MFEM  v3.4
Finite element discretization library
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bilininteg.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_BILININTEG
13 #define MFEM_BILININTEG
14 
15 #include "../config/config.hpp"
16 #include "nonlininteg.hpp"
17 
18 namespace mfem
19 {
20 
21 /// Abstract base class BilinearFormIntegrator
22 class BilinearFormIntegrator : public NonlinearFormIntegrator
23 {
24 protected:
25  BilinearFormIntegrator(const IntegrationRule *ir = NULL) :
26  NonlinearFormIntegrator(ir) { }
27 
28 public:
29  /// Given a particular Finite Element computes the element matrix elmat.
30  virtual void AssembleElementMatrix(const FiniteElement &el,
31  ElementTransformation &Trans,
32  DenseMatrix &elmat);
33 
34  /** Compute the local matrix representation of a bilinear form
35  a(u,v) defined on different trial (given by u) and test
36  (given by v) spaces. The rows in the local matrix correspond
37  to the test dofs and the columns -- to the trial dofs. */
38  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
39  const FiniteElement &test_fe,
40  ElementTransformation &Trans,
41  DenseMatrix &elmat);
42 
43  virtual void AssembleFaceMatrix(const FiniteElement &el1,
44  const FiniteElement &el2,
45  FaceElementTransformations &Trans,
46  DenseMatrix &elmat);
47 
48  /** Abstract method used for assembling TraceFaceIntegrators in a
49  MixedBilinearForm. */
50  virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe,
51  const FiniteElement &test_fe1,
52  const FiniteElement &test_fe2,
53  FaceElementTransformations &Trans,
54  DenseMatrix &elmat);
55 
56  /// Perform the local action of the BilinearFormIntegrator
57  virtual void AssembleElementVector(const FiniteElement &el,
58  ElementTransformation &Tr,
59  const Vector &elfun, Vector &elvect);
60 
61  virtual void AssembleElementGrad(const FiniteElement &el,
62  ElementTransformation &Tr,
63  const Vector &elfun, DenseMatrix &elmat)
64  { AssembleElementMatrix(el, Tr, elmat); }
65 
66  virtual void AssembleFaceGrad(const FiniteElement &el1,
67  const FiniteElement &el2,
68  FaceElementTransformations &Tr,
69  const Vector &elfun, DenseMatrix &elmat)
70  { AssembleFaceMatrix(el1, el2, Tr, elmat); }
71 
72  virtual void ComputeElementFlux(const FiniteElement &el,
73  ElementTransformation &Trans,
74  Vector &u,
75  const FiniteElement &fluxelem,
76  Vector &flux, int with_coef = 1) { }
77 
78  virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
79  ElementTransformation &Trans,
80  Vector &flux, Vector *d_energy = NULL)
81  { return 0.0; }
82 
83  virtual ~BilinearFormIntegrator() { }
84 };
85 
86 class TransposeIntegrator : public BilinearFormIntegrator
87 {
88 private:
89  int own_bfi;
90  BilinearFormIntegrator *bfi;
91 
92  DenseMatrix bfi_elmat;
93 
94 public:
95  TransposeIntegrator (BilinearFormIntegrator *_bfi, int _own_bfi = 1)
96  { bfi = _bfi; own_bfi = _own_bfi; }
97 
98  virtual void AssembleElementMatrix(const FiniteElement &el,
99  ElementTransformation &Trans,
100  DenseMatrix &elmat);
101 
102  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
103  const FiniteElement &test_fe,
104  ElementTransformation &Trans,
105  DenseMatrix &elmat);
106 
107  using BilinearFormIntegrator::AssembleFaceMatrix;
108  virtual void AssembleFaceMatrix(const FiniteElement &el1,
109  const FiniteElement &el2,
110  FaceElementTransformations &Trans,
111  DenseMatrix &elmat);
112 
113  virtual ~TransposeIntegrator() { if (own_bfi) { delete bfi; } }
114 };
115 
116 class LumpedIntegrator : public BilinearFormIntegrator
117 {
118 private:
119  int own_bfi;
120  BilinearFormIntegrator *bfi;
121 
122 public:
123  LumpedIntegrator (BilinearFormIntegrator *_bfi, int _own_bfi = 1)
124  { bfi = _bfi; own_bfi = _own_bfi; }
125 
126  virtual void AssembleElementMatrix(const FiniteElement &el,
127  ElementTransformation &Trans,
128  DenseMatrix &elmat);
129 
130  virtual ~LumpedIntegrator() { if (own_bfi) { delete bfi; } }
131 };
132 
133 /// Integrator that inverts the matrix assembled by another integrator.
134 class InverseIntegrator : public BilinearFormIntegrator
135 {
136 private:
137  int own_integrator;
138  BilinearFormIntegrator *integrator;
139 
140 public:
141  InverseIntegrator(BilinearFormIntegrator *integ, int own_integ = 1)
142  { integrator = integ; own_integrator = own_integ; }
143 
144  virtual void AssembleElementMatrix(const FiniteElement &el,
145  ElementTransformation &Trans,
146  DenseMatrix &elmat);
147 
148  virtual ~InverseIntegrator() { if (own_integrator) { delete integrator; } }
149 };
150 
151 /// Integrator defining a sum of multiple Integrators.
152 class SumIntegrator : public BilinearFormIntegrator
153 {
154 private:
155  int own_integrators;
156  DenseMatrix elem_mat;
157  Array<BilinearFormIntegrator*> integrators;
158 
159 public:
160  SumIntegrator(int own_integs = 1) { own_integrators = own_integs; }
161 
162  void AddIntegrator(BilinearFormIntegrator *integ)
163  { integrators.Append(integ); }
164 
165  virtual void AssembleElementMatrix(const FiniteElement &el,
166  ElementTransformation &Trans,
167  DenseMatrix &elmat);
168 
169  virtual ~SumIntegrator();
170 };
171 
172 /** An abstract class for integrating the product of two scalar basis functions
173  with an optional scalar coefficient. */
174 class MixedScalarIntegrator: public BilinearFormIntegrator
175 {
176 public:
177 
178  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
179  const FiniteElement &test_fe,
180  ElementTransformation &Trans,
181  DenseMatrix &elmat);
182 
183  /// Support for use in BilinearForm. Can be used only when appropriate.
184  virtual void AssembleElementMatrix(const FiniteElement &fe,
185  ElementTransformation &Trans,
186  DenseMatrix &elmat)
187  { AssembleElementMatrix2(fe, fe, Trans, elmat); }
188 
189 protected:
190  /// This parameter can be set by derived methods to enable single shape
191  /// evaluation in case CalcTestShape() and CalcTrialShape() return the same
192  /// result if given the same FiniteElement. The default is false.
193  bool same_calc_shape;
194 
195  MixedScalarIntegrator() : same_calc_shape(false), Q(NULL) {}
196  MixedScalarIntegrator(Coefficient &q) : same_calc_shape(false), Q(&q) {}
197 
198  inline virtual bool VerifyFiniteElementTypes(
199  const FiniteElement & trial_fe,
200  const FiniteElement & test_fe) const
201  {
202  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
203  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
204  }
205 
206  inline virtual const char * FiniteElementTypeFailureMessage() const
207  {
208  return "MixedScalarIntegrator: "
209  "Trial and test spaces must both be scalar fields.";
210  }
211 
212  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
213  const FiniteElement & test_fe,
214  ElementTransformation &Trans)
215  { return trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW(); }
216 
217 
218  inline virtual void CalcTestShape(const FiniteElement & test_fe,
219  ElementTransformation &Trans,
220  Vector & shape)
221  { test_fe.CalcPhysShape(Trans, shape); }
222 
223  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
224  ElementTransformation &Trans,
225  Vector & shape)
226  { trial_fe.CalcPhysShape(Trans, shape); }
227 
228 private:
229 
230  Coefficient *Q;
231 
232 #ifndef MFEM_THREAD_SAFE
233  Vector test_shape;
234  Vector trial_shape;
235 #endif
236 
237 };
238 
239 /** An abstract class for integrating the inner product of two vector basis
240  functions with an optional scalar, vector, or matrix coefficient. */
241 class MixedVectorIntegrator: public BilinearFormIntegrator
242 {
243 public:
244 
245  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
246  const FiniteElement &test_fe,
247  ElementTransformation &Trans,
248  DenseMatrix &elmat);
249 
250  /// Support for use in BilinearForm. Can be used only when appropriate.
251  virtual void AssembleElementMatrix(const FiniteElement &fe,
252  ElementTransformation &Trans,
253  DenseMatrix &elmat)
254  { AssembleElementMatrix2(fe, fe, Trans, elmat); }
255 
256 protected:
257  /// This parameter can be set by derived methods to enable single shape
258  /// evaluation in case CalcTestShape() and CalcTrialShape() return the same
259  /// result if given the same FiniteElement. The default is false.
260  bool same_calc_shape;
261 
262  MixedVectorIntegrator()
263  : same_calc_shape(false), Q(NULL), VQ(NULL), DQ(NULL), MQ(NULL) {}
264  MixedVectorIntegrator(Coefficient &q)
265  : same_calc_shape(false), Q(&q), VQ(NULL), DQ(NULL), MQ(NULL) {}
266  MixedVectorIntegrator(VectorCoefficient &dq, bool diag = true)
267  : same_calc_shape(false), Q(NULL), VQ(diag?NULL:&dq), DQ(diag?&dq:NULL),
268  MQ(NULL) {}
269  MixedVectorIntegrator(MatrixCoefficient &mq)
270  : same_calc_shape(false), Q(NULL), VQ(NULL), DQ(NULL), MQ(&mq) {}
271 
272  inline virtual bool VerifyFiniteElementTypes(
273  const FiniteElement & trial_fe,
274  const FiniteElement & test_fe) const
275  {
276  return (trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
277  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
278  }
279 
280  inline virtual const char * FiniteElementTypeFailureMessage() const
281  {
282  return "MixedVectorIntegrator: "
283  "Trial and test spaces must both be vector fields";
284  }
285 
286  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
287  const FiniteElement & test_fe,
288  ElementTransformation &Trans)
289  { return trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW(); }
290 
291 
292  inline virtual void CalcTestShape(const FiniteElement & test_fe,
293  ElementTransformation &Trans,
294  DenseMatrix & shape)
295  { test_fe.CalcVShape(Trans, shape); }
296 
297  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
298  ElementTransformation &Trans,
299  DenseMatrix & shape)
300  { trial_fe.CalcVShape(Trans, shape); }
301 
302 private:
303 
304  Coefficient *Q;
305  VectorCoefficient *VQ;
306  VectorCoefficient *DQ;
307  MatrixCoefficient *MQ;
308 
309 #ifndef MFEM_THREAD_SAFE
310  Vector V;
311  Vector D;
312  DenseMatrix M;
313  DenseMatrix test_shape;
314  DenseMatrix trial_shape;
315  DenseMatrix test_shape_tmp;
316 #endif
317 
318 };
319 
320 /** An abstract class for integrating the product of a scalar basis function and
321  the inner product of a vector basis function with a vector coefficient. In
322  2D the inner product can be replaced with a cross product. */
323 class MixedScalarVectorIntegrator: public BilinearFormIntegrator
324 {
325 public:
326 
327  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
328  const FiniteElement &test_fe,
329  ElementTransformation &Trans,
330  DenseMatrix &elmat);
331 
332 protected:
333 
334  MixedScalarVectorIntegrator(VectorCoefficient &vq, bool _transpose = false,
335  bool _cross_2d = false)
336  : VQ(&vq), transpose(_transpose), cross_2d(_cross_2d) {}
337 
338  inline virtual bool VerifyFiniteElementTypes(
339  const FiniteElement & trial_fe,
340  const FiniteElement & test_fe) const
341  {
342  return ((transpose &&
343  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
344  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR ) ||
345  (!transpose &&
346  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
347  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR )
348  );
349  }
350 
351  inline virtual const char * FiniteElementTypeFailureMessage() const
352  {
353  if ( transpose )
354  {
355  return "MixedScalarVectorIntegrator: "
356  "Trial space must be a vector field "
357  "and the test space must be a scalar field";
358  }
359  else
360  {
361  return "MixedScalarVectorIntegrator: "
362  "Trial space must be a scalar field "
363  "and the test space must be a vector field";
364  }
365  }
366 
367  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
368  const FiniteElement & test_fe,
369  ElementTransformation &Trans)
370  { return trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW(); }
371 
372 
373  inline virtual void CalcVShape(const FiniteElement & vector_fe,
374  ElementTransformation &Trans,
375  DenseMatrix & shape)
376  { vector_fe.CalcVShape(Trans, shape); }
377 
378  inline virtual void CalcShape(const FiniteElement & scalar_fe,
379  ElementTransformation &Trans,
380  Vector & shape)
381  { scalar_fe.CalcPhysShape(Trans, shape); }
382 
383 private:
384 
385  VectorCoefficient *VQ;
386  bool transpose;
387  bool cross_2d; // In 2D use a cross product rather than a dot product
388 
389 #ifndef MFEM_THREAD_SAFE
390  Vector V;
391  DenseMatrix vshape;
392  Vector shape;
393  Vector vshape_tmp;
394 #endif
395 
396 };
397 
398 /** Class for integrating the bilinear form a(u,v) := (Q u, v) in either 1D, 2D,
399  or 3D and where Q is an optional scalar coefficient, u and v are each in H1
400  or L2. */
401 class MixedScalarMassIntegrator : public MixedScalarIntegrator
402 {
403 public:
404  MixedScalarMassIntegrator() { same_calc_shape = true; }
405  MixedScalarMassIntegrator(Coefficient &q)
406  : MixedScalarIntegrator(q) { same_calc_shape = true; }
407 };
408 
409 /** Class for integrating the bilinear form a(u,v) := (Q u, v) in either 2D, or
410  3D and where Q is a vector coefficient, u is in H1 or L2 and v is in H(Curl)
411  or H(Div). */
412 class MixedVectorProductIntegrator : public MixedScalarVectorIntegrator
413 {
414 public:
415  MixedVectorProductIntegrator(VectorCoefficient &vq)
416  : MixedScalarVectorIntegrator(vq) {}
417 };
418 
419 /** Class for integrating the bilinear form a(u,v) := (Q D u, v) in 1D where Q
420  is an optional scalar coefficient, u is in H1, and v is in L2. */
421 class MixedScalarDerivativeIntegrator : public MixedScalarIntegrator
422 {
423 public:
424  MixedScalarDerivativeIntegrator() {}
425  MixedScalarDerivativeIntegrator(Coefficient &q)
426  : MixedScalarIntegrator(q) {}
427 
428 protected:
429  inline virtual bool VerifyFiniteElementTypes(
430  const FiniteElement & trial_fe,
431  const FiniteElement & test_fe) const
432  {
433  return (trial_fe.GetDim() == 1 && test_fe.GetDim() == 1 &&
434  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
