+1)(p+2)(p+3)/6 (dof).
1651  static void CalcShape(const int p, const double x, const double y,
1652  const double z, double *shape);
1653 
1654  // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
1655  static void CalcDShape(const int p, const double x, const double y,
1656  const double z, double *dshape_1d, double *dshape);
1657 
1658  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1659  virtual void CalcDShape(const IntegrationPoint &ip,
1660  DenseMatrix &dshape) const;
1661 };
1662 
1663 
1664 class L2_SegmentElement : public NodalFiniteElement
1665 {
1666 private:
1667  int type;
1668  Poly_1D::Basis &basis1d;
1669 #ifndef MFEM_THREAD_SAFE
1670  mutable Vector shape_x, dshape_x;
1671 #endif
1672 
1673 public:
1674  L2_SegmentElement(const int p, const int type = Quadrature1D::GaussLegendre);
1675  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1676  virtual void CalcDShape(const IntegrationPoint &ip,
1677  DenseMatrix &dshape) const;
1678  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1679 };
1680 
1681 
1682 class L2Pos_SegmentElement : public PositiveFiniteElement
1683 {
1684 private:
1685 #ifndef MFEM_THREAD_SAFE
1686  mutable Vector shape_x, dshape_x;
1687 #endif
1688 
1689 public:
1690  L2Pos_SegmentElement(const int p);
1691  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1692  virtual void CalcDShape(const IntegrationPoint &ip,
1693  DenseMatrix &dshape) const;
1694  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1695 };
1696 
1697 
1698 class L2_QuadrilateralElement : public NodalFiniteElement
1699 {
1700 private:
1701  int type;
1702  Poly_1D::Basis &basis1d;
1703 #ifndef MFEM_THREAD_SAFE
1704  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1705 #endif
1706 
1707 public:
1708  L2_QuadrilateralElement(const int p,
1709  const int _type = Quadrature1D::GaussLegendre);
1710  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1711  virtual void CalcDShape(const IntegrationPoint &ip,
1712  DenseMatrix &dshape) const;
1713  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1714  virtual void ProjectCurl(const FiniteElement &fe,
1715  ElementTransformation &Trans,
1716  DenseMatrix &curl) const
1717  { ProjectCurl_2D(fe, Trans, curl); }
1718 };
1719 
1720 
1721 class L2Pos_QuadrilateralElement : public PositiveFiniteElement
1722 {
1723 private:
1724 #ifndef MFEM_THREAD_SAFE
1725  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1726 #endif
1727 
1728 public:
1729  L2Pos_QuadrilateralElement(const int p);
1730  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1731  virtual void CalcDShape(const IntegrationPoint &ip,
1732  DenseMatrix &dshape) const;
1733  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1734 };
1735 
1736 
1737 class L2_HexahedronElement : public NodalFiniteElement
1738 {
1739 private:
1740  int type;
1741  Poly_1D::Basis &basis1d;
1742 #ifndef MFEM_THREAD_SAFE
1743  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1744 #endif
1745 
1746 public:
1747  L2_HexahedronElement(const int p,
1748  const int _type = Quadrature1D::GaussLegendre);
1749  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1750  virtual void CalcDShape(const IntegrationPoint &ip,
1751  DenseMatrix &dshape) const;
1752  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1753 };
1754 
1755 
1756 class L2Pos_HexahedronElement : public PositiveFiniteElement
1757 {
1758 private:
1759 #ifndef MFEM_THREAD_SAFE
1760  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1761 #endif
1762 
1763 public:
1764  L2Pos_HexahedronElement(const int p);
1765  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1766  virtual void CalcDShape(const IntegrationPoint &ip,
1767  DenseMatrix &dshape) const;
1768  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1769 };
1770 
1771 
1772 class L2_TriangleElement : public NodalFiniteElement
1773 {
1774 private:
1775 #ifndef MFEM_THREAD_SAFE
1776  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1777  mutable DenseMatrix du;
1778 #endif
1779  DenseMatrixInverse Ti;
1780 
1781 public:
1782  L2_TriangleElement(const int p,
1783  const int type = Quadrature1D::GaussLegendre);
1784  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1785  virtual void CalcDShape(const IntegrationPoint &ip,
1786  DenseMatrix &dshape) const;
1787  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1788  virtual void ProjectCurl(const FiniteElement &fe,
1789  ElementTransformation &Trans,
1790  DenseMatrix &curl) const
1791  { ProjectCurl_2D(fe, Trans, curl); }
1792 };
1793 
1794 
1795 class L2Pos_TriangleElement : public PositiveFiniteElement
1796 {
1797 private:
1798 #ifndef MFEM_THREAD_SAFE
1799  mutable Vector dshape_1d;
1800 #endif
1801 
1802 public:
1803  L2Pos_TriangleElement(const int p);
1804  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1805  virtual void CalcDShape(const IntegrationPoint &ip,
1806  DenseMatrix &dshape) const;
1807  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1808 };
1809 
1810 
1811 class L2_TetrahedronElement : public NodalFiniteElement
1812 {
1813 private:
1814 #ifndef MFEM_THREAD_SAFE
1815  mutable Vector shape_x, shape_y, shape_z, shape_l;
1816  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1817  mutable DenseMatrix du;
1818 #endif
1819  DenseMatrixInverse Ti;
1820 
1821 public:
1822  L2_TetrahedronElement(const int p,
1823  const int type = Quadrature1D::GaussLegendre);
1824  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1825  virtual void CalcDShape(const IntegrationPoint &ip,
1826  DenseMatrix &dshape) const;
1827  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1828 };
1829 
1830 
1831 class L2Pos_TetrahedronElement : public PositiveFiniteElement
1832 {
1833 private:
1834 #ifndef MFEM_THREAD_SAFE
1835  mutable Vector dshape_1d;
1836 #endif
1837 
1838 public:
1839  L2Pos_TetrahedronElement(const int p);
1840  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1841  virtual void CalcDShape(const IntegrationPoint &ip,
1842  DenseMatrix &dshape) const;
1843  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1844 };
1845 
1846 
1847 class RT_QuadrilateralElement : public VectorFiniteElement