435  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
436  }
437 
438  inline virtual const char * FiniteElementTypeFailureMessage() const
439  {
440  return "MixedScalarDerivativeIntegrator: "
441  "Trial and test spaces must both be scalar fields in 1D "
442  "and the trial space must implement CaldDShape.";
443  }
444 
445  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
446  ElementTransformation &Trans,
447  Vector & shape)
448  {
449  DenseMatrix dshape(shape.GetData(), shape.Size(), 1);
450  trial_fe.CalcPhysDShape(Trans, dshape);
451  }
452 };
453 
454 /** Class for integrating the bilinear form a(u,v) := -(Q u, D v) in 1D where Q
455  is an optional scalar coefficient, u is in L2, and v is in H1. */
456 class MixedScalarWeakDerivativeIntegrator : public MixedScalarIntegrator
457 {
458 public:
459  MixedScalarWeakDerivativeIntegrator() {}
460  MixedScalarWeakDerivativeIntegrator(Coefficient &q)
461  : MixedScalarIntegrator(q) {}
462 
463 protected:
464  inline virtual bool VerifyFiniteElementTypes(
465  const FiniteElement & trial_fe,
466  const FiniteElement & test_fe) const
467  {
468  return (trial_fe.GetDim() == 1 && test_fe.GetDim() == 1 &&
469  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
470  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
471  }
472 
473  inline virtual const char * FiniteElementTypeFailureMessage() const
474  {
475  return "MixedScalarWeakDerivativeIntegrator: "
476  "Trial and test spaces must both be scalar fields in 1D "
477  "and the test space must implement CalcDShape with "
478  "map type \"VALUE\".";
479  }
480 
481  inline virtual void CalcTestShape(const FiniteElement & test_fe,
482  ElementTransformation &Trans,
483  Vector & shape)
484  {
485  DenseMatrix dshape(shape.GetData(), shape.Size(), 1);
486  test_fe.CalcPhysDShape(Trans, dshape);
487  shape *= -1.0;
488  }
489 };
490 
491 /** Class for integrating the bilinear form a(u,v) := (Q div u, v) in either 2D
492  or 3D where Q is an optional scalar coefficient, u is in H(Div), and v is a
493  scalar field. */
494 class MixedScalarDivergenceIntegrator : public MixedScalarIntegrator
495 {
496 public:
497  MixedScalarDivergenceIntegrator() {}
498  MixedScalarDivergenceIntegrator(Coefficient &q)
499  : MixedScalarIntegrator(q) {}
500 
501 protected:
502  inline virtual bool VerifyFiniteElementTypes(
503  const FiniteElement & trial_fe,
504  const FiniteElement & test_fe) const
505  {
506  return (trial_fe.GetDerivType() == mfem::FiniteElement::DIV &&
507  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
508  }
509 
510  inline virtual const char * FiniteElementTypeFailureMessage() const
511  {
512  return "MixedScalarDivergenceIntegrator: "
513  "Trial must be H(Div) and the test space must be a "
514  "scalar field";
515  }
516 
517  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
518  const FiniteElement & test_fe,
519  ElementTransformation &Trans)
520  { return trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW() - 1; }
521 
522  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
523  ElementTransformation &Trans,
524  Vector & shape)
525  { trial_fe.CalcPhysDivShape(Trans, shape); }
526 };
527 
528 /** Class for integrating the bilinear form a(u,v) := (V div u, v) in either 2D
529  or 3D where V is a vector coefficient, u is in H(Div), and v is a vector
530  field. */
531 class MixedVectorDivergenceIntegrator : public MixedScalarVectorIntegrator
532 {
533 public:
534  MixedVectorDivergenceIntegrator(VectorCoefficient &vq)
535  : MixedScalarVectorIntegrator(vq) {}
536 
537 protected:
538  inline virtual bool VerifyFiniteElementTypes(
539  const FiniteElement & trial_fe,
540  const FiniteElement & test_fe) const
541  {
542  return (trial_fe.GetDerivType() == mfem::FiniteElement::DIV &&
543  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
544  }
545 
546  inline virtual const char * FiniteElementTypeFailureMessage() const
547  {
548  return "MixedVectorDivergenceIntegrator: "
549  "Trial must be H(Div) and the test space must be a "
550  "vector field";
551  }
552 
553  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
554  const FiniteElement & test_fe,
555  ElementTransformation &Trans)
556  { return trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW() - 1; }
557 
558  inline virtual void CalcShape(const FiniteElement & scalar_fe,
559  ElementTransformation &Trans,
560  Vector & shape)
561  { scalar_fe.CalcPhysDivShape(Trans, shape); }
562 };
563 
564 /** Class for integrating the bilinear form a(u,v) := -(Q u, div v) in either 2D
565  or 3D where Q is an optional scalar coefficient, u is in L2 or H1, and v is
566  in H(Div). */
567 class MixedScalarWeakGradientIntegrator : public MixedScalarIntegrator
568 {
569 public:
570  MixedScalarWeakGradientIntegrator() {}
571  MixedScalarWeakGradientIntegrator(Coefficient &q)
572  : MixedScalarIntegrator(q) {}
573 
574 protected:
575  inline virtual bool VerifyFiniteElementTypes(
576  const FiniteElement & trial_fe,
577  const FiniteElement & test_fe) const
578  {
579  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
580  test_fe.GetDerivType() == mfem::FiniteElement::DIV );
581  }
582 
583  inline virtual const char * FiniteElementTypeFailureMessage() const
584  {
585  return "MixedScalarWeakGradientIntegrator: "
586  "Trial space must be a scalar field "
587  "and the test space must be H(Div)";
588  }
589 
590  virtual void CalcTestShape(const FiniteElement & test_fe,
591  ElementTransformation &Trans,
592  Vector & shape)
593  {
594  test_fe.CalcPhysDivShape(Trans, shape);
595  shape *= -1.0;
596  }
597 };
598 
599 /** Class for integrating the bilinear form a(u,v) := (Q curl u, v) in 2D where
600  Q is an optional scalar coefficient, u is in H(Curl), and v is in L2 or
601  H1. */
602 class MixedScalarCurlIntegrator : public MixedScalarIntegrator
603 {
604 public:
605  MixedScalarCurlIntegrator() {}
606  MixedScalarCurlIntegrator(Coefficient &q)
607  : MixedScalarIntegrator(q) {}
608 
609 protected:
610  inline virtual bool VerifyFiniteElementTypes(
611  const FiniteElement & trial_fe,
612  const FiniteElement & test_fe) const
613  {
614  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
615  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
616  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
617  }
618 
619  inline virtual const char * FiniteElementTypeFailureMessage() const
620  {
621  return "MixedScalarCurlIntegrator: "
622  "Trial must be H(Curl) and the test space must be a "
623  "scalar field";
624  }
625 
626  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
627  const FiniteElement & test_fe,
628  ElementTransformation &Trans)
629  { return trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW() - 1; }
630 
631  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
632  ElementTransformation &Trans,
633  Vector & shape)
634  {
635  DenseMatrix dshape(shape.GetData(), shape.Size(), 1);
636  trial_fe.CalcPhysCurlShape(Trans, dshape);
637  }
638 };
639 
640 /** Class for integrating the bilinear form a(u,v) := (Q u, curl v) in 2D where
641  Q is an optional scalar coefficient, u is in L2 or H1, and v is in
642  H(Curl). */
643 class MixedScalarWeakCurlIntegrator : public MixedScalarIntegrator
644 {
645 public:
646  MixedScalarWeakCurlIntegrator() {}
647  MixedScalarWeakCurlIntegrator(Coefficient &q)
648  : MixedScalarIntegrator(q) {}
649 
650 protected:
651  inline virtual bool VerifyFiniteElementTypes(
652  const FiniteElement & trial_fe,
653  const FiniteElement & test_fe) const
654  {
655  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
656  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
657  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
658  }
659 
660  inline virtual const char * FiniteElementTypeFailureMessage() const
661  {
662  return "MixedScalarWeakCurlIntegrator: "
663  "Trial space must be a scalar field "
664  "and the test space must be H(Curl)";
665  }
666 
667  inline virtual void CalcTestShape(const FiniteElement & test_fe,
668  ElementTransformation &Trans,
669  Vector & shape)
670  {
671  DenseMatrix dshape(shape.GetData(), shape.Size(), 1);
672  test_fe.CalcPhysCurlShape(Trans, dshape);
673  }
674 };
675 
676 /** Class for integrating the bilinear form a(u,v) := (Q u, v) in either 2D or
677  3D and where Q is an optional coefficient (of type scalar, matrix, or
678  diagonal matrix) u and v are each in H(Curl) or H(Div). */
679 class MixedVectorMassIntegrator : public MixedVectorIntegrator
680 {
681 public:
682  MixedVectorMassIntegrator() { same_calc_shape = true; }
683  MixedVectorMassIntegrator(Coefficient &q)
684  : MixedVectorIntegrator(q) { same_calc_shape = true; }
685  MixedVectorMassIntegrator(VectorCoefficient &dq)
686  : MixedVectorIntegrator(dq, true) { same_calc_shape = true; }
687  MixedVectorMassIntegrator(MatrixCoefficient &mq)
688  : MixedVectorIntegrator(mq) { same_calc_shape = true; }
689 };
690 
691 /** Class for integrating the bilinear form a(u,v) := (V x u, v) in 3D and where
692  V is a vector coefficient u and v are each in H(Curl) or H(Div). */
693 class MixedCrossProductIntegrator : public MixedVectorIntegrator
694 {
695 public:
696  MixedCrossProductIntegrator(VectorCoefficient &vq)
697  : MixedVectorIntegrator(vq, false) { same_calc_shape = true; }
698 };
699 
700 /** Class for integrating the bilinear form a(u,v) := (V . u, v) in 2D or 3D and
701  where V is a vector coefficient u is in H(Curl) or H(Div) and v is in H1 or
702  L2. */
703 class MixedDotProductIntegrator : public MixedScalarVectorIntegrator
704 {
705 public:
706  MixedDotProductIntegrator(VectorCoefficient &vq)
707  : MixedScalarVectorIntegrator(vq, true) {}
708 
709  inline virtual bool VerifyFiniteElementTypes(
710  const FiniteElement & trial_fe,
711  const FiniteElement & test_fe) const
712  {
713  return (trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
714  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
715  }
716 
717  inline virtual const char * FiniteElementTypeFailureMessage() const
718  {
719  return "MixedDotProductIntegrator: "
720  "Trial space must be a vector field "
721  "and the test space must be a scalar field";
722  }
723 };
724 
725 /** Class for integrating the bilinear form a(u,v) := (-V . u, Div v) in 2D or
726  3D and where V is a vector coefficient u is in H(Curl) or H(Div) and v is in
727  RT. */
728 class MixedWeakGradDotIntegrator : public MixedScalarVectorIntegrator
729 {
730 public:
731  MixedWeakGradDotIntegrator(VectorCoefficient &vq)
732  : MixedScalarVectorIntegrator(vq, true) {}
733 
734  inline virtual bool VerifyFiniteElementTypes(
735  const FiniteElement & trial_fe,
736  const FiniteElement & test_fe) const
737  {
738  return (trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
739  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
740  test_fe.GetDerivType() == mfem::FiniteElement::DIV );
741  }
742 
743  inline virtual const char * FiniteElementTypeFailureMessage() const
744  {
745  return "MixedWeakGradDotIntegrator: "
746  "Trial space must be a vector field "
747  "and the test space must be a vector field with a divergence";
748  }
749 
750  inline virtual void CalcShape(const FiniteElement & scalar_fe,
751  ElementTransformation &Trans,
752  Vector & shape)
753  { scalar_fe.CalcPhysDivShape(Trans, shape); shape *= -1.0; }
754 };
755 
756 /** Class for integrating the bilinear form a(u,v) := (V x u, Grad v) in 3D and
757  where V is a vector coefficient u is in H(Curl) or H(Div) and v is in H1. */
758 class MixedWeakDivCrossIntegrator : public MixedVectorIntegrator
759 {
760 public:
761  MixedWeakDivCrossIntegrator(VectorCoefficient &vq)
762  : MixedVectorIntegrator(vq, false) {}
763 
764  inline virtual bool VerifyFiniteElementTypes(
765  const FiniteElement & trial_fe,
766  const FiniteElement & test_fe) const
767  {
768  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
769  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
770  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
771  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
772  }
773 
774  inline virtual const char * FiniteElementTypeFailureMessage() const
775  {
776  return "MixedWeakDivCrossIntegrator: "
777  "Trial space must be a vector field in 3D "
778  "and the test space must be a scalar field with a gradient";
779  }
780 
781  inline virtual void CalcTestShape(const FiniteElement & test_fe,
782  ElementTransformation &Trans,
783  DenseMatrix & shape)
784  { test_fe.CalcPhysDShape(Trans, shape); shape *= -1.0; }
785 };
786 
787 /** Class for integrating the bilinear form a(u,v) := (Q Grad u, Grad v) in 3D
788  or in 2D and where Q is a scalar or matrix coefficient u and v are both in
789  H1. */
790 class MixedGradGradIntegrator : public MixedVectorIntegrator
791 {
792 public:
793  MixedGradGradIntegrator() { same_calc_shape = true; }
794  MixedGradGradIntegrator(Coefficient &q)
795  : MixedVectorIntegrator(q) { same_calc_shape = true; }
796  MixedGradGradIntegrator(VectorCoefficient &dq)
797  : MixedVectorIntegrator(dq, true) { same_calc_shape = true; }
798  MixedGradGradIntegrator(MatrixCoefficient &mq)
799  : MixedVectorIntegrator(mq) { same_calc_shape = true; }
800 
801  inline virtual bool VerifyFiniteElementTypes(
802  const FiniteElement & trial_fe,
803  const FiniteElement & test_fe) const
804  {
805  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
806  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
807  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
808  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
809  }
810 
811  inline virtual const char * FiniteElementTypeFailureMessage() const
812  {
813  return "MixedGradGradIntegrator: "
814  "Trial and test spaces must both be scalar fields "
815  "with a gradient operator.";
816  }
817 
818  inline virtual int GetIntegrationOrder(const FiniteElement & trial_fe,
819  const FiniteElement & test_fe,
820  ElementTransformation &Trans)
821  {
822  // Same as DiffusionIntegrator
823  return test_fe.Space() == FunctionSpace::Pk ?
824  trial_fe.GetOrder() + test_fe.GetOrder() - 2 :
825  trial_fe.GetOrder() + test_fe.GetOrder() + test_fe.GetDim() - 1;
826  }
827 
828  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
829  ElementTransformation &Trans,
830  DenseMatrix & shape)
831  { trial_fe.CalcPhysDShape(Trans, shape); }
832 
833  inline virtual void CalcTestShape(const FiniteElement & test_fe,
834  ElementTransformation &Trans,
835  DenseMatrix & shape)
836  { test_fe.CalcPhysDShape(Trans, shape); }
837 };
838 
839 /** Class for integrating the bilinear form a(u,v) := (V x Grad u, Grad v) in 3D
840  or in 2D and where V is a vector coefficient u and v are both in H1. */
841 class MixedCrossGradGradIntegrator : public MixedVectorIntegrator
842 {
843 public:
844  MixedCrossGradGradIntegrator(VectorCoefficient &vq)
845  : MixedVectorIntegrator(vq, false) { same_calc_shape = true; }
846 
847  inline virtual bool VerifyFiniteElementTypes(
848  const FiniteElement & trial_fe,
849  const FiniteElement & test_fe) const
850  {
851  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
852  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
853  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
854  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
855  }
856 
857  inline virtual const char * FiniteElementTypeFailureMessage() const
858  {
859  return "MixedCrossGradGradIntegrator: "
860  "Trial and test spaces must both be scalar fields "
861  "with a gradient operator.";
862  }
863 
864  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
865  ElementTransformation &Trans,
866  DenseMatrix & shape)
867  { trial_fe.CalcPhysDShape(Trans, shape); }
868 
869  inline virtual void CalcTestShape(const FiniteElement & test_fe,
870  ElementTransformation &Trans,
871  DenseMatrix & shape)
872  { test_fe.CalcPhysDShape(Trans, shape); }
873 };
874 
875 /** Class for integrating the bilinear form a(u,v) := (Q Curl u, Curl v) in 3D
876  and where Q is a scalar or matrix coefficient u and v are both in
877  H(Curl). */
878 class MixedCurlCurlIntegrator : public MixedVectorIntegrator
879 {
880 public:
881  MixedCurlCurlIntegrator() { same_calc_shape = true; }
882  MixedCurlCurlIntegrator(Coefficient &q)
883  : MixedVectorIntegrator(q) { same_calc_shape = true; }
884  MixedCurlCurlIntegrator(VectorCoefficient &dq)
885  : MixedVectorIntegrator(dq, true) { same_calc_shape = true; }
886  MixedCurlCurlIntegrator(MatrixCoefficient &mq)
887  : MixedVectorIntegrator(mq) { same_calc_shape = true; }
888 
889  inline virtual bool VerifyFiniteElementTypes(
890  const FiniteElement & trial_fe,
891  const FiniteElement & test_fe) const
892  {
893  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
894  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
895  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
896  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
897  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
898  }
899 
900  inline virtual const char * FiniteElementTypeFailureMessage() const
901  {
902  return "MixedCurlCurlIntegrator"
903  "Trial and test spaces must both be vector fields in 3D "
904  "with a curl.";
905  }
906 
907  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
908  ElementTransformation &Trans,
909  DenseMatrix & shape)
910  { trial_fe.CalcPhysCurlShape(Trans, shape); }
911 
912  inline virtual void CalcTestShape(const FiniteElement & test_fe,
913  ElementTransformation &Trans,
914  DenseMatrix & shape)
915  { test_fe.CalcPhysCurlShape(Trans, shape); }
916 };
917 
918 /** Class for integrating the bilinear form a(u,v) := (V x Curl u, Curl v) in 3D
919  and where V is a vector coefficient u and v are both in H(Curl). */
920 class MixedCrossCurlCurlIntegrator : public MixedVectorIntegrator
921 {
922 public:
923  MixedCrossCurlCurlIntegrator(VectorCoefficient &vq)
924  : MixedVectorIntegrator(vq, false) { same_calc_shape = true; }
925 
926  inline virtual bool VerifyFiniteElementTypes(
927  const FiniteElement & trial_fe,
928  const FiniteElement & test_fe) const
929  {
930  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
931  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
932  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
933  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
934  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
935  }
936 
937  inline virtual const char * FiniteElementTypeFailureMessage() const
938  {
939  return "MixedCrossCurlCurlIntegrator: "
940  "Trial and test spaces must both be vector fields in 3D "
941  "with a curl.";
942  }
943 
944  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
945  ElementTransformation &Trans,
946  DenseMatrix & shape)
947  { trial_fe.CalcPhysCurlShape(Trans, shape); }
948 
949  inline virtual void CalcTestShape(const FiniteElement & test_fe,
950  ElementTransformation &Trans,
951  DenseMatrix & shape)
952  { test_fe.CalcPhysCurlShape(Trans, shape); }
953 };
954 
955 /** Class for integrating the bilinear form a(u,v) := (V x Curl u, Grad v) in 3D
956  and where V is a vector coefficient u is in H(Curl) and v is in H1. */
957 class MixedCrossCurlGradIntegrator : public MixedVectorIntegrator
958 {
959 public:
960  MixedCrossCurlGradIntegrator(VectorCoefficient &vq)
961  : MixedVectorIntegrator(vq, false) {}
962 
963  inline virtual bool VerifyFiniteElementTypes(
964  const FiniteElement & trial_fe,
965  const FiniteElement & test_fe) const
966  {
967  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
968  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
969  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
970  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
971  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
972  }
973 
974  inline virtual const char * FiniteElementTypeFailureMessage() const
975  {
976  return "MixedCrossCurlGradIntegrator"
977  "Trial space must be a vector field in 3D with a curl"
978  "and the test space must be a scalar field with a gradient";
979  }
980 
981  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
982  ElementTransformation &Trans,
983  DenseMatrix & shape)
984  { trial_fe.CalcPhysCurlShape(Trans, shape); }
985 
986  inline virtual void CalcTestShape(const FiniteElement & test_fe,
987  ElementTransformation &Trans,
988  DenseMatrix & shape)
989  { test_fe.CalcPhysDShape(Trans, shape); }
990 };
991 
992 /** Class for integrating the bilinear form a(u,v) := (V x Grad u, Curl v) in 3D
993  and where V is a scalar coefficient u is in H1 and v is in H(Curl). */
994 class MixedCrossGradCurlIntegrator : public MixedVectorIntegrator
995 {
996 public:
997  MixedCrossGradCurlIntegrator(VectorCoefficient &vq)
998  : MixedVectorIntegrator(vq, false) {}
999 
1000  inline virtual bool VerifyFiniteElementTypes(
1001  const FiniteElement & trial_fe,
1002  const FiniteElement & test_fe) const
1003  {
1004  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
1005  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1006  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
1007  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1008  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
1009  }
1010 
1011  inline virtual const char * FiniteElementTypeFailureMessage() const
1012  {
1013  return "MixedCrossGradCurlIntegrator"
1014  "Trial space must be a scalar field in 3D with a gradient"
1015  "and the test space must be a vector field with a curl";
1016  }
1017 
1018  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
1019  ElementTransformation &Trans,
1020  DenseMatrix & shape)
1021  { trial_fe.CalcPhysDShape(Trans, shape); }
1022 
1023  inline virtual void CalcTestShape(const FiniteElement & test_fe,
1024  ElementTransformation &Trans,
1025  DenseMatrix & shape)
1026  { test_fe.CalcPhysCurlShape(Trans, shape); }
1027 };
1028 
1029 /** Class for integrating the bilinear form a(u,v) := (V x u, Curl v) in 3D and
1030  where V is a vector coefficient u is in H(Curl) or H(Div) and v is in
1031  H(Curl). */
1032 class MixedWeakCurlCrossIntegrator : public MixedVectorIntegrator
1033 {
1034 public:
1035  MixedWeakCurlCrossIntegrator(VectorCoefficient &vq)
1036  : MixedVectorIntegrator(vq, false) {}
1037 
1038  inline virtual bool VerifyFiniteElementTypes(
1039  const FiniteElement & trial_fe,
1040  const FiniteElement & test_fe) const
1041  {
1042  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
1043  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1044  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1045  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
1046  }
1047 
1048  inline virtual const char * FiniteElementTypeFailureMessage() const
1049  {
1050  return "MixedWeakCurlCrossIntegrator: "
1051  "Trial space must be a vector field in 3D "
1052  "and the test space must be a vector field with a curl";
1053  }
1054 
1055  inline virtual void CalcTestShape(const FiniteElement & test_fe,
1056  ElementTransformation &Trans,
1057  DenseMatrix & shape)
1058  { test_fe.CalcPhysCurlShape(Trans, shape); }
1059 };
1060 
1061 /** Class for integrating the bilinear form a(u,v) := (V x u, Curl v) in 2D and
1062  where V is a vector coefficient u is in H(Curl) or H(Div) and v is in
1063  H(Curl). */
1064 class MixedScalarWeakCurlCrossIntegrator : public MixedScalarVectorIntegrator
1065 {
1066 public:
1067  MixedScalarWeakCurlCrossIntegrator(VectorCoefficient &vq)
1068  : MixedScalarVectorIntegrator(vq, true, true) {}
1069 
1070  inline virtual bool VerifyFiniteElementTypes(
1071  const FiniteElement & trial_fe,
1072  const FiniteElement & test_fe) const
1073  {
1074  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
1075  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1076  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1077  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
1078  }
1079 
1080  inline virtual const char * FiniteElementTypeFailureMessage() const
1081  {
1082  return "MixedScalarWeakCurlCrossIntegrator: "
1083  "Trial space must be a vector field in 2D "
1084  "and the test space must be a vector field with a curl";
1085  }
1086 
1087  inline virtual void CalcShape(const FiniteElement & scalar_fe,
1088  ElementTransformation &Trans,
1089  Vector & shape)
1090  {
1091  DenseMatrix dshape(shape.GetData(), shape.Size(), 1);
1092  scalar_fe.CalcPhysCurlShape(Trans, dshape);
1093  }
1094 };
1095 
1096 /** Class for integrating the bilinear form a(u,v) := (V x Grad u, v) in 3D or
1097  in 2D and where V is a vector coefficient u is in H1 and v is in H(Curl) or
1098  H(Div). */
1099 class MixedCrossGradIntegrator : public MixedVectorIntegrator
1100 {
1101 public:
1102  MixedCrossGradIntegrator(VectorCoefficient &vq)
1103  : MixedVectorIntegrator(vq, false) {}
1104 
1105  inline virtual bool VerifyFiniteElementTypes(
1106  const FiniteElement & trial_fe,
1107  const FiniteElement & test_fe) const
1108  {
1109  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
1110  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1111  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
1112  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
1113  }
1114 
1115  inline virtual const char * FiniteElementTypeFailureMessage() const
1116  {
1117  return "MixedCrossGradIntegrator: "
1118  "Trial space must be a scalar field with a gradient operator"
1119  " and the test space must be a vector field both in 3D.";
1120  }
1121 
1122  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
1123  ElementTransformation &Trans,
1124  DenseMatrix & shape)
1125  { trial_fe.CalcPhysDShape(Trans, shape); }
1126 
1127  inline virtual void CalcTestShape(const FiniteElement & test_fe,
1128  ElementTransformation &Trans,
1129  DenseMatrix & shape)
1130  { test_fe.CalcVShape(Trans, shape); }
1131 };
1132 
1133 /** Class for integrating the bilinear form a(u,v) := (V x Curl u, v) in 3D and
1134  where V is a vector coefficient u is in H(Curl) and v is in H(Curl) or
1135  H(Div). */