1848 {
1849 private:
1850  static const double nk[8];
1851 
1852  Poly_1D::Basis &cbasis1d, &obasis1d;
1853 #ifndef MFEM_THREAD_SAFE
1854  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
1855  mutable Vector dshape_cx, dshape_cy;
1856 #endif
1857  Array<int> dof_map, dof2nk;
1858 
1859 public:
1860  RT_QuadrilateralElement(const int p,
1861  const int cp_type = Quadrature1D::GaussLobatto,
1862  const int op_type = Quadrature1D::GaussLegendre);
1863  virtual void CalcVShape(const IntegrationPoint &ip,
1864  DenseMatrix &shape) const;
1865  virtual void CalcVShape(ElementTransformation &Trans,
1866  DenseMatrix &shape) const
1867  { CalcVShape_RT(Trans, shape); }
1868  virtual void CalcDivShape(const IntegrationPoint &ip,
1869  Vector &divshape) const;
1870  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1871  DenseMatrix &I) const
1872  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1873  using FiniteElement::Project;
1874  virtual void Project(VectorCoefficient &vc,
1875  ElementTransformation &Trans, Vector &dofs) const
1876  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1877  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1878  DenseMatrix &I) const
1879  { Project_RT(nk, dof2nk, fe, Trans, I); }
1880  // Gradient + rotation = Curl: H1 -> H(div)
1881  virtual void ProjectGrad(const FiniteElement &fe,
1882  ElementTransformation &Trans,
1883  DenseMatrix &grad) const
1884  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1885  // Curl = Gradient + rotation: H1 -> H(div)
1886  virtual void ProjectCurl(const FiniteElement &fe,
1887  ElementTransformation &Trans,
1888  DenseMatrix &curl) const
1889  { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
1890 };
1891 
1892 
1893 class RT_HexahedronElement : public VectorFiniteElement
1894 {
1895  static const double nk[18];
1896 
1897  Poly_1D::Basis &cbasis1d, &obasis1d;
1898 #ifndef MFEM_THREAD_SAFE
1899  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
1900  mutable Vector dshape_cx, dshape_cy, dshape_cz;
1901 #endif
1902  Array<int> dof_map, dof2nk;
1903 
1904 public:
1905  RT_HexahedronElement(const int p,
1906  const int cp_type = Quadrature1D::GaussLobatto,
1907  const int op_type = Quadrature1D::GaussLegendre);
1908 
1909  virtual void CalcVShape(const IntegrationPoint &ip,
1910  DenseMatrix &shape) const;
1911  virtual void CalcVShape(ElementTransformation &Trans,
1912  DenseMatrix &shape) const
1913  { CalcVShape_RT(Trans, shape); }
1914  virtual void CalcDivShape(const IntegrationPoint &ip,
1915  Vector &divshape) const;
1916  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1917  DenseMatrix &I) const
1918  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1919  using FiniteElement::Project;
1920  virtual void Project(VectorCoefficient &vc,
1921  ElementTransformation &Trans, Vector &dofs) const
1922  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1923  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1924  DenseMatrix &I) const
1925  { Project_RT(nk, dof2nk, fe, Trans, I); }
1926  virtual void ProjectCurl(const FiniteElement &fe,
1927  ElementTransformation &Trans,
1928  DenseMatrix &curl) const
1929  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
1930 };
1931 
1932 
1933 class RT_TriangleElement : public VectorFiniteElement
1934 {
1935  static const double nk[6], c;
1936 
1937 #ifndef MFEM_THREAD_SAFE
1938  mutable Vector shape_x, shape_y, shape_l;
1939  mutable Vector dshape_x, dshape_y, dshape_l;
1940  mutable DenseMatrix u;
1941  mutable Vector divu;
1942 #endif
1943  Array<int> dof2nk;
1944  DenseMatrixInverse Ti;
1945 
1946 public:
1947  RT_TriangleElement(const int p);
1948  virtual void CalcVShape(const IntegrationPoint &ip,
1949  DenseMatrix &shape) const;
1950  virtual void CalcVShape(ElementTransformation &Trans,
1951  DenseMatrix &shape) const
1952  { CalcVShape_RT(Trans, shape); }
1953  virtual void CalcDivShape(const IntegrationPoint &ip,
1954  Vector &divshape) const;
1955  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1956  DenseMatrix &I) const
1957  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1958  using FiniteElement::Project;
1959  virtual void Project(VectorCoefficient &vc,
1960  ElementTransformation &Trans, Vector &dofs) const
1961  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1962  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1963  DenseMatrix &I) const
1964  { Project_RT(nk, dof2nk, fe, Trans, I); }
1965  // Gradient + rotation = Curl: H1 -> H(div)
1966  virtual void ProjectGrad(const FiniteElement &fe,
1967  ElementTransformation &Trans,
1968  DenseMatrix &grad) const
1969  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1970  // Curl = Gradient + rotation: H1 -> H(div)
1971  virtual void ProjectCurl(const FiniteElement &fe,
1972  ElementTransformation &Trans,
1973  DenseMatrix &curl) const
1974  { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
1975 };
1976 
1977 
1978 class RT_TetrahedronElement : public VectorFiniteElement
1979 {
1980  static const double nk[12], c;
1981 
1982 #ifndef MFEM_THREAD_SAFE
1983  mutable Vector shape_x, shape_y, shape_z, shape_l;
1984  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
1985  mutable DenseMatrix u;
1986  mutable Vector divu;
1987 #endif
1988  Array<int> dof2nk;
1989  DenseMatrixInverse Ti;
1990 
1991 public:
1992  RT_TetrahedronElement(const int p);
1993  virtual void CalcVShape(const IntegrationPoint &ip,
1994  DenseMatrix &shape) const;
1995  virtual void CalcVShape(ElementTransformation &Trans,
1996  DenseMatrix &shape) const
1997  { CalcVShape_RT(Trans, shape); }
1998  virtual void CalcDivShape(const IntegrationPoint &ip,
1999  Vector &divshape) const;
2000  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2001  DenseMatrix &I) const
2002  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
2003  using FiniteElement::Project;
2004  virtual void Project(VectorCoefficient &vc,
2005  ElementTransformation &Trans, Vector &dofs) const
2006  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
2007  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