1136 class MixedCrossCurlIntegrator : public MixedVectorIntegrator
1137 {
1138 public:
1139  MixedCrossCurlIntegrator(VectorCoefficient &vq)
1140  : MixedVectorIntegrator(vq, false) {}
1141 
1142  inline virtual bool VerifyFiniteElementTypes(
1143  const FiniteElement & trial_fe,
1144  const FiniteElement & test_fe) const
1145  {
1146  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
1147  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1148  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
1149  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
1150  }
1151 
1152  inline virtual const char * FiniteElementTypeFailureMessage() const
1153  {
1154  return "MixedCrossCurlIntegrator: "
1155  "Trial space must be a vector field in 3D with a curl "
1156  "and the test space must be a vector field";
1157  }
1158 
1159  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
1160  ElementTransformation &Trans,
1161  DenseMatrix & shape)
1162  { trial_fe.CalcPhysCurlShape(Trans, shape); }
1163 };
1164 
1165 /** Class for integrating the bilinear form a(u,v) := (V x Curl u, v) in 2D and
1166  where V is a vector coefficient u is in H(Curl) and v is in H(Curl) or
1167  H(Div). */
1168 class MixedScalarCrossCurlIntegrator : public MixedScalarVectorIntegrator
1169 {
1170 public:
1171  MixedScalarCrossCurlIntegrator(VectorCoefficient &vq)
1172  : MixedScalarVectorIntegrator(vq, false, true) {}
1173 
1174  inline virtual bool VerifyFiniteElementTypes(
1175  const FiniteElement & trial_fe,
1176  const FiniteElement & test_fe) const
1177  {
1178  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
1179  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1180  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
1181  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
1182  }
1183 
1184  inline virtual const char * FiniteElementTypeFailureMessage() const
1185  {
1186  return "MixedCrossCurlIntegrator: "
1187  "Trial space must be a vector field in 2D with a curl "
1188  "and the test space must be a vector field";
1189  }
1190 
1191  inline virtual void CalcShape(const FiniteElement & scalar_fe,
1192  ElementTransformation &Trans,
1193  Vector & shape)
1194  {
1195  DenseMatrix dshape(shape.GetData(), shape.Size(), 1);
1196  scalar_fe.CalcPhysCurlShape(Trans, dshape); shape *= -1.0;
1197  }
1198 };
1199 
1200 /** Class for integrating the bilinear form a(u,v) := (V x Grad u, v) in 2D and
1201  where V is a vector coefficient u is in H1 and v is in H1 or L2. */
1202 class MixedScalarCrossGradIntegrator : public MixedScalarVectorIntegrator
1203 {
1204 public:
1205  MixedScalarCrossGradIntegrator(VectorCoefficient &vq)
1206  : MixedScalarVectorIntegrator(vq, true, true) {}
1207 
1208  inline virtual bool VerifyFiniteElementTypes(
1209  const FiniteElement & trial_fe,
1210  const FiniteElement & test_fe) const
1211  {
1212  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
1213  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1214  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
1215  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
1216  }
1217 
1218  inline virtual const char * FiniteElementTypeFailureMessage() const
1219  {
1220  return "MixedScalarCrossGradIntegrator: "
1221  "Trial space must be a scalar field in 2D with a gradient "
1222  "and the test space must be a scalar field";
1223  }
1224 
1225  inline virtual void CalcVShape(const FiniteElement & vector_fe,
1226  ElementTransformation &Trans,
1227  DenseMatrix & shape)
1228  { vector_fe.CalcPhysDShape(Trans, shape); }
1229 };
1230 
1231 /** Class for integrating the bilinear form a(u,v) := (V x u, v) in 2D and where
1232  V is a vector coefficient u is in ND or RT and v is in H1 or L2. */
1233 class MixedScalarCrossProductIntegrator : public MixedScalarVectorIntegrator
1234 {
1235 public:
1236  MixedScalarCrossProductIntegrator(VectorCoefficient &vq)
1237  : MixedScalarVectorIntegrator(vq, true, true) {}
1238 
1239  inline virtual bool VerifyFiniteElementTypes(
1240  const FiniteElement & trial_fe,
1241  const FiniteElement & test_fe) const
1242  {
1243  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
1244  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1245  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
1246  }
1247 
1248  inline virtual const char * FiniteElementTypeFailureMessage() const
1249  {
1250  return "MixedScalarCrossProductIntegrator: "
1251  "Trial space must be a vector field in 2D "
1252  "and the test space must be a scalar field";
1253  }
1254 };
1255 
1256 /** Class for integrating the bilinear form a(u,v) := (V x z u, v) in 2D and
1257  where V is a vector coefficient u is in H1 or L2 and v is in ND or RT. */
1258 class MixedScalarWeakCrossProductIntegrator : public MixedScalarVectorIntegrator
1259 {
1260 public:
1261  MixedScalarWeakCrossProductIntegrator(VectorCoefficient &vq)
1262  : MixedScalarVectorIntegrator(vq, false, true) {}
1263 
1264  inline virtual bool VerifyFiniteElementTypes(
1265  const FiniteElement & trial_fe,
1266  const FiniteElement & test_fe) const
1267  {
1268  return (trial_fe.GetDim() == 2 && test_fe.GetDim() == 2 &&
1269  trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1270  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
1271  }
1272 
1273  inline virtual const char * FiniteElementTypeFailureMessage() const
1274  {
1275  return "MixedScalarWeakCrossProductIntegrator: "
1276  "Trial space must be a scalar field in 2D "
1277  "and the test space must be a vector field";
1278  }
1279 
1280  inline virtual void CalcShape(const FiniteElement & scalar_fe,
1281  ElementTransformation &Trans,
1282  Vector & shape)
1283  { scalar_fe.CalcPhysShape(Trans, shape); shape *= -1.0; }
1284 };
1285 
1286 /** Class for integrating the bilinear form a(u,v) := (V . Grad u, v) in 2D or
1287  3D and where V is a vector coefficient, u is in H1 and v is in H1 or L2. */
1288 class MixedDirectionalDerivativeIntegrator : public MixedScalarVectorIntegrator
1289 {
1290 public:
1291  MixedDirectionalDerivativeIntegrator(VectorCoefficient &vq)
1292  : MixedScalarVectorIntegrator(vq, true) {}
1293 
1294  inline virtual bool VerifyFiniteElementTypes(
1295  const FiniteElement & trial_fe,
1296  const FiniteElement & test_fe) const
1297  {
1298  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1299  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
1300  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR );
1301  }
1302 
1303  inline virtual const char * FiniteElementTypeFailureMessage() const
1304  {
1305  return "MixedDirectionalDerivativeIntegrator: "
1306  "Trial space must be a scalar field with a gradient "
1307  "and the test space must be a scalar field";
1308  }
1309 
1310  inline virtual void CalcVShape(const FiniteElement & vector_fe,
1311  ElementTransformation &Trans,
1312  DenseMatrix & shape)
1313  { vector_fe.CalcPhysDShape(Trans, shape); }
1314 };
1315 
1316 /** Class for integrating the bilinear form a(u,v) := (-V . Grad u, Div v) in 2D
1317  or 3D and where V is a vector coefficient, u is in H1 and v is in RT. */
1318 class MixedGradDivIntegrator : public MixedScalarVectorIntegrator
1319 {
1320 public:
1321  MixedGradDivIntegrator(VectorCoefficient &vq)
1322  : MixedScalarVectorIntegrator(vq, true) {}
1323 
1324  inline virtual bool VerifyFiniteElementTypes(
1325  const FiniteElement & trial_fe,
1326  const FiniteElement & test_fe) const
1327  {
1328  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1329  trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
1330  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1331  test_fe.GetDerivType() == mfem::FiniteElement::DIV );
1332  }
1333 
1334  inline virtual const char * FiniteElementTypeFailureMessage() const
1335  {
1336  return "MixedGradDivIntegrator: "
1337  "Trial space must be a scalar field with a gradient"
1338  "and the test space must be a vector field with a divergence";
1339  }
1340 
1341  inline virtual void CalcVShape(const FiniteElement & vector_fe,
1342  ElementTransformation &Trans,
1343  DenseMatrix & shape)
1344  { vector_fe.CalcPhysDShape(Trans, shape); shape *= -1.0; }
1345 
1346  inline virtual void CalcShape(const FiniteElement & scalar_fe,
1347  ElementTransformation &Trans,
1348  Vector & shape)
1349  { scalar_fe.CalcPhysDivShape(Trans, shape); }
1350 };
1351 
1352 /** Class for integrating the bilinear form a(u,v) := (-V Div u, Grad v) in 2D
1353  or 3D and where V is a vector coefficient, u is in RT and v is in H1. */
1354 class MixedDivGradIntegrator : public MixedScalarVectorIntegrator
1355 {
1356 public:
1357  MixedDivGradIntegrator(VectorCoefficient &vq)
1358  : MixedScalarVectorIntegrator(vq, false) {}
1359 
1360  inline virtual bool VerifyFiniteElementTypes(
1361  const FiniteElement & trial_fe,
1362  const FiniteElement & test_fe) const
1363  {
1364  return (trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1365  trial_fe.GetDerivType() == mfem::FiniteElement::DIV &&
1366  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1367  test_fe.GetDerivType() == mfem::FiniteElement::GRAD
1368  );
1369  }
1370 
1371  inline virtual const char * FiniteElementTypeFailureMessage() const
1372  {
1373  return "MixedDivGradIntegrator: "
1374  "Trial space must be a vector field with a divergence"
1375  "and the test space must be a scalar field with a gradient";
1376  }
1377 
1378  inline virtual void CalcVShape(const FiniteElement & vector_fe,
1379  ElementTransformation &Trans,
1380  DenseMatrix & shape)
1381  { vector_fe.CalcPhysDShape(Trans, shape); shape *= -1.0; }
1382 
1383  inline virtual void CalcShape(const FiniteElement & scalar_fe,
1384  ElementTransformation &Trans,
1385  Vector & shape)
1386  { scalar_fe.CalcPhysDivShape(Trans, shape); }
1387 };
1388 
1389 /** Class for integrating the bilinear form a(u,v) := (-V u, Grad v) in 2D or 3D
1390  and where V is a vector coefficient, u is in H1 and v is in H1. */
1391 class MixedScalarWeakDivergenceIntegrator : public MixedScalarVectorIntegrator
1392 {
1393 public:
1394  MixedScalarWeakDivergenceIntegrator(VectorCoefficient &vq)
1395  : MixedScalarVectorIntegrator(vq, false) {}
1396 
1397  inline virtual bool VerifyFiniteElementTypes(
1398  const FiniteElement & trial_fe,
1399  const FiniteElement & test_fe) const
1400  {
1401  return (trial_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1402  test_fe.GetRangeType() == mfem::FiniteElement::SCALAR &&
1403  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
1404  }
1405 
1406  inline virtual const char * FiniteElementTypeFailureMessage() const
1407  {
1408  return "MixedScalarWeakDivergenceIntegrator: "
1409  "Trial space must be a scalar field "
1410  "and the test space must be a scalar field with a gradient";
1411  }
1412 
1413  inline virtual void CalcVShape(const FiniteElement & vector_fe,
1414  ElementTransformation &Trans,
1415  DenseMatrix & shape)
1416  { vector_fe.CalcPhysDShape(Trans, shape); shape *= -1.0; }
1417 };
1418 
1419 /** Class for integrating the bilinear form a(u,v) := (Q grad u, v) in either 2D
1420  or 3D and where Q is an optional coefficient (of type scalar, matrix, or
1421  diagonal matrix) u is in H1 and v is in H(Curl) or H(Div). */
1422 class MixedVectorGradientIntegrator : public MixedVectorIntegrator
1423 {
1424 public:
1425  MixedVectorGradientIntegrator() {}
1426  MixedVectorGradientIntegrator(Coefficient &q)
1427  : MixedVectorIntegrator(q) {}
1428  MixedVectorGradientIntegrator(VectorCoefficient &dq)
1429  : MixedVectorIntegrator(dq, true) {}
1430  MixedVectorGradientIntegrator(MatrixCoefficient &mq)
1431  : MixedVectorIntegrator(mq) {}
1432 
1433 protected:
1434  inline virtual bool VerifyFiniteElementTypes(
1435  const FiniteElement & trial_fe,
1436  const FiniteElement & test_fe) const
1437  {
1438  return (trial_fe.GetDerivType() == mfem::FiniteElement::GRAD &&
1439  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
1440  }
1441 
1442  inline virtual const char * FiniteElementTypeFailureMessage() const