2008  DenseMatrix &I) const
2009  { Project_RT(nk, dof2nk, fe, Trans, I); }
2010  virtual void ProjectCurl(const FiniteElement &fe,
2011  ElementTransformation &Trans,
2012  DenseMatrix &curl) const
2013  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
2014 };
2015 
2016 
2017 class ND_HexahedronElement : public VectorFiniteElement
2018 {
2019  static const double tk[18];
2020 
2021  Poly_1D::Basis &cbasis1d, &obasis1d;
2022 #ifndef MFEM_THREAD_SAFE
2023  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
2024  mutable Vector dshape_cx, dshape_cy, dshape_cz;
2025 #endif
2026  Array<int> dof_map, dof2tk;
2027 
2028 public:
2029  ND_HexahedronElement(const int p,
2030  const int cp_type = Quadrature1D::GaussLobatto,
2031  const int op_type = Quadrature1D::GaussLegendre);
2032 
2033  virtual void CalcVShape(const IntegrationPoint &ip,
2034  DenseMatrix &shape) const;
2035 
2036  virtual void CalcVShape(ElementTransformation &Trans,
2037  DenseMatrix &shape) const
2038  { CalcVShape_ND(Trans, shape); }
2039 
2040  virtual void CalcCurlShape(const IntegrationPoint &ip,
2041  DenseMatrix &curl_shape) const;
2042 
2043  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2044  DenseMatrix &I) const
2045  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2046 
2047  using FiniteElement::Project;
2048 
2049  virtual void Project(VectorCoefficient &vc,
2050  ElementTransformation &Trans, Vector &dofs) const
2051  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2052 
2053  virtual void Project(const FiniteElement &fe,
2054  ElementTransformation &Trans,
2055  DenseMatrix &I) const
2056  { Project_ND(tk, dof2tk, fe, Trans, I); }
2057 
2058  virtual void ProjectGrad(const FiniteElement &fe,
2059  ElementTransformation &Trans,
2060  DenseMatrix &grad) const
2061  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2062 
2063  virtual void ProjectCurl(const FiniteElement &fe,
2064  ElementTransformation &Trans,
2065  DenseMatrix &curl) const
2066  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
2067 };
2068 
2069 
2070 class ND_QuadrilateralElement : public VectorFiniteElement
2071 {
2072  static const double tk[8];
2073 
2074  Poly_1D::Basis &cbasis1d, &obasis1d;
2075 #ifndef MFEM_THREAD_SAFE
2076  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
2077  mutable Vector dshape_cx, dshape_cy;
2078 #endif
2079  Array<int> dof_map, dof2tk;
2080 
2081 public:
2082  ND_QuadrilateralElement(const int p,
2083  const int cp_type = Quadrature1D::GaussLobatto,
2084  const int op_type = Quadrature1D::GaussLegendre);
2085  virtual void CalcVShape(const IntegrationPoint &ip,
2086  DenseMatrix &shape) const;
2087  virtual void CalcVShape(ElementTransformation &Trans,
2088  DenseMatrix &shape) const
2089  { CalcVShape_ND(Trans, shape); }
2090  virtual void CalcCurlShape(const IntegrationPoint &ip,
2091  DenseMatrix &curl_shape) const;
2092  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2093  DenseMatrix &I) const
2094  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2095  using FiniteElement::Project;
2096  virtual void Project(VectorCoefficient &vc,
2097  ElementTransformation &Trans, Vector &dofs) const
2098  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2099  virtual void Project(const FiniteElement &fe,
2100  ElementTransformation &Trans,
2101  DenseMatrix &I) const
2102  { Project_ND(tk, dof2tk, fe, Trans, I); }
2103  virtual void ProjectGrad(const FiniteElement &fe,
2104  ElementTransformation &Trans,
2105  DenseMatrix &grad) const
2106  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2107 };
2108 
2109 
2110 class ND_TetrahedronElement : public VectorFiniteElement
2111 {
2112  static const double tk[18], c;
2113 
2114 #ifndef MFEM_THREAD_SAFE
2115  mutable Vector shape_x, shape_y, shape_z, shape_l;
2116  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
2117  mutable DenseMatrix u;
2118 #endif
2119  Array<int> dof2tk;
2120  DenseMatrixInverse Ti;
2121 
2122 public:
2123  ND_TetrahedronElement(const int p);
2124  virtual void CalcVShape(const IntegrationPoint &ip,
2125  DenseMatrix &shape) const;
2126  virtual void CalcVShape(ElementTransformation &Trans,
2127  DenseMatrix &shape) const
2128  { CalcVShape_ND(Trans, shape); }
2129  virtual void CalcCurlShape(const IntegrationPoint &ip,
2130  DenseMatrix &curl_shape) const;
2131  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2132  DenseMatrix &I) const
2133  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2134  using FiniteElement::Project;
2135  virtual void Project(VectorCoefficient &vc,
2136  ElementTransformation &Trans, Vector &dofs) const
2137  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2138  virtual void Project(const FiniteElement &fe,
2139  ElementTransformation &Trans,
2140  DenseMatrix &I) const
2141  { Project_ND(tk, dof2tk, fe, Trans, I); }
2142  virtual void ProjectGrad(const FiniteElement &fe,
2143  ElementTransformation &Trans,
2144  DenseMatrix &grad) const
2145  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2146 
2147  virtual void ProjectCurl(const FiniteElement &fe,
2148  ElementTransformation &Trans,
2149  DenseMatrix &curl) const
2150  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
2151 };
2152 
2153 class ND_TriangleElement : public VectorFiniteElement
2154 {
2155  static const double tk[8], c;
2156 
2157 #ifndef MFEM_THREAD_SAFE
2158  mutable Vector shape_x, shape_y, shape_l;
2159  mutable Vector dshape_x, dshape_y, dshape_l;
2160  mutable DenseMatrix u;
2161  mutable Vector curlu;
2162 #endif
2163  Array<int> dof2tk;
2164  DenseMatrixInverse Ti;
2165 
2166 public:
2167  ND_TriangleElement(const int p);
2168  virtual void CalcVShape(const IntegrationPoint &ip,
2169  DenseMatrix &shape) const;
2170  virtual void CalcVShape(ElementTransformation &Trans,
2171  DenseMatrix &shape) const
2172  { CalcVShape_ND(Trans, shape); }
2173  virtual void CalcCurlShape(const IntegrationPoint &ip,
2174  DenseMatrix &curl_shape) const;
2175  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2176  DenseMatrix &I) const
2177  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2178  using FiniteElement::Project;