1443  {
1444  return "MixedVectorGradientIntegrator: "
1445  "Trial spaces must be H1 and the test space must be a "
1446  "vector field in 2D or 3D";
1447  }
1448 
1449  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
1450  ElementTransformation &Trans,
1451  DenseMatrix & shape)
1452  {
1453  trial_fe.CalcPhysDShape(Trans, shape);
1454  }
1455 
1456 private:
1457  DenseMatrix Jinv;
1458 };
1459 
1460 /** Class for integrating the bilinear form a(u,v) := (Q curl u, v) in 3D and
1461  where Q is an optional coefficient (of type scalar, matrix, or diagonal
1462  matrix) u is in H(Curl) and v is in H(Div) or H(Curl). */
1463 class MixedVectorCurlIntegrator : public MixedVectorIntegrator
1464 {
1465 public:
1466  MixedVectorCurlIntegrator() {}
1467  MixedVectorCurlIntegrator(Coefficient &q)
1468  : MixedVectorIntegrator(q) {}
1469  MixedVectorCurlIntegrator(VectorCoefficient &dq)
1470  : MixedVectorIntegrator(dq, true) {}
1471  MixedVectorCurlIntegrator(MatrixCoefficient &mq)
1472  : MixedVectorIntegrator(mq) {}
1473 
1474 protected:
1475  inline virtual bool VerifyFiniteElementTypes(
1476  const FiniteElement & trial_fe,
1477  const FiniteElement & test_fe) const
1478  {
1479  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
1480  trial_fe.GetDerivType() == mfem::FiniteElement::CURL &&
1481  test_fe.GetRangeType() == mfem::FiniteElement::VECTOR );
1482  }
1483 
1484  inline virtual const char * FiniteElementTypeFailureMessage() const
1485  {
1486  return "MixedVectorCurlIntegrator: "
1487  "Trial space must be H(Curl) and the test space must be a "
1488  "vector field in 3D";
1489  }
1490 
1491  inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
1492  ElementTransformation &Trans,
1493  DenseMatrix & shape)
1494  {
1495  trial_fe.CalcPhysCurlShape(Trans, shape);
1496  }
1497 };
1498 
1499 /** Class for integrating the bilinear form a(u,v) := (Q u, curl v) in 3D and
1500  where Q is an optional coefficient (of type scalar, matrix, or diagonal
1501  matrix) u is in H(Div) or H(Curl) and v is in H(Curl). */
1502 class MixedVectorWeakCurlIntegrator : public MixedVectorIntegrator
1503 {
1504 public:
1505  MixedVectorWeakCurlIntegrator() {}
1506  MixedVectorWeakCurlIntegrator(Coefficient &q)
1507  : MixedVectorIntegrator(q) {}
1508  MixedVectorWeakCurlIntegrator(VectorCoefficient &dq)
1509  : MixedVectorIntegrator(dq, true) {}
1510  MixedVectorWeakCurlIntegrator(MatrixCoefficient &mq)
1511  : MixedVectorIntegrator(mq) {}
1512 
1513 protected:
1514  inline virtual bool VerifyFiniteElementTypes(
1515  const FiniteElement & trial_fe,
1516  const FiniteElement & test_fe) const
1517  {
1518  return (trial_fe.GetDim() == 3 && test_fe.GetDim() == 3 &&
1519  trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1520  test_fe.GetDerivType() == mfem::FiniteElement::CURL );
1521  }
1522 
1523  inline virtual const char * FiniteElementTypeFailureMessage() const
1524  {
1525  return "MixedVectorWeakCurlIntegrator: "
1526  "Trial space must be vector field in 3D and the "
1527  "test space must be H(Curl)";
1528  }
1529 
1530  inline virtual void CalcTestShape(const FiniteElement & test_fe,
1531  ElementTransformation &Trans,
1532  DenseMatrix & shape)
1533  {
1534  test_fe.CalcPhysCurlShape(Trans, shape);
1535  }
1536 };
1537 
1538 /** Class for integrating the bilinear form a(u,v) := - (Q u, grad v) in either
1539  2D or 3D and where Q is an optional coefficient (of type scalar, matrix, or
1540  diagonal matrix) u is in H(Div) or H(Curl) and v is in H1. */
1541 class MixedVectorWeakDivergenceIntegrator : public MixedVectorIntegrator
1542 {
1543 public:
1544  MixedVectorWeakDivergenceIntegrator() {}
1545  MixedVectorWeakDivergenceIntegrator(Coefficient &q)
1546  : MixedVectorIntegrator(q) {}
1547  MixedVectorWeakDivergenceIntegrator(VectorCoefficient &dq)
1548  : MixedVectorIntegrator(dq, true) {}
1549  MixedVectorWeakDivergenceIntegrator(MatrixCoefficient &mq)
1550  : MixedVectorIntegrator(mq) {}
1551 
1552 protected:
1553  inline virtual bool VerifyFiniteElementTypes(
1554  const FiniteElement & trial_fe,
1555  const FiniteElement & test_fe) const
1556  {
1557  return (trial_fe.GetRangeType() == mfem::FiniteElement::VECTOR &&
1558  test_fe.GetDerivType() == mfem::FiniteElement::GRAD );
1559  }
1560 
1561  inline virtual const char * FiniteElementTypeFailureMessage() const
1562  {
1563  return "MixedVectorWeakDivergenceIntegrator: "
1564  "Trial space must be vector field and the "
1565  "test space must be H1";
1566  }
1567 
1568  inline virtual void CalcTestShape(const FiniteElement & test_fe,
1569  ElementTransformation &Trans,
1570  DenseMatrix & shape)
1571  {
1572  test_fe.CalcPhysDShape(Trans, shape);
1573  shape *= -1.0;
1574  }
1575 };
1576 
1577 /** Class for integrating the bilinear form a(u,v) := (Q grad u, grad v) where Q
1578  can be a scalar or a matrix coefficient. */
1579 class DiffusionIntegrator: public BilinearFormIntegrator
1580 {
1581 private:
1582  Vector vec, pointflux, shape;
1583 #ifndef MFEM_THREAD_SAFE
1584  DenseMatrix dshape, dshapedxt, invdfdx, mq;
1585  DenseMatrix te_dshape, te_dshapedxt;
1586 #endif
1587  Coefficient *Q;
1588  MatrixCoefficient *MQ;
1589 
1590 public:
1591  /// Construct a diffusion integrator with coefficient Q = 1
1592  DiffusionIntegrator() { Q = NULL; MQ = NULL; }
1593 
1594  /// Construct a diffusion integrator with a scalar coefficient q
1595  DiffusionIntegrator (Coefficient &q) : Q(&q) { MQ = NULL; }
1596 
1597  /// Construct a diffusion integrator with a matrix coefficient q
1598  DiffusionIntegrator (MatrixCoefficient &q) : MQ(&q) { Q = NULL; }
1599 
1600  /** Given a particular Finite Element
1601  computes the element stiffness matrix elmat. */
1602  virtual void AssembleElementMatrix(const FiniteElement &el,
1603  ElementTransformation &Trans,
1604  DenseMatrix &elmat);
1605  /** Given a trial and test Finite Element computes the element stiffness
1606  matrix elmat. */
1607  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1608  const FiniteElement &test_fe,
1609  ElementTransformation &Trans,
1610  DenseMatrix &elmat);
1611 
1612  /// Perform the local action of the BilinearFormIntegrator
1613  virtual void AssembleElementVector(const FiniteElement &el,
1614  ElementTransformation &Tr,
1615  const Vector &elfun, Vector &elvect);
1616 
1617  virtual void ComputeElementFlux(const FiniteElement &el,
1618  ElementTransformation &Trans,
1619  Vector &u, const FiniteElement &fluxelem,
1620  Vector &flux, int with_coef = 1);
1621 
1622  virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
1623  ElementTransformation &Trans,
1624  Vector &flux, Vector *d_energy = NULL);
1625 };
1626 
1627 /** Class for local mass matrix assembling a(u,v) := (Q u, v) */
1628 class MassIntegrator: public BilinearFormIntegrator
1629 {
1630 protected:
1631 #ifndef MFEM_THREAD_SAFE
1632  Vector shape, te_shape;
1633 #endif
1634  Coefficient *Q;
1635 
1636 public:
1637  MassIntegrator(const IntegrationRule *ir = NULL)
1638  : BilinearFormIntegrator(ir) { Q = NULL; }
1639  /// Construct a mass integrator with coefficient q
1640  MassIntegrator(Coefficient &q, const IntegrationRule *ir = NULL)
1641  : BilinearFormIntegrator(ir), Q(&q) { }
1642 
1643  /** Given a particular Finite Element
1644  computes the element mass matrix elmat. */
1645  virtual void AssembleElementMatrix(const FiniteElement &el,
1646  ElementTransformation &Trans,
1647  DenseMatrix &elmat);
1648  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1649  const FiniteElement &test_fe,
1650  ElementTransformation &Trans,
1651  DenseMatrix &elmat);
1652 };
1653 
1654 class BoundaryMassIntegrator : public MassIntegrator
1655 {
1656 public:
1657  BoundaryMassIntegrator(Coefficient &q) : MassIntegrator(q) { }
1658 
1659  using BilinearFormIntegrator::AssembleFaceMatrix;
1660 
1661  virtual void AssembleFaceMatrix(const FiniteElement &el1,
1662  const FiniteElement &el2,
1663  FaceElementTransformations &Trans,
1664  DenseMatrix &elmat);
1665 };
1666 
1667 /// alpha (q . grad u, v)
1668 class ConvectionIntegrator : public BilinearFormIntegrator
1669 {
1670 private:
1671 #ifndef MFEM_THREAD_SAFE
1672  DenseMatrix dshape, adjJ, Q_ir;
1673  Vector shape, vec2, BdFidxT;
1674 #endif
1675  VectorCoefficient &Q;
1676  double alpha;
1677 
1678 public:
1679  ConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
1680  : Q(q) { alpha = a; }
1681  virtual void AssembleElementMatrix(const FiniteElement &,
1682  ElementTransformation &,
1683  DenseMatrix &);
1684 };
1685 
1686 /// alpha (q . grad u, v) using the "group" FE discretization
1687 class GroupConvectionIntegrator : public BilinearFormIntegrator
1688 {
1689 private:
1690  DenseMatrix dshape, adjJ, Q_nodal, grad;
1691  Vector shape;
1692  VectorCoefficient &Q;
1693  double alpha;
1694 
1695 public:
1696  GroupConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
1697  : Q(q) { alpha = a; }
1698  virtual void AssembleElementMatrix(const FiniteElement &,
1699  ElementTransformation &,
1700  DenseMatrix &);
1701 };
1702 
1703 /** Class for integrating the bilinear form a(u,v) := (Q u, v),
1704  where u=(u1,...,un) and v=(v1,...,vn); ui and vi are defined
1705  by scalar FE through standard transformation. */
1706 class VectorMassIntegrator: public BilinearFormIntegrator
1707 {
1708 private:
1709  Vector shape, te_shape, vec;
1710  DenseMatrix partelmat;
1711  DenseMatrix mcoeff;
1712  Coefficient *Q;
1713  VectorCoefficient *VQ;
1714  MatrixCoefficient *MQ;
1715 
1716  int Q_order;
1717 
1718 public:
1719  /// Construct an integrator with coefficient 1.0
1720  VectorMassIntegrator()
1721  { Q = NULL; VQ = NULL; MQ = NULL; Q_order = 0; }
1722  /** Construct an integrator with scalar coefficient q.
1723  If possible, save memory by using a scalar integrator since
1724  the resulting matrix is block diagonal with the same diagonal
1725  block repeated. */
1726  VectorMassIntegrator(Coefficient &q, int qo = 0)
1727  : Q(&q) { VQ = NULL; MQ = NULL; Q_order = qo; }
1728  VectorMassIntegrator(Coefficient &q, const IntegrationRule *ir)
1729  : BilinearFormIntegrator(ir), Q(&q)
1730  { VQ = NULL; MQ = NULL; Q_order = 0; }
1731  /// Construct an integrator with diagonal coefficient q
1732  VectorMassIntegrator(VectorCoefficient &q, int qo = 0)
1733  : VQ(&q) { Q = NULL; MQ = NULL; Q_order = qo; }
1734  /// Construct an integrator with matrix coefficient q
1735  VectorMassIntegrator(MatrixCoefficient &q, int qo = 0)
1736  : MQ(&q) { Q = NULL; VQ = NULL; Q_order = qo; }
1737 
1738  virtual void AssembleElementMatrix(const FiniteElement &el,
1739  ElementTransformation &Trans,
1740  DenseMatrix &elmat);
1741  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1742  const FiniteElement &test_fe,
1743  ElementTransformation &Trans,
1744  DenseMatrix &elmat);
1745 };
1746 
1747 
1748 /** Class for integrating (div u, p) where u is a vector field given
1749  by VectorFiniteElement through Piola transformation (for RT
1750  elements); p is scalar function given by FiniteElement through
1751  standard transformation. Here, u is the trial function and p is
1752  the test function.
1753  Note: the element matrix returned by AssembleElementMatrix2
1754  does NOT depend on the ElementTransformation Trans. */
1755 class VectorFEDivergenceIntegrator : public BilinearFormIntegrator
1756 {
1757 private:
1758  Coefficient *Q;
1759 #ifndef MFEM_THREAD_SAFE
1760  Vector divshape, shape;
1761 #endif
1762 public:
1763  VectorFEDivergenceIntegrator() { Q = NULL; }
1764  VectorFEDivergenceIntegrator(Coefficient &q) { Q = &q; }
1765  virtual void AssembleElementMatrix(const FiniteElement &el,
1766  ElementTransformation &Trans,
1767  DenseMatrix &elmat) { }
1768  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1769  const FiniteElement &test_fe,
1770  ElementTransformation &Trans,
1771  DenseMatrix &elmat);
1772 };
1773 
1774 
1775 /** Integrator for `(-Q u, grad v)` for Nedelec (`u`) and H1 (`v`) elements.
1776  This is equivalent to a weak divergence of the Nedelec basis functions. */
1777 class VectorFEWeakDivergenceIntegrator: public BilinearFormIntegrator
1778 {
1779 private:
1780  Coefficient *Q;
1781 #ifndef MFEM_THREAD_SAFE
1782  DenseMatrix dshape;
1783  DenseMatrix dshapedxt;
1784  DenseMatrix vshape;
1785  DenseMatrix invdfdx;
1786 #endif
1787 public:
1788  VectorFEWeakDivergenceIntegrator() { Q = NULL; }
1789  VectorFEWeakDivergenceIntegrator(Coefficient &q) { Q = &q; }
1790  virtual void AssembleElementMatrix(const FiniteElement &el,
1791  ElementTransformation &Trans,
1792  DenseMatrix &elmat) { }
1793  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1794  const FiniteElement &test_fe,
1795  ElementTransformation &Trans,
1796  DenseMatrix &elmat);
1797 };
1798 
1799 /** Integrator for (curl u, v) for Nedelec and RT elements. If the trial and
1800  test spaces are switched, assembles the form (u, curl v). */
1801 class VectorFECurlIntegrator: public BilinearFormIntegrator
1802 {
1803 private:
1804  Coefficient *Q;
1805 #ifndef MFEM_THREAD_SAFE
1806  DenseMatrix curlshapeTrial;
1807  DenseMatrix vshapeTest;
1808  DenseMatrix curlshapeTrial_dFT;
1809 #endif
1810 public:
1811  VectorFECurlIntegrator() { Q = NULL; }
1812  VectorFECurlIntegrator(Coefficient &q) { Q = &q; }
1813  virtual void AssembleElementMatrix(const FiniteElement &el,
1814  ElementTransformation &Trans,
1815  DenseMatrix &elmat) { }
1816  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1817  const FiniteElement &test_fe,
1818  ElementTransformation &Trans,
1819  DenseMatrix &elmat);
1820 };
1821 
1822 
1823 /// Class for integrating (Q D_i(u), v); u and v are scalars
1824 class DerivativeIntegrator : public BilinearFormIntegrator
1825 {
1826 private:
1827  Coefficient & Q;
1828  int xi;
1829  DenseMatrix dshape, dshapedxt, invdfdx;
1830  Vector shape, dshapedxi;
1831 public:
1832  DerivativeIntegrator(Coefficient &q, int i) : Q(q), xi(i) { }
1833  virtual void AssembleElementMatrix(const FiniteElement &el,
1834  ElementTransformation &Trans,
1835  DenseMatrix &elmat)
1836  { AssembleElementMatrix2(el,el,Trans,elmat); }
1837  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1838  const FiniteElement &test_fe,
1839  ElementTransformation &Trans,
1840  DenseMatrix &elmat);
1841 };
1842 
1843 /// Integrator for (curl u, curl v) for Nedelec elements
1844 class CurlCurlIntegrator: public BilinearFormIntegrator
1845 {
1846 private:
1847  Vector vec, pointflux;
1848 #ifndef MFEM_THREAD_SAFE
1849  DenseMatrix curlshape, curlshape_dFt, M;
1850  DenseMatrix vshape, projcurl;
1851 #endif
1852  Coefficient *Q;
1853  MatrixCoefficient *MQ;
1854 
1855 public:
1856  CurlCurlIntegrator() { Q = NULL; MQ = NULL; }
1857  /// Construct a bilinear form integrator for Nedelec elements
1858  CurlCurlIntegrator(Coefficient &q) : Q(&q) { MQ = NULL; }
1859  CurlCurlIntegrator(MatrixCoefficient &m) : MQ(&m) { Q = NULL; }
1860 
1861  /* Given a particular Finite Element, compute the
1862  element curl-curl matrix elmat */
1863  virtual void AssembleElementMatrix(const FiniteElement &el,
1864  ElementTransformation &Trans,
1865  DenseMatrix &elmat);
1866 
1867  virtual void ComputeElementFlux(const FiniteElement &el,
1868  ElementTransformation &Trans,
1869  Vector &u, const FiniteElement &fluxelem,
1870  Vector &flux, int with_coef);
1871 
1872  virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
1873  ElementTransformation &Trans,
1874  Vector &flux, Vector *d_energy = NULL);
1875 };
1876 
1877 /** Integrator for (curl u, curl v) for FE spaces defined by 'dim' copies of a
1878  scalar FE space. */
1879 class VectorCurlCurlIntegrator: public BilinearFormIntegrator
1880 {
1881 private:
1882 #ifndef MFEM_THREAD_SAFE
1883  DenseMatrix dshape_hat, dshape, curlshape, Jadj, grad_hat, grad;
1884 #endif
1885  Coefficient *Q;
1886 
1887 public:
1888  VectorCurlCurlIntegrator() { Q = NULL; }
1889 
1890  VectorCurlCurlIntegrator(Coefficient &q) : Q(&q) { }
1891 
1892  /// Assemble an element matrix
1893  virtual void AssembleElementMatrix(const FiniteElement &el,
1894  ElementTransformation &Trans,
1895  DenseMatrix &elmat);
1896  /// Compute element energy: (1/2) (curl u, curl u)_E
1897  virtual double GetElementEnergy(const FiniteElement &el,
1898  ElementTransformation &Tr,
1899  const Vector &elfun);
1900 };
1901 
1902 /// Integrator for (Q u, v) for VectorFiniteElements
1903 class VectorFEMassIntegrator: public BilinearFormIntegrator
1904 {
1905 private:
1906  Coefficient *Q;
1907  VectorCoefficient *VQ;
1908  MatrixCoefficient *MQ;
1909  void Init(Coefficient *q, VectorCoefficient *vq, MatrixCoefficient *mq)
1910  { Q = q; VQ = vq; MQ = mq; }
1911 
1912 #ifndef MFEM_THREAD_SAFE
1913  Vector shape;
1914  Vector D;
1915  DenseMatrix K;
1916  DenseMatrix test_vshape;
1917  DenseMatrix trial_vshape;
1918 #endif
1919 
1920 public:
1921  VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
1922  VectorFEMassIntegrator(Coefficient *_q) { Init(_q, NULL, NULL); }
1923  VectorFEMassIntegrator(Coefficient &q) { Init(&q, NULL, NULL); }
1924  VectorFEMassIntegrator(VectorCoefficient *_vq) { Init(NULL, _vq, NULL); }
1925  VectorFEMassIntegrator(VectorCoefficient &vq) { Init(NULL, &vq, NULL); }
1926  VectorFEMassIntegrator(MatrixCoefficient *_mq) { Init(NULL, NULL, _mq); }
1927  VectorFEMassIntegrator(MatrixCoefficient &mq) { Init(NULL, NULL, &mq); }
1928 
1929  virtual void AssembleElementMatrix(const FiniteElement &el,
1930  ElementTransformation &Trans,
1931  DenseMatrix &elmat);
1932  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1933  const FiniteElement &test_fe,
1934  ElementTransformation &Trans,
1935  DenseMatrix &elmat);
1936 };
1937 
1938 /** Integrator for (Q div u, p) where u=(v1,...,vn) and all vi are in the same
1939  scalar FE space; p is also in a (different) scalar FE space. */
1940 class VectorDivergenceIntegrator : public BilinearFormIntegrator
1941 {
1942 private:
1943  Coefficient *Q;
1944 
1945  Vector shape;
1946  Vector divshape;
1947  DenseMatrix dshape;
1948  DenseMatrix gshape;
1949  DenseMatrix Jadj;
1950 
1951 public:
1952  VectorDivergenceIntegrator() { Q = NULL; }
1953  VectorDivergenceIntegrator(Coefficient *_q) { Q = _q; }
1954  VectorDivergenceIntegrator(Coefficient &q) { Q = &q; }
1955 
1956  virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
1957  const FiniteElement &test_fe,
1958  ElementTransformation &Trans,
1959  DenseMatrix &elmat);
1960 };
1961 
1962 /// (Q div u, div v) for RT elements
1963 class DivDivIntegrator: public BilinearFormIntegrator
1964 {
1965 private:
1966  Coefficient *Q;
1967 
1968 #ifndef MFEM_THREAD_SAFE
1969  Vector divshape;
1970 #endif
1971 
1972 public:
1973  DivDivIntegrator() { Q = NULL; }
1974  DivDivIntegrator(Coefficient &q) : Q(&q) { }
1975 
1976  virtual void AssembleElementMatrix(const FiniteElement &el,
1977  ElementTransformation &Trans,
1978  DenseMatrix &elmat);
1979 };
1980 
1981 /** Integrator for
1982  (Q grad u, grad v) = sum_i (Q grad u_i, grad v_i) e_i e_i^T
1983  for FE spaces defined by 'dim' copies of a scalar FE space. Where e_i
1984  is the unit vector in the i-th direction. The resulting local element
1985  matrix is a block-diagonal matrix consisting of 'dim' copies of a scalar
1986  diffusion matrix in each diagonal block. */
1987 class VectorDiffusionIntegrator : public BilinearFormIntegrator
1988 {
1989 private:
1990  Coefficient *Q;
1991 
1992  DenseMatrix Jinv;
1993  DenseMatrix dshape;
1994  DenseMatrix gshape;
1995  DenseMatrix pelmat;
1996 
1997 public:
1998  VectorDiffusionIntegrator() { Q = NULL; }
1999  VectorDiffusionIntegrator(Coefficient &q) { Q = &q; }
2000 
2001  virtual void AssembleElementMatrix(const FiniteElement &el,
2002  ElementTransformation &Trans,
2003  DenseMatrix &elmat);
2004  virtual void AssembleElementVector(const FiniteElement &el,
2005  ElementTransformation &Tr,
2006  const Vector &elfun, Vector &elvect);
2007 };
2008 
2009 /** Integrator for the linear elasticity form:
2010  a(u,v) = (lambda div(u), div(v)) + (2 mu e(u), e(v)),
2011  where e(v) = (1/2) (grad(v) + grad(v)^T).
2012  This is a 'Vector' integrator, i.e. defined for FE spaces
2013  using multiple copies of a scalar FE space. */
2014 class ElasticityIntegrator : public BilinearFormIntegrator
2015 {
2016 private:
2017  double q_lambda, q_mu;
2018  Coefficient *lambda, *mu;
2019 
2020 #ifndef MFEM_THREAD_SAFE
2021  DenseMatrix dshape, Jinv, gshape, pelmat;
2022  Vector divshape;
2023 #endif
2024 
2025 public:
2026  ElasticityIntegrator(Coefficient &l, Coefficient &m)
2027  { lambda = &l; mu = &m; }
2028  /** With this constructor lambda = q_l * m and mu = q_m * m;
2029  if dim * q_l + 2 * q_m = 0 then trace(sigma) = 0. */
2030  ElasticityIntegrator(Coefficient &m, double q_l, double q_m)
2031  { lambda = NULL; mu = &m; q_lambda = q_l; q_mu = q_m; }
2032 
2033  virtual void AssembleElementMatrix(const FiniteElement &,
2034  ElementTransformation &,
2035  DenseMatrix &);
2036 };
2037 
2038 /** Integrator for the DG form:
2039  alpha < rho_u (u.n) {v},[w] > + beta < rho_u |u.n| [v],[w] >,
2040  where v and w are the trial and test variables, respectively, and rho/u are
2041  given scalar/vector coefficients. The vector coefficient, u, is assumed to
2042  be continuous across the faces and when given the scalar coefficient, rho,
2043  is assumed to be discontinuous. The integrator uses the upwind value of rho,
2044  rho_u, which is value from the side into which the vector coefficient, u,
2045  points. */
2046 class DGTraceIntegrator : public BilinearFormIntegrator
2047 {
2048 private:
2049  Coefficient *rho;
2050  VectorCoefficient *u;
2051  double alpha, beta;
2052 
2053  Vector shape1, shape2;
2054 
2055 public:
2056  /// Construct integrator with rho = 1.
2057  DGTraceIntegrator(VectorCoefficient &_u, double a, double b)
2058  { rho = NULL; u = &_u; alpha = a; beta = b; }
2059 
2060  DGTraceIntegrator(Coefficient &_rho, VectorCoefficient &_u,
2061  double a, double b)
2062  { rho = &_rho; u = &_u; alpha = a; beta = b; }
2063 
2064  using BilinearFormIntegrator::AssembleFaceMatrix;
2065  virtual void AssembleFaceMatrix(const FiniteElement &el1,
2066  const FiniteElement &el2,
2067  FaceElementTransformations &Trans,
2068  DenseMatrix &elmat);
2069 };
2070 
2071 /** Integrator for the DG form:
2072 
2073  - < {(Q grad(u)).n}, [v] > + sigma < [u], {(Q grad(v)).n} >
2074  + kappa < {h^{-1} Q} [u], [v] >,
2075 
2076  where Q is a scalar or matrix diffusion coefficient and u, v are the trial
2077  and test spaces, respectively. The parameters sigma and kappa determine the
2078  DG method to be used (when this integrator is added to the "broken"
2079  DiffusionIntegrator):
2080  * sigma = -1, kappa >= kappa0: symm. interior penalty (IP or SIPG) method,
2081  * sigma = +1, kappa > 0: non-symmetric interior penalty (NIPG) method,
2082  * sigma = +1, kappa = 0: the method of Baumann and Oden. */
2083 class DGDiffusionIntegrator : public BilinearFormIntegrator
2084 {
2085 protected:
2086  Coefficient *Q;
2087  MatrixCoefficient *MQ;
2088  double sigma, kappa;
2089 
2090  // these are not thread-safe!
2091  Vector shape1, shape2, dshape1dn, dshape2dn, nor, nh, ni;
2092  DenseMatrix jmat, dshape1, dshape2, mq, adjJ;
2093 
2094 public:
2095  DGDiffusionIntegrator(const double s, const double k)
2096  : Q(NULL), MQ(NULL), sigma(s), kappa(k) { }
2097  DGDiffusionIntegrator(Coefficient &q, const double s, const double k)
2098  : Q(&q), MQ(NULL), sigma(s), kappa(k) { }
2099  DGDiffusionIntegrator(MatrixCoefficient &q, const double s, const double k)
2100  : Q(NULL), MQ(&q), sigma(s), kappa(k) { }
2101  using BilinearFormIntegrator::AssembleFaceMatrix;
2102  virtual void AssembleFaceMatrix(const FiniteElement &el1,
2103  const FiniteElement &el2,
2104  FaceElementTransformations &Trans,
2105  DenseMatrix &elmat);
2106 };
2107 
2108 /** Integrator for the DG elasticity form, for the formulations see:
2109  - PhD Thesis of Jonas De Basabe, High-Order Finite %Element Methods for
2110  Seismic Wave Propagation, UT Austin, 2009, p. 23, and references therein
2111  - Peter Hansbo and Mats G. Larson, Discontinuous Galerkin and the
2112  Crouzeix-Raviart %Element: Application to Elasticity, PREPRINT 2000-09,
2113  p.3
2114 
2115  \f[
2116  - \left< \{ \tau(u) \}, [v] \right> + \alpha \left< \{ \tau(v) \}, [u]
2117  \right> + \kappa \left< h^{-1} \{ \lambda + 2 \mu \} [u], [v] \right>
2118  \f]
2119 
2120  where \f$ \left<u, v\right> = \int_{F} u \cdot v \f$, and \f$ F \f$ is a
2121  face which is either a boundary face \f$ F_b \f$ of an element \f$ K \f$ or
2122  an interior face \f$ F_i \f$ separating elements \f$ K_1 \f$ and \f$ K_2 \f$.