2179  virtual void Project(VectorCoefficient &vc,
2180  ElementTransformation &Trans, Vector &dofs) const
2181  { Project_ND(tk, dof2tk, vc, Trans, 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 
2192 
2193 class ND_SegmentElement : public VectorFiniteElement
2194 {
2195  static const double tk[1];
2196 
2197  Poly_1D::Basis &obasis1d;
2198  Array<int> dof2tk;
2199 
2200 public:
2201  ND_SegmentElement(const int p,
2202  const int op_type = Quadrature1D::GaussLegendre );
2203  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
2204  { obasis1d.Eval(ip.x, shape); }
2205  virtual void CalcVShape(const IntegrationPoint &ip,
2206  DenseMatrix &shape) const;
2207  virtual void CalcVShape(ElementTransformation &Trans,
2208  DenseMatrix &shape) const
2209  { CalcVShape_ND(Trans, shape); }
2210  // virtual void CalcCurlShape(const IntegrationPoint &ip,
2211  // DenseMatrix &curl_shape) const;
2212  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2213  DenseMatrix &I) const
2214  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2215  using FiniteElement::Project;
2216  virtual void Project(VectorCoefficient &vc,
2217  ElementTransformation &Trans, Vector &dofs) const
2218  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2219  virtual void Project(const FiniteElement &fe,
2220  ElementTransformation &Trans,
2221  DenseMatrix &I) const
2222  { Project_ND(tk, dof2tk, fe, Trans, I); }
2223  virtual void ProjectGrad(const FiniteElement &fe,
2224  ElementTransformation &Trans,
2225  DenseMatrix &grad) const
2226  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2227 };
2228 
2229 
2230 class NURBSFiniteElement : public ScalarFiniteElement
2231 {
2232 protected:
2233  mutable Array <KnotVector*> kv;
2234  mutable int *ijk, patch, elem;
2235  mutable Vector weights;
2236 
2237 public:
2238  NURBSFiniteElement(int D, int G, int Do, int O, int F)
2239  : ScalarFiniteElement(D, G, Do, O, F)
2240  {
2241  ijk = NULL;
2242  patch = elem = -1;
2243  kv.SetSize(Dim);
2244  weights.SetSize(Dof);
2245  weights = 1.0;
2246  }
2247 
2248  void Reset () const { patch = elem = -1; }
2249  void SetIJK (int *IJK) const { ijk = IJK; }
2250  int GetPatch () const { return patch; }
2251  void SetPatch (int p) const { patch = p; }
2252  int GetElement () const { return elem; }
2253  void SetElement (int e) const { elem = e; }
2254  Array <KnotVector*> &KnotVectors() const { return kv; }
2255  Vector &Weights () const { return weights; }
2256 };
2257 
2258 class NURBS1DFiniteElement : public NURBSFiniteElement
2259 {
2260 protected:
2261  mutable Vector shape_x;
2262 
2263 public:
2264  NURBS1DFiniteElement(int p)
2265  : NURBSFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
2266  shape_x(p + 1) { }
2267 
2268  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2269  virtual void CalcDShape(const IntegrationPoint &ip,
2270  DenseMatrix &dshape) const;
2271 };
2272 
2273 class NURBS2DFiniteElement : public NURBSFiniteElement
2274 {
2275 protected:
2276  mutable Vector u, shape_x, shape_y, dshape_x, dshape_y;
2277 
2278 public:
2279  NURBS2DFiniteElement(int p)
2280  : NURBSFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
2281  FunctionSpace::Qk), u(Dof),
2282  shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1), dshape_y(p + 1) { }
2283 
2284  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2285  virtual void CalcDShape(const IntegrationPoint &ip,
2286  DenseMatrix &dshape) const;
2287 };
2288 
2289 class NURBS3DFiniteElement : public NURBSFiniteElement
2290 {
2291 protected:
2292  mutable Vector u, shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
2293 
2294 public:
2295  NURBS3DFiniteElement(int p)
2296  : NURBSFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
2297  FunctionSpace::Qk), u(Dof),
2298  shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
2299  dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1) { }
2300 
2301  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2302  virtual void CalcDShape(const IntegrationPoint &ip,
2303  DenseMatrix &dshape) const;
2304 };
2305 
2306 } // namespace mfem
2307 
2308 #endif
mfem::FiniteElement
Abstract class for Finite Elements.
Definition: fe.hpp:46
mfem::RefinedLinear3DFiniteElement::RefinedLinear3DFiniteElement
RefinedLinear3DFiniteElement()
Construct a quadratic FE on tetrahedron.
Definition: fe.cpp:4186
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:1315
mfem::BiQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1303
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:8201
mfem::ND_SegmentElement
Definition: fe.hpp:2193
mfem::VectorFiniteElement::curlshape_J
DenseMatrix curlshape_J
Definition: fe.hpp:401
mfem::H1Pos_SegmentElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1534
mfem::RT0TetFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5985
mfem::RT_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1920
mfem::FiniteElement::GetDim
int GetDim() const
Returns the reference space dimension for the finite element.
Definition: fe.hpp:115
mfem::H1Pos_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7101
mfem::RT1TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2827
mfem::L2_SegmentElement::L2_SegmentElement
L2_SegmentElement(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8075
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:1287
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:3764
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:1051
mfem::Poly_1D::CalcBernstein
static void CalcBernstein(const int p, const double x, double *u, double *d)
Definition: fe.hpp:1446
mfem::RT_QuadrilateralElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1886
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:1025
mfem::P2SegmentFiniteElement
Quadratic 1D element with nodes the Gaussian points in [0,1] (trace of RT2)
Definition: fe.hpp:1035
mfem::L2Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8596
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:10914
mfem::Linear3DFiniteElement::Linear3DFiniteElement
Linear3DFiniteElement()
Construct a linear FE on tetrahedron.
Definition: fe.cpp:2226
mfem::Poly_1D::CalcDelta
static double CalcDelta(const int p, const double x)
Definition: fe.hpp:1428
mfem::RT1QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:3009
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:1950
mfem::RT_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2000
mfem::L2Pos_TriangleElement
Definition: fe.hpp:1795
mfem::L2Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8353
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:9770
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:4418
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:1621
mfem::L2Pos_TriangleElement::L2Pos_TriangleElement
L2Pos_TriangleElement(const int p)
Definition: fe.cpp:8740
mfem::ND_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2103
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:880
mfem::H1Pos_SegmentElement::H1Pos_SegmentElement
H1Pos_SegmentElement(const int p)
Definition: fe.cpp:7039
mfem::NURBSFiniteElement::GetPatch
int GetPatch() const
Definition: fe.hpp:2250
mfem::RT_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2010
mfem::FiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:156
mfem::L2_TriangleElement
Definition: fe.hpp:1772
mfem::P0QuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:772
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:5030
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:683
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:2464
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:2243
mfem::Poly_1D::OpenPoints
const double * OpenPoints(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.hpp:1389
mfem::Poly_1D::Poly_1D
Poly_1D()
Definition: fe.hpp:1377
mfem::L2Pos_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8779
mfem::ND_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2147
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:2781
mfem::RT1QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:3061
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:1417
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:7081
mfem::L2_HexahedronElement
Definition: fe.hpp:1737
mfem::VectorFiniteElement::FiniteElement
FiniteElement(D, G, Do, O, F)
mfem::FiniteElement::GetDerivMapType
int GetDerivMapType() const
Definition: fe.hpp:137
mfem::L2Pos_TetrahedronElement::L2Pos_TetrahedronElement
L2Pos_TetrahedronElement(const int p)
Definition: fe.cpp:8934
mfem::NURBSFiniteElement::kv
Array< KnotVector * > kv
Definition: fe.hpp:2233
mfem::VectorFiniteElement::CalcVShape_RT
void CalcVShape_RT(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:508
mfem::L2_TriangleElement::L2_TriangleElement
L2_TriangleElement(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8615
mfem::Vector::SetSize
void SetSize(int s)
Resize the vector to size s.
Definition: vector.hpp:310
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:9152
mfem::Nedelec1HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5092
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:3551
mfem::GaussLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:972
mfem::NodalFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:237
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:1441
mfem::VectorFiniteElement::LocalInterpolation_ND
void LocalInterpolation_ND(const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:801
mfem::BiCubic2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1799
mfem::RT_TriangleElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1971
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:1710
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:2546
mfem::P0TriangleFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
evaluate derivatives of shape function - constant 0
Definition: fe.cpp:2197
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:1235
mfem::L2Pos_SegmentElement
Definition: fe.hpp:1682
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:2036
mfem::Linear1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:861
mfem::H1_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6601
mfem::H1Pos_TetrahedronElement::H1Pos_TetrahedronElement
H1Pos_TetrahedronElement(const int p)
Definition: fe.cpp:7823
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:10862
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:8220
mfem::RT_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1870
mfem::LagrangeHexFiniteElement::LagrangeHexFiniteElement
LagrangeHexFiniteElement(int degree)
Definition: fe.cpp:3816
mfem::FiniteElement::GetOrder
int GetOrder() const
Returns the order of the finite element.
Definition: fe.hpp:124
mfem::H1_QuadrilateralElement
Definition: fe.hpp:1475
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:2559
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:3672
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:3978
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:2087
mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition: densemat.hpp:22
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:3626
mfem::NodalFiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:319
mfem::NURBSFiniteElement::Reset
void Reset() const
Definition: fe.hpp:2248
mfem::RT_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1959
mfem::FunctionSpace::Pk
Polynomials of order k.
Definition: fe.hpp:34
mfem::Quad2DFiniteElement
Class for quadratic FE on triangle.
Definition: fe.hpp:609
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:10876
mfem::PositiveFiniteElement::PositiveFiniteElement
PositiveFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:366
mfem::Quad1DFiniteElement
Class for quadratic FE on interval.
Definition: fe.hpp:580
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:1865
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:9626
mfem::ND_TetrahedronElement
Definition: fe.hpp:2110
mfem::Nedelec1TetFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5258
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:625
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:2212
mfem::FiniteElement::Space
int Space() const
Returns the type of space on each element.
Definition: fe.hpp:127
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:1870
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:1923
mfem::RefinedTriLinear3DFiniteElement::RefinedTriLinear3DFiniteElement
RefinedTriLinear3DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:4565
mfem::FiniteElement::vshape
DenseMatrix vshape
Definition: fe.hpp:57
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:3803
mfem::Quadratic3DFiniteElement::Quadratic3DFiniteElement
Quadratic3DFiniteElement()
Construct a quadratic FE on tetrahedron.
Definition: fe.cpp:2282
mfem::FiniteElement::GetMapType
int GetMapType() const
Definition: fe.hpp:133
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:8093
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:5608
mfem::RT1HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5795
mfem::L2Pos_TetrahedronElement
Definition: fe.hpp:1831
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:2658
mfem::H1_HexahedronElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1512
mfem::L2_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8899
mfem::ND_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:2063
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:1922
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:8964
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:2489
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:2481
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:8155
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:6689
mfem::P0HexFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:1085
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:663
mfem::H1Pos_HexahedronElement::H1Pos_HexahedronElement
H1Pos_HexahedronElement(const int p)
Definition: fe.cpp:7211
mfem::FiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:140
mfem::H1Pos_TetrahedronElement::CalcShape
static void CalcShape(const int p, const double x, const double y, const double z, double *shape)
Definition: fe.cpp:7925
mfem::H1Pos_TetrahedronElement::m_dshape
DenseMatrix m_dshape
Definition: fe.hpp:1643
mfem::ND_TriangleElement
Definition: fe.hpp:2153
mfem::H1_SegmentElement::H1_SegmentElement
H1_SegmentElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:6539
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:8841
mfem::BiLinear2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:933
mfem::H1_TetrahedronElement::H1_TetrahedronElement
H1_TetrahedronElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:7508
mfem::NURBSFiniteElement::GetElement
int GetElement() const
Definition: fe.hpp:2252
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:7183
mfem::Linear2DFiniteElement::Linear2DFiniteElement
Linear2DFiniteElement()
Construct a linear FE on triangle.
Definition: fe.cpp:875
mfem::RT_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1874
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:2339
mfem::RefinedBiLinear2DFiniteElement
Class for refined bi-linear FE on quadrilateral.
Definition: fe.hpp:1164
mfem::RT0TetFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5930
mfem::RefinedTriLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4754
mfem::L2_QuadrilateralElement::L2_QuadrilateralElement
L2_QuadrilateralElement(const int p, const int _type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8179
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:10758
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:842
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:1942
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:8523
mfem::ND_TriangleElement::ND_TriangleElement
ND_TriangleElement(const int p)
Definition: fe.cpp:10677
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:8991
mfem::L2_TriangleElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1788
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:6468
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:9806
mfem::FiniteElement::DIV
Implements CalcDivShape methods.