2123 
2124  In the bilinear form above \f$ \tau(u) \f$ is traction, and it's also
2125  \f$ \tau(u) = \sigma(u) \cdot \vec{n} \f$, where \f$ \sigma(u) \f$ is
2126  stress, and \f$ \vec{n} \f$ is the unit normal vector w.r.t. to \f$ F \f$.
2127 
2128  In other words, we have
2129  \f[
2130  - \left< \{ \sigma(u) \cdot \vec{n} \}, [v] \right> + \alpha \left< \{
2131  \sigma(v) \cdot \vec{n} \}, [u] \right> + \kappa \left< h^{-1} \{
2132  \lambda + 2 \mu \} [u], [v] \right>
2133  \f]
2134 
2135  For isotropic media
2136  \f[
2137  \begin{split}
2138  \sigma(u) &= \lambda \nabla \cdot u I + 2 \mu \varepsilon(u) \\
2139  &= \lambda \nabla \cdot u I + 2 \mu \frac{1}{2} (\nabla u + \nabla
2140  u^T) \\
2141  &= \lambda \nabla \cdot u I + \mu (\nabla u + \nabla u^T)
2142  \end{split}
2143  \f]
2144 
2145  where \f$ I \f$ is identity matrix, \f$ \lambda \f$ and \f$ \mu \f$ are Lame
2146  coefficients (see ElasticityIntegrator), \f$ u, v \f$ are the trial and test
2147  functions, respectively.
2148 
2149  The parameters \f$ \alpha \f$ and \f$ \kappa \f$ determine the DG method to
2150  use (when this integrator is added to the "broken" ElasticityIntegrator):
2151 
2152  - IIPG, \f$\alpha = 0\f$,
2153  C. Dawson, S. Sun, M. Wheeler, Compatible algorithms for coupled flow and
2154  transport, Comp. Meth. Appl. Mech. Eng., 193(23-26), 2565-2580, 2004.
2155 
2156  - SIPG, \f$\alpha = -1\f$,
2157  M. Grote, A. Schneebeli, D. Schotzau, Discontinuous Galerkin Finite
2158  %Element Method for the Wave Equation, SINUM, 44(6), 2408-2431, 2006.
2159 
2160  - NIPG, \f$\alpha = 1\f$,
2161  B. Riviere, M. Wheeler, V. Girault, A Priori Error Estimates for Finite
2162  %Element Methods Based on Discontinuous Approximation Spaces for Elliptic
2163  Problems, SINUM, 39(3), 902-931, 2001.
2164 
2165  This is a '%Vector' integrator, i.e. defined for FE spaces using multiple
2166  copies of a scalar FE space.
2167  */
2168 class DGElasticityIntegrator : public BilinearFormIntegrator
2169 {
2170 public:
2171  DGElasticityIntegrator(double alpha_, double kappa_)
2172  : lambda(NULL), mu(NULL), alpha(alpha_), kappa(kappa_) { }
2173 
2174  DGElasticityIntegrator(Coefficient &lambda_, Coefficient &mu_,
2175  double alpha_, double kappa_)
2176  : lambda(&lambda_), mu(&mu_), alpha(alpha_), kappa(kappa_) { }
2177 
2178  using BilinearFormIntegrator::AssembleFaceMatrix;
2179  virtual void AssembleFaceMatrix(const FiniteElement &el1,
2180  const FiniteElement &el2,
2181  FaceElementTransformations &Trans,
2182  DenseMatrix &elmat);
2183 
2184 protected:
2185  Coefficient *lambda, *mu;
2186  double alpha, kappa;
2187 
2188 #ifndef MFEM_THREAD_SAFE
2189  // values of all scalar basis functions for one component of u (which is a
2190  // vector) at the integration point in the reference space
2191  Vector shape1, shape2;
2192  // values of derivatives of all scalar basis functions for one component
2193  // of u (which is a vector) at the integration point in the reference space
2194  DenseMatrix dshape1, dshape2;
2195  // Adjugate of the Jacobian of the transformation: adjJ = det(J) J^{-1}
2196  DenseMatrix adjJ;
2197  // gradient of shape functions in the real (physical, not reference)
2198  // coordinates, scaled by det(J):
2199  // dshape_ps(jdof,jm) = sum_{t} adjJ(t,jm)*dshape(jdof,t)
2200  DenseMatrix dshape1_ps, dshape2_ps;
2201  Vector nor; // nor = |weight(J_face)| n
2202  Vector nL1, nL2; // nL1 = (lambda1 * ip.weight / detJ1) nor
2203  Vector nM1, nM2; // nM1 = (mu1 * ip.weight / detJ1) nor
2204  Vector dshape1_dnM, dshape2_dnM; // dshape1_dnM = dshape1_ps . nM1
2205  // 'jmat' corresponds to the term: kappa <h^{-1} {lambda + 2 mu} [u], [v]>
2206  DenseMatrix jmat;
2207 #endif
2208 
2209  static void AssembleBlock(
2210  const int dim, const int row_ndofs, const int col_ndofs,
2211  const int row_offset, const int col_offset,
2212  const double jmatcoef, const Vector &col_nL, const Vector &col_nM,
2213  const Vector &row_shape, const Vector &col_shape,
2214  const Vector &col_dshape_dnM, const DenseMatrix &col_dshape,
2215  DenseMatrix &elmat, DenseMatrix &jmat);
2216 };
2217 
2218 /** Integrator for the DPG form: < v, [w] > over all faces (the interface) where
2219  the trial variable v is defined on the interface and the test variable w is
2220  defined inside the elements, generally in a DG space. */
2221 class TraceJumpIntegrator : public BilinearFormIntegrator
2222 {
2223 private:
2224  Vector face_shape, shape1, shape2;
2225 
2226 public:
2227  TraceJumpIntegrator() { }
2228  using BilinearFormIntegrator::AssembleFaceMatrix;
2229  virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe,
2230  const FiniteElement &test_fe1,
2231  const FiniteElement &test_fe2,
2232  FaceElementTransformations &Trans,
2233  DenseMatrix &elmat);
2234 };
2235 
2236 /** Integrator for the form: < v, [w.n] > over all faces (the interface) where
2237  the trial variable v is defined on the interface and the test variable w is
2238  in an H(div)-conforming space. */
2239 class NormalTraceJumpIntegrator : public BilinearFormIntegrator
2240 {
2241 private:
2242  Vector face_shape, normal, shape1_n, shape2_n;
2243  DenseMatrix shape1, shape2;
2244 
2245 public:
2246  NormalTraceJumpIntegrator() { }
2247  using BilinearFormIntegrator::AssembleFaceMatrix;
2248  virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe,
2249  const FiniteElement &test_fe1,
2250  const FiniteElement &test_fe2,
2251  FaceElementTransformations &Trans,
2252  DenseMatrix &elmat);
2253 };
2254 
2255 /** Abstract class to serve as a base for local interpolators to be used in the
2256  DiscreteLinearOperator class. */
2257 class DiscreteInterpolator : public BilinearFormIntegrator { };
2258 
2259 
2260 /** Class for constructing the gradient as a DiscreteLinearOperator from an
2261  H1-conforming space to an H(curl)-conforming space. The range space can be
2262  vector L2 space as well. */
2263 class GradientInterpolator : public DiscreteInterpolator
2264 {
2265 public:
2266  virtual void AssembleElementMatrix2(const FiniteElement &h1_fe,
2267  const FiniteElement &nd_fe,
2268  ElementTransformation &Trans,
2269  DenseMatrix &elmat)
2270  { nd_fe.ProjectGrad(h1_fe, Trans, elmat); }
2271 };
2272 
2273 
2274 /** Class for constructing the identity map as a DiscreteLinearOperator. This
2275  is the discrete embedding matrix when the domain space is a subspace of
2276  the range space. Otherwise, a dof projection matrix is constructed. */
2277 class IdentityInterpolator : public DiscreteInterpolator
2278 {
2279 public:
2280  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2281  const FiniteElement &ran_fe,
2282  ElementTransformation &Trans,
2283  DenseMatrix &elmat)
2284  { ran_fe.Project(dom_fe, Trans, elmat); }
2285 };
2286 
2287 
2288 /** Class for constructing the (local) discrete curl matrix which can be used
2289  as an integrator in a DiscreteLinearOperator object to assemble the global
2290  discrete curl matrix. */
2291 class CurlInterpolator : public DiscreteInterpolator
2292 {
2293 public:
2294  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2295  const FiniteElement &ran_fe,
2296  ElementTransformation &Trans,
2297  DenseMatrix &elmat)
2298  { ran_fe.ProjectCurl(dom_fe, Trans, elmat); }
2299 };
2300 
2301 
2302 /** Class for constructing the (local) discrete divergence matrix which can
2303  be used as an integrator in a DiscreteLinearOperator object to assemble
2304  the global discrete divergence matrix.
2305 
2306  Note: Since the dofs in the L2_FECollection are nodal values, the local
2307  discrete divergence matrix (with an RT-type domain space) will depend on
2308  the transformation. On the other hand, the local matrix returned by
2309  VectorFEDivergenceIntegrator is independent of the transformation. */
2310 class DivergenceInterpolator : public DiscreteInterpolator
2311 {
2312 public:
2313  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2314  const FiniteElement &ran_fe,
2315  ElementTransformation &Trans,
2316  DenseMatrix &elmat)
2317  { ran_fe.ProjectDiv(dom_fe, Trans, elmat); }
2318 };
2319 
2320 
2321 /** A trace face interpolator class for interpolating the normal component of
2322  the domain space, e.g. vector H1, into the range space, e.g. the trace of
2323  RT which uses FiniteElement::INTEGRAL map type. */
2324 class NormalInterpolator : public DiscreteInterpolator
2325 {
2326 public:
2327  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2328  const FiniteElement &ran_fe,
2329  ElementTransformation &Trans,
2330  DenseMatrix &elmat);
2331 };
2332 
2333 /** Interpolator of a scalar coefficient multiplied by a scalar field onto
2334  another scalar field. Note that this can produce inaccurate fields unless
2335  the target is sufficiently high order. */
2336 class ScalarProductInterpolator : public DiscreteInterpolator
2337 {
2338 public:
2339  ScalarProductInterpolator(Coefficient & sc) : Q(sc) { }
2340 
2341  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2342  const FiniteElement &ran_fe,
2343  ElementTransformation &Trans,
2344  DenseMatrix &elmat);
2345 
2346 protected:
2347  Coefficient &Q;
2348 };
2349 
2350 /** Interpolator of a scalar coefficient multiplied by a vector field onto
2351  another vector field. Note that this can produce inaccurate fields unless
2352  the target is sufficiently high order. */
2353 class ScalarVectorProductInterpolator : public DiscreteInterpolator
2354 {
2355 public:
2356  ScalarVectorProductInterpolator(Coefficient & sc)
2357  : Q(sc) { }
2358 
2359  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2360  const FiniteElement &ran_fe,
2361  ElementTransformation &Trans,
2362  DenseMatrix &elmat);
2363 protected:
2364  Coefficient &Q;
2365 };
2366 
2367 /** Interpolator of a vector coefficient multiplied by a scalar field onto
2368  another vector field. Note that this can produce inaccurate fields unless
2369  the target is sufficiently high order. */
2370 class VectorScalarProductInterpolator : public DiscreteInterpolator
2371 {
2372 public:
2373  VectorScalarProductInterpolator(VectorCoefficient & vc)
2374  : VQ(vc) { }
2375 
2376  virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
2377  const FiniteElement &ran_fe,
2378  ElementTransformation &Trans,
2379  DenseMatrix &elmat);
2380 protected:
2381  VectorCoefficient &VQ;
2382 };
2383 
2384 /** Interpolator of the cross product between a vector coefficient and an
2385  H(curl)-conforming field onto an H(div)-conforming field. The range space
2386  can also be vector L2. */
2387 class VectorCrossProductInterpolator : public DiscreteInterpolator
2388 {
2389 public:
2390  VectorCrossProductInterpolator(VectorCoefficient & vc)
2391  : VQ(vc) { }
2392 
2393  virtual void AssembleElementMatrix2(const FiniteElement &nd_fe,
2394  const FiniteElement &rt_fe,
2395  ElementTransformation &Trans,
2396  DenseMatrix &elmat);
2397 protected:
2398  VectorCoefficient &VQ;
2399 };
2400 
2401 /** Interpolator of the inner product between a vector coefficient and an
2402  H(div)-conforming field onto an L2-conforming field. The range space can
2403  also be H1. */
2404 class VectorInnerProductInterpolator : public DiscreteInterpolator
2405 {
2406 public:
2407  VectorInnerProductInterpolator(VectorCoefficient & vc) : VQ(vc) { }
2408 
2409  virtual void AssembleElementMatrix2(const FiniteElement &rt_fe,
2410  const FiniteElement &l2_fe,
2411  ElementTransformation &Trans,
2412  DenseMatrix &elmat);
2413 protected:
2414  VectorCoefficient &VQ;
2415 };
2416 
2417 }
2418 
2419 #endif
mfem::FiniteElement
Abstract class for Finite Elements.
Definition: fe.hpp:140
mfem::VectorFECurlIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.hpp:1813
mfem::MixedDivGradIntegrator::CalcVShape
virtual void CalcVShape(const FiniteElement &vector_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1378
mfem::MixedScalarWeakDerivativeIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:464
mfem::MixedScalarIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &elmat)
Support for use in BilinearForm. Can be used only when appropriate.
Definition: bilininteg.hpp:184
mfem::MixedCrossGradGradIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:857
mfem::MixedVectorIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &elmat)
Support for use in BilinearForm. Can be used only when appropriate.
Definition: bilininteg.hpp:251
mfem::MixedCrossGradCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1000
mfem::VectorFEMassIntegrator::VectorFEMassIntegrator
VectorFEMassIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1923
mfem::TransposeIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:65
mfem::MixedCrossCurlGradIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:963
mfem::FiniteElement::GetDim
int GetDim() const
Returns the reference space dimension for the finite element.