Definition: fe.hpp:101
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:7958
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u)
Definition: fe.hpp:1412
mfem::H1_HexahedronElement::H1_HexahedronElement
H1_HexahedronElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:6779
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:907
mfem::P0TriangleFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
evaluate shape function - constant 1
Definition: fe.cpp:2191
mfem::Cubic2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1970
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:6303
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:7678
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:3263
mfem::ScalarFiniteElement::SetMapType
void SetMapType(int M)
Definition: fe.hpp:303
mfem::FiniteElement::VerifyOpen
static int VerifyOpen(int pt_type)
Definition: fe.hpp:287
mfem::Cubic3DFiniteElement::Cubic3DFiniteElement
Cubic3DFiniteElement()
Construct a cubic FE on tetrahedron.
Definition: fe.cpp:2017
mfem::Linear1DFiniteElement::Linear1DFiniteElement
Linear1DFiniteElement()
Construct a linear FE on interval.
Definition: fe.cpp:854
mfem::RefinedLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4127
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:5918
mfem::BiQuadPos2DFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:1490
mfem::FiniteElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:148
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:1108
mfem::RT_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1916
mfem::H1Pos_TriangleElement::CalcShape
static void CalcShape(const int p, const double x, const double y, double *shape)
Definition: fe.cpp:7733
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:2512
mfem::H1Pos_TriangleElement::dshape_1d
Vector dshape_1d
Definition: fe.hpp:1616
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:2110
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:3569
mfem::P1OnQuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:575
mfem::L2Pos_QuadrilateralElement
Definition: fe.hpp:1721
mfem::FiniteElement::Dof
int Dof
Number of degrees of freedom.
Definition: fe.hpp:49
mfem::GaussBiLinear2DFiniteElement
Class for bilinear FE on quad with nodes at the 4 Gaussian points.
Definition: fe.hpp:555
mfem::RefinedLinear1DFiniteElement
Class for refined linear FE on interval.
Definition: fe.hpp:1111
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:8099
mfem::RefinedLinear2DFiniteElement
Class for refined linear FE on triangle.
Definition: fe.hpp:1131
mfem::RefinedLinear3DFiniteElement
Class for refined linear FE on tetrahedron.
Definition: fe.hpp:1151
mfem::L2_SegmentElement
Definition: fe.hpp:1664
mfem::NURBSFiniteElement::SetPatch
void SetPatch(int p) const
Definition: fe.hpp:2251
mfem::Quad1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1068
mfem::Quad1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1079
mfem::BiQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1327
mfem::P0TriangleFiniteElement
Class for constant FE on triangle.
Definition: fe.hpp:748
mfem::ND_SegmentElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2223
mfem::RefinedLinear1DFiniteElement::RefinedLinear1DFiniteElement
RefinedLinear1DFiniteElement()
Construct a quadratic FE on interval.
Definition: fe.cpp:4016
mfem::H1_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6954
mfem::H1Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7204
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:1594
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:8682
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:7456
mfem::RT_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1926
mfem::RefinedLinear1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4043
mfem::VectorFiniteElement::VectorFiniteElement
VectorFiniteElement(int D, int G, int Do, int O, int M, int F=FunctionSpace::Pk)
Definition: fe.hpp:455
mfem::VectorFiniteElement::LocalInterpolation_RT
void LocalInterpolation_RT(const double *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:767
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:3202
mfem::Poly_1D::ChebyshevPoints
static void ChebyshevPoints(const int p, double *x)
Definition: fe.cpp:6271
mfem::NURBSFiniteElement::NURBSFiniteElement
NURBSFiniteElement(int D, int G, int Do, int O, int F)
Definition: fe.hpp:2238
mfem::FiniteElement::GRAD
Implements CalcDShape methods.
Definition: fe.hpp:100
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:6055
mfem::H1_QuadrilateralElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1492
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:3788
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:5896
mfem::RefinedTriLinear3DFiniteElement
Class for refined trilinear FE on a hexahedron.
Definition: fe.hpp:1184
mfem::ND_TetrahedronElement::ND_TetrahedronElement
ND_TetrahedronElement(const int p)
Definition: fe.cpp:10415
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:8768
mfem::Poly_1D
Definition: fe.hpp:1342
mfem::FiniteElement::DerivMapType
int DerivMapType
Definition: fe.hpp:49
mfem::Quadratic3DFiniteElement
Class for quadratic FE on tetrahedron.
Definition: fe.hpp:803
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:2126
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:848
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:1995
mfem::FiniteElement::VALUE
For scalar fields; preserves point values.
Definition: fe.hpp:84
mfem::FiniteElement::GeomType
int GeomType
Geometry::Type of the reference element.
Definition: fe.hpp:49
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:1885
mfem::ND_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2131
mfem::FiniteElement::GetNodes
const IntegrationRule & GetNodes() const
Definition: fe.hpp:166
mfem::FiniteElement::INTEGRAL
For scalar fields; preserves volume integrals.
Definition: fe.hpp:85
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:5145
mfem::Quad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1149
mfem::L2_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8438
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:2317
mfem::RT_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1881
mfem::L2Pos_QuadrilateralElement::L2Pos_QuadrilateralElement
L2Pos_QuadrilateralElement(const int p)
Definition: fe.cpp:8289
mfem::P0SegmentFiniteElement::P0SegmentFiniteElement
P0SegmentFiniteElement(int Ord=0)
Definition: fe.cpp:2452
mfem::H1_TetrahedronElement
Definition: fe.hpp:1593
mfem::H1Pos_TriangleElement::CalcDShape
static void CalcDShape(const int p, const double x, const double y, double *dshape_1d, double *dshape)
Definition: fe.cpp:7759
mfem::FiniteElement::GetDerivRangeType
int GetDerivRangeType() const
Definition: fe.hpp:131
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:2804
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:10949
mfem::FiniteElement::CURL
Implements CalcCurlShape methods.
Definition: fe.hpp:102
mfem::VectorFiniteElement::curlshape
DenseMatrix curlshape
Definition: fe.hpp:401
mfem::ND_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2135
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:987
mfem::Linear3DFiniteElement
Class for linear FE on tetrahedron.
Definition: fe.hpp:778
mfem::Linear1DFiniteElement
Class for linear FE on interval.
Definition: fe.hpp:478
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:9366
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:5196
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:174
mfem::CrouzeixRaviartQuadFiniteElement
Crouzeix-Raviart finite element on quadrilateral.
Definition: fe.hpp:851
mfem::Linear2DFiniteElement
Class for linear FE on triangle.
Definition: fe.hpp:498
mfem::GaussQuad2DFiniteElement
Class for quadratic FE on triangle with nodes at the &quot;Gaussian&quot; points.
Definition: fe.hpp:633
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:8660
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:9105
mfem::ND_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2175
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:1749
mfem::RT2QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:3461
mfem::ND_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2092
mfem::BiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:924
mfem::Linear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2252
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:9440
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:7619
mfem::Quad2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1173
mfem::NURBSFiniteElement::SetElement
void SetElement(int e) const
Definition: fe.hpp:2253
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:1251
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:746
mfem::ScalarFiniteElement::ScalarFiniteElement
ScalarFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:299
mfem::FiniteElement::CalcPhysVShape
void CalcPhysVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Equivalent to the CalcVShape() method with the same arguments.
Definition: fe.hpp:188
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:8762
mfem::RT_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2007
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:934
mfem::L2_QuadrilateralElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1714
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:10973
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:1265
mfem::FiniteElement::GetGeomType
int GetGeomType() const
Returns the Geometry::Type of the reference element.
Definition: fe.hpp:118
mfem::H1Pos_TriangleElement::m_dshape
DenseMatrix m_dshape
Definition: fe.hpp:1617
mfem::FiniteElement::Dim
int Dim
Dimension of reference space.
Definition: fe.hpp:49
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:10361
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:8314
mfem::FiniteElement::Nodes
IntegrationRule Nodes
Definition: fe.hpp:55
mfem::H1Pos_HexahedronElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1572
mfem::ND_SegmentElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2219
mfem::L2_TetrahedronElement
Definition: fe.hpp:1811
mfem::Quad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1135
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:8551
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:7061
mfem::H1Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7382
mfem::RT2QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:3513
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:10792
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:2673
mfem::RefinedBiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4441
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:1978
mfem::FiniteElement::~FiniteElement
virtual ~FiniteElement()
Definition: fe.hpp:278
mfem::RT0TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2570
mfem::H1Pos_QuadrilateralElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1553
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:2203
mfem::VectorFiniteElement::CalcVShape_ND
void CalcVShape_ND(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:520
mfem::VectorFiniteElement::Jinv
DenseMatrix Jinv
Definition: fe.hpp:400
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:1259
mfem::FiniteElement::NONE
No derivatives implemented.
Definition: fe.hpp:99
mfem::ND_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2216
mfem::L2_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8110
mfem::FiniteElement::GetDof
int GetDof() const
Returns the number of degrees of freedom in the finite element.
Definition: fe.hpp:121
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:7644
mfem::BiQuad2DFiniteElement
Class for bi-quadratic FE on quadrilateral.
Definition: fe.hpp:649
mfem::H1Pos_HexahedronElement
Definition: fe.hpp:1557
mfem::TriLinear3DFiniteElement
Class for tri-linear FE on cube.
Definition: fe.hpp:816
mfem::Coefficient
Base class Coefficient that may optionally depend on time.
Definition: coefficient.hpp:31
mfem::H1Pos_TetrahedronElement::m_shape
Vector m_shape
Definition: fe.hpp:1642
mfem::GaussBiLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1019
mfem::P0TetFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:1074
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:5226
mfem::H1Pos_TetrahedronElement::dof_map
Array< int > dof_map
Definition: fe.hpp:1645
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:8957
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:164
mfem::Poly_1D::OpenBasis
Basis & OpenBasis(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.hpp:1403
mfem::CrouzeixRaviartFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:846
mfem::Linear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:886
mfem::RefinedTriLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4611
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:4308
mfem::P0TriangleFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:760
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:6254
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:3363
mfem::H1_HexahedronElement
Definition: fe.hpp:1496
mfem::H1Pos_TetrahedronElement
Definition: fe.hpp:1638
mfem::H1Pos_TetrahedronElement::dshape_1d
Vector dshape_1d
Definition: fe.hpp:1642
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:954
mfem::RT_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1877
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:1213
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:8866
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:10070
mfem::RT_TriangleElement
Definition: fe.hpp:1933
mfem::RT0QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2737
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:1376
mfem::TriLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2397
mfem::BiLinear2DFiniteElement
Class for bilinear FE on quadrilateral.
Definition: fe.hpp:520
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:371
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:9852
mfem::Quad1DFiniteElement::Quad1DFiniteElement
Quad1DFiniteElement()
Construct a quadratic FE on interval.
Definition: fe.cpp:1060
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:9202
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:2207
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:7337
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:544
mfem::H1Pos_TriangleElement::m_shape
Vector m_shape
Definition: fe.hpp:1616
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:1008
mfem::ND_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2043
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:1008
mfem::BiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:915
mfem::Poly_1D::ClosedBasis
Basis & ClosedBasis(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.hpp:1406
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:7108
mfem::ND_QuadrilateralElement
Definition: fe.hpp:2070
mfem::ND_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2179
mfem::NURBSFiniteElement::KnotVectors
Array< KnotVector * > & KnotVectors() const
Definition: fe.hpp:2254
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:868
mfem::L2_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8711
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:6489
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:7358
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:8161
mfem::NodalFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:335
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:2218
mfem::RT_QuadrilateralElement
Definition: fe.hpp:1847
mfem::GaussBiQuad2DFiniteElement
Bi-quadratic element on quad with nodes at the 9 Gaussian points.
Definition: fe.hpp:688
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:961
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:8572
mfem::VectorFiniteElement::Project_RT
void Project_RT(const double *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:531
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:6909
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:1043
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:3177
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:10563
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:2937
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:10312
mfem::Linear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:515
mfem::ND_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2186
mfem::NodalFiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:348
mfem::FiniteElement::VerifyClosed
static int VerifyClosed(int pt_type)
Definition: fe.hpp:280
mfem::FiniteElement::DerivRangeType
int DerivRangeType
Definition: fe.hpp:49
mfem::H1_TriangleElement
Definition: fe.hpp:1576
mfem::RT0QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2685
mfem::L2Pos_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8172
mfem::RefinedLinear2DFiniteElement::RefinedLinear2DFiniteElement
RefinedLinear2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:4062
mfem::L2_QuadrilateralElement
Definition: fe.hpp:1698
mfem::NodalFiniteElement::NodalLocalInterpolation
void NodalLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I, const NodalFiniteElement &fine_fe) const
Definition: fe.cpp:185
mfem::H1_SegmentElement
Definition: fe.hpp:1455
mfem::RT1HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5850
mfem::NodalFiniteElement::ProjectCurl_2D
void ProjectCurl_2D(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:218
mfem::NURBSFiniteElement::SetIJK
void SetIJK(int *IJK) const
Definition: fe.hpp:2249
mfem::ND_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2096
mfem::ND_HexahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2058
mfem::RefinedLinear1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4024
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:3752
mfem::H1Pos_TriangleElement::dof_map
Array< int > dof_map
Definition: fe.hpp:1619
mfem::RT_TetrahedronElement::RT_TetrahedronElement
RT_TetrahedronElement(const int p)
Definition: fe.cpp:9668
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:10223
mfem::Poly_1D::Basis
Definition: fe.hpp:1345
mfem::RT0HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5406
mfem::L2_TetrahedronElement::L2_TetrahedronElement
L2_TetrahedronElement(const int p, const int type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8791
mfem::H1Pos_SegmentElement
Definition: fe.hpp:1515
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:3957
mfem::NURBSFiniteElement::Weights
Vector & Weights() const
Definition: fe.hpp:2255
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:6582
mfem::BiQuad2DFiniteElement::BiQuad2DFiniteElement
BiQuad2DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:1280
mfem::Linear3DFiniteElement::GetFaceDofs
virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const
Definition: fe.cpp:2272
mfem::LagrangeHexFiniteElement
Tensor products of 1D FEs (only degree 2 is functional)
Definition: fe.hpp:1090
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:2974
mfem::P0TriangleFiniteElement::P0TriangleFiniteElement
P0TriangleFiniteElement()
Construct P0 triangle finite element.
Definition: fe.cpp:2184
mfem::ND_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2182
mfem::Poly_1D::ClosedPoints
const double * ClosedPoints(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.hpp:1392
mfem::ND_HexahedronElement
Definition: fe.hpp:2017
mfem::H1Pos_QuadrilateralElement
Definition: fe.hpp:1538
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:2458
mfem::L2Pos_HexahedronElement
Definition: fe.hpp:1756
mfem::RT_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1962
mfem::RT_TriangleElement::RT_TriangleElement
RT_TriangleElement(const int p)
Definition: fe.cpp:9515
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:6563
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:10853
mfem::ND_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2049
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:10144
mfem::Poly_1D::Basis::Eval
void Eval(const double x, Vector &u) const
Definition: fe.cpp:6140
mfem::L2Pos_SegmentElement::L2Pos_SegmentElement
L2Pos_SegmentElement(const int p)
Definition: fe.cpp:8134
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:4221
mfem::RT0HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5461
mfem::Cubic3DFiniteElement
Class for cubic FE on tetrahedron.
Definition: fe.hpp:735
mfem::Vector
Vector data type.
Definition: vector.hpp:36
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:5392
mfem::Poly_1D::CalcBernstein
static void CalcBernstein(const int p, const double x, double *u)
Definition: fe.hpp:1444
mfem::ND_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2053
mfem::FiniteElement::GetDerivType
int GetDerivType() const
Definition: fe.hpp:135
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:7163
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:8414
mfem::Quad2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1201
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:9593
mfem::Quad2DFiniteElement::Quad2DFiniteElement
Quad2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:1118
mfem::ND_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2099
mfem::RT_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2004
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:6629
mfem::TriLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2413
mfem::ND_SegmentElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2212
mfem::Nedelec1TetFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5311
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:8333
mfem::PositiveFiniteElement::PositiveLocalInterpolation
void PositiveLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I, const PositiveFiniteElement &fine_fe) const
Definition: fe.cpp:379
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:10605
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:3809
mfem::BiQuadPos2DFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:1519
mfem::Linear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:894
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:2082
mfem::NodalFiniteElement::NodalFiniteElement
NodalFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:328
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:2523
mfem::H1_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6730
mfem::TriLinear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:834
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:5362
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:3581
mfem::BiLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:539
mfem::RefinedBiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4492
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:1893
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:10895
mfem::RT_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1955
mfem::ND_TetrahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2142
mfem::VectorFiniteElement::Project_ND
void Project_ND(const double *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:682
mfem::FiniteElement::GetRangeType
int GetRangeType() const
Definition: fe.hpp:129
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:997
mfem::FiniteElement::Order
int Order
Order/degree of the shape functions.
Definition: fe.hpp:49
mfem::RT1TriangleFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2879
mfem::H1_TriangleElement::H1_TriangleElement
H1_TriangleElement(const int p, const int type=Quadrature1D::GaussLobatto)
Definition: fe.cpp:7389
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u, double *d)
Definition: fe.hpp:1421
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:2138
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:3782
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:6930
mfem::RT_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1966
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:6708
mfem::Poly_1D::Basis::Basis
Basis(const int p, const double *nodes, const int _mode=1)
Definition: fe.cpp:6090
mfem::Poly_1D::CalcDBinomTerms
static void CalcDBinomTerms(const int p, const double x, const double y, double *d)
Definition: fe.cpp:6367
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:4975
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:2361
mfem::ND_SegmentElement::ND_SegmentElement
ND_SegmentElement(const int p, const int op_type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:10837
mfem::FiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:127
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:1098
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:8393
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:1911
mfem::RefinedLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4079
mfem::H1Pos_TriangleElement
Definition: fe.hpp:1612
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:3542
mfem::BiLinear2DFiniteElement::BiLinear2DFiniteElement
BiLinear2DFiniteElement()
Construct a bilinear FE on quadrilateral.
Definition: fe.cpp:902
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:2170
mfem::L2_HexahedronElement::L2_HexahedronElement
L2_HexahedronElement(const int p, const int _type=Quadrature1D::GaussLegendre)
Definition: fe.cpp:8368
mfem::poly1d
Poly_1D poly1d
Definition: fe.cpp:6535
mfem::CrouzeixRaviartFiniteElement
Crouzeix-Raviart finite element on triangle.
Definition: fe.hpp:839
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:6038
mfem::Lagrange1DFiniteElement::Lagrange1DFiniteElement
Lagrange1DFiniteElement(int degree)
Definition: fe.cpp:3594
mfem::Poly_1D::~Poly_1D
~Poly_1D()
Definition: fe.cpp:6510
mfem::RT0TriangleFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2622
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:5731
mfem::H1_SegmentElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1471
mfem::L2Pos_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8975
mfem::L2_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8240
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:964
mfem::Linear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:796
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:7478
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:598
mfem::PositiveFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:419
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