Definition: fe.hpp:211
mfem::DerivativeIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.hpp:1833
mfem::MixedScalarCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:619
mfem::IntegrationRule
Class for an integration rule - an Array of IntegrationPoint.
Definition: intrules.hpp:83
mfem::MixedScalarWeakGradientIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:590
mfem::MixedCrossCurlGradIntegrator::MixedCrossCurlGradIntegrator
MixedCrossCurlGradIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:960
mfem::DGTraceIntegrator::DGTraceIntegrator
DGTraceIntegrator(VectorCoefficient &_u, double a, double b)
Construct integrator with rho = 1.
Definition: bilininteg.hpp:2057
mfem::MixedGradDivIntegrator::MixedGradDivIntegrator
MixedGradDivIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1321
mfem::MixedVectorCurlIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1491
mfem::DGDiffusionIntegrator::DGDiffusionIntegrator
DGDiffusionIntegrator(Coefficient &q, const double s, const double k)
Definition: bilininteg.hpp:2097
mfem::SumIntegrator
Integrator defining a sum of multiple Integrators.
Definition: bilininteg.hpp:152
mfem::SumIntegrator::SumIntegrator
SumIntegrator(int own_integs=1)
Definition: bilininteg.hpp:160
mfem::MixedVectorGradientIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1434
mfem::VectorFEMassIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:1718
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:40
mfem::MixedDivGradIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1371
mfem::MixedScalarCrossGradIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1218
mfem::DiffusionIntegrator::DiffusionIntegrator
DiffusionIntegrator(Coefficient &q)
Construct a diffusion integrator with a scalar coefficient q.
Definition: bilininteg.hpp:1595
mfem::MixedVectorIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:272
mfem::MixedScalarCrossProductIntegrator::MixedScalarCrossProductIntegrator
MixedScalarCrossProductIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1236
mfem::CurlCurlIntegrator::CurlCurlIntegrator
CurlCurlIntegrator(MatrixCoefficient &m)
Definition: bilininteg.hpp:1859
mfem::MixedCrossGradGradIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:864
mfem::FiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:171
mfem::MixedWeakCurlCrossIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1048
mfem::VectorFEDivergenceIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1125
mfem::MixedCrossCurlGradIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:981
mfem::MixedScalarVectorIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:367
mfem::DivDivIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:2015
mfem::FiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:124
mfem::MixedVectorWeakDivergenceIntegrator::MixedVectorWeakDivergenceIntegrator
MixedVectorWeakDivergenceIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:1547
mfem::CurlCurlIntegrator::ComputeFluxEnergy
virtual double ComputeFluxEnergy(const FiniteElement &fluxelem, ElementTransformation &Trans, Vector &flux, Vector *d_energy=NULL)
Definition: bilininteg.cpp:1499
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:61
mfem::MixedWeakGradDotIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:750
mfem::ElasticityIntegrator::ElasticityIntegrator
ElasticityIntegrator(Coefficient &l, Coefficient &m)
Definition: bilininteg.hpp:2026
mfem::VectorFEMassIntegrator::VectorFEMassIntegrator
VectorFEMassIntegrator(VectorCoefficient *_vq)
Definition: bilininteg.hpp:1924
mfem::VectorDiffusionIntegrator::VectorDiffusionIntegrator
VectorDiffusionIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1999
mfem::VectorFEWeakDivergenceIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1164
mfem::MixedScalarIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:218
mfem::MixedScalarDerivativeIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:445
mfem::CurlCurlIntegrator
Integrator for (curl u, curl v) for Nedelec elements.
Definition: bilininteg.hpp:1844
mfem::VectorDivergenceIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1960
mfem::VectorCurlCurlIntegrator::VectorCurlCurlIntegrator
VectorCurlCurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1890
mfem::MixedScalarWeakDerivativeIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:481
mfem::MixedCrossCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1152
mfem::DGElasticityIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:2669
mfem::MixedScalarMassIntegrator::MixedScalarMassIntegrator
MixedScalarMassIntegrator(Coefficient &q)
Definition: bilininteg.hpp:405
mfem::VectorMassIntegrator::VectorMassIntegrator
VectorMassIntegrator(Coefficient &q, const IntegrationRule *ir)
Definition: bilininteg.hpp:1728
mfem::MixedGradGradIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:833
mfem::GroupConvectionIntegrator
alpha (q . grad u, v) using the &quot;group&quot; FE discretization
Definition: bilininteg.hpp:1687
mfem::VectorMassIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:957
mfem::FiniteElement::GetOrder
int GetOrder() const
Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order...
Definition: fe.hpp:221
mfem::VectorFEMassIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1783
mfem::MixedScalarWeakGradientIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:575
mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition: densemat.hpp:23
mfem::DivDivIntegrator::DivDivIntegrator
DivDivIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1974
mfem::Vector::Size
int Size() const
Returns the size of the vector.
Definition: vector.hpp:120
mfem::MixedCrossCurlIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1159
mfem::MixedVectorWeakCurlIntegrator::MixedVectorWeakCurlIntegrator
MixedVectorWeakCurlIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:1510
mfem::MixedDivGradIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:1383
mfem::MixedScalarWeakDivergenceIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1406
mfem::MixedCurlCurlIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:912
mfem::TransposeIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:82
mfem::LumpedIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:91
mfem::BilinearFormIntegrator::BilinearFormIntegrator
BilinearFormIntegrator(const IntegrationRule *ir=NULL)
Definition: bilininteg.hpp:25
mfem::FiniteElement::Space
int Space() const
Returns the type of space on each element.
Definition: fe.hpp:231
mfem::SumIntegrator::AddIntegrator
void AddIntegrator(BilinearFormIntegrator *integ)
Definition: bilininteg.hpp:162
mfem::MixedGradGradIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:811
mfem::MixedVectorCurlIntegrator::MixedVectorCurlIntegrator
MixedVectorCurlIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:1469
mfem::MixedScalarIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:223
mfem::FunctionSpace::Pk
Polynomials of order k.
Definition: fe.hpp:127
mfem::BilinearFormIntegrator::ComputeFluxEnergy
virtual double ComputeFluxEnergy(const FiniteElement &fluxelem, ElementTransformation &Trans, Vector &flux, Vector *d_energy=NULL)
Definition: bilininteg.hpp:78
mfem::MixedCrossProductIntegrator::MixedCrossProductIntegrator
MixedCrossProductIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:696
mfem::MixedScalarVectorIntegrator::MixedScalarVectorIntegrator
MixedScalarVectorIntegrator(VectorCoefficient &vq, bool _transpose=false, bool _cross_2d=false)
Definition: bilininteg.hpp:334
mfem::VectorFEDivergenceIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.hpp:1765
mfem::FiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:155
mfem::Vector::GetData
double * GetData() const
Return a pointer to the beginning of the Vector data.
Definition: vector.hpp:129
mfem::MixedVectorGradientIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1449
mfem::FiniteElement::DIV
Implements CalcDivShape methods.
Definition: fe.hpp:197
mfem::MixedVectorGradientIntegrator::MixedVectorGradientIntegrator
MixedVectorGradientIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1426
mfem::DivDivIntegrator
(Q div u, div v) for RT elements
Definition: bilininteg.hpp:1963
mfem::MixedWeakGradDotIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:734
mfem::MixedScalarVectorIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:351
mfem::MixedScalarCrossGradIntegrator::MixedScalarCrossGradIntegrator
MixedScalarCrossGradIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1205
mfem::MixedGradGradIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:828
mfem::DiffusionIntegrator::ComputeElementFlux
virtual void ComputeElementFlux(const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, int with_coef=1)
Definition: bilininteg.cpp:595
mfem::BoundaryMassIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:811
mfem::MixedGradGradIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:801
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:75
mfem::MixedScalarWeakDivergenceIntegrator::CalcVShape
virtual void CalcVShape(const FiniteElement &vector_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1413
mfem::MixedScalarIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:129
mfem::MixedWeakCurlCrossIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1055
mfem::MixedCurlCurlIntegrator::MixedCurlCurlIntegrator
MixedCurlCurlIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:886
mfem::DGDiffusionIntegrator::MQ
MatrixCoefficient * MQ
Definition: bilininteg.hpp:2087
mfem::VectorFEMassIntegrator::VectorFEMassIntegrator
VectorFEMassIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1925
mfem::VectorMassIntegrator::VectorMassIntegrator
VectorMassIntegrator()
Construct an integrator with coefficient 1.0.
Definition: bilininteg.hpp:1720
mfem::MixedScalarCrossCurlIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:1191
mfem::VectorMassIntegrator::VectorMassIntegrator
VectorMassIntegrator(VectorCoefficient &q, int qo=0)
Construct an integrator with diagonal coefficient q.
Definition: bilininteg.hpp:1732
mfem::VectorCrossProductInterpolator::VectorCrossProductInterpolator
VectorCrossProductInterpolator(VectorCoefficient &vc)
Definition: bilininteg.hpp:2390
mfem::MixedVectorWeakCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1514
mfem::MixedScalarIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:198
mfem::MixedScalarWeakDivergenceIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1397
mfem::MixedScalarVectorIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:378
mfem::MixedScalarVectorIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:297
mfem::ScalarProductInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:3051
mfem::IdentityInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.hpp:2280
mfem::TransposeIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:73
mfem::MixedGradGradIntegrator::MixedGradGradIntegrator
MixedGradGradIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:796
mfem::InverseIntegrator
Integrator that inverts the matrix assembled by another integrator.
Definition: bilininteg.hpp:134
mfem::FiniteElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:163
mfem::MixedCrossGradIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1127
mfem::ElasticityIntegrator::ElasticityIntegrator
ElasticityIntegrator(Coefficient &m, double q_l, double q_m)
Definition: bilininteg.hpp:2030
mfem::MixedCrossGradIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1115
mfem::NormalTraceJumpIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe, const FiniteElement &test_fe1, const FiniteElement &test_fe2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:2936
mfem::MixedScalarCrossCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1184
mfem::FiniteElement::CURL
Implements CalcCurlShape methods.
Definition: fe.hpp:198
mfem::MixedGradDivIntegrator::CalcVShape
virtual void CalcVShape(const FiniteElement &vector_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1341
mfem::CurlCurlIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:1411
mfem::MassIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:721
mfem::VectorInnerProductInterpolator::VectorInnerProductInterpolator
VectorInnerProductInterpolator(VectorCoefficient &vc)
Definition: bilininteg.hpp:2407
mfem::MixedWeakDivCrossIntegrator::MixedWeakDivCrossIntegrator
MixedWeakDivCrossIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:761
mfem::MixedDirectionalDerivativeIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1303
mfem::MixedGradDivIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1334
dim
int dim
Definition: ex3.cpp:47
mfem::VectorDivergenceIntegrator::VectorDivergenceIntegrator
VectorDivergenceIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1954
mfem::MixedCrossCurlCurlIntegrator::MixedCrossCurlCurlIntegrator
MixedCrossCurlCurlIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:923
mfem::InverseIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:98
mfem::MixedCrossCurlGradIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:986
mfem::MixedWeakCurlCrossIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1038
mfem::MixedVectorWeakCurlIntegrator::MixedVectorWeakCurlIntegrator
MixedVectorWeakCurlIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:1508
mfem::MixedScalarWeakCurlIntegrator::MixedScalarWeakCurlIntegrator
MixedScalarWeakCurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:647
mfem::MixedCurlCurlIntegrator::MixedCurlCurlIntegrator
MixedCurlCurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:882
mfem::MixedScalarDivergenceIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:502
mfem::SumIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:105
mfem::MixedVectorGradientIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1442
mfem::BilinearFormIntegrator::AssembleElementGrad
virtual void AssembleElementGrad(const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, DenseMatrix &elmat)
Assemble the local gradient matrix.
Definition: bilininteg.hpp:61
mfem::VectorFEDivergenceIntegrator::VectorFEDivergenceIntegrator
VectorFEDivergenceIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1764
mfem::MixedCurlCurlIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:907
mfem::MixedWeakDivCrossIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:764
mfem::MixedDirectionalDerivativeIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1294
mfem::VectorFECurlIntegrator::VectorFECurlIntegrator
VectorFECurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1812
mfem::FiniteElement::GRAD
Implements CalcDShape methods.
Definition: fe.hpp:196
mfem::GradientInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &h1_fe, const FiniteElement &nd_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.hpp:2266
mfem::MixedVectorWeakCurlIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1530
mfem::BilinearFormIntegrator::ComputeElementFlux
virtual void ComputeElementFlux(const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, int with_coef=1)
Definition: bilininteg.hpp:72
mfem::MixedVectorIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:280
mfem::DiffusionIntegrator::DiffusionIntegrator
DiffusionIntegrator()
Construct a diffusion integrator with coefficient Q = 1.
Definition: bilininteg.hpp:1592
mfem::MixedVectorMassIntegrator::MixedVectorMassIntegrator
MixedVectorMassIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:687
mfem::VectorDiffusionIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:2059
mfem::MixedScalarDivergenceIntegrator::MixedScalarDivergenceIntegrator
MixedScalarDivergenceIntegrator(Coefficient &q)
Definition: bilininteg.hpp:498
mfem::MixedVectorIntegrator::MixedVectorIntegrator
MixedVectorIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:269
mfem::MixedVectorIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:292
mfem::MixedVectorMassIntegrator::MixedVectorMassIntegrator
MixedVectorMassIntegrator(Coefficient &q)
Definition: bilininteg.hpp:683
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:189
mfem::MixedScalarWeakCrossProductIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1264
mfem::MixedDirectionalDerivativeIntegrator::MixedDirectionalDerivativeIntegrator
MixedDirectionalDerivativeIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1291
mfem::VectorFEWeakDivergenceIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.hpp:1790
mfem::MixedCrossGradIntegrator::MixedCrossGradIntegrator
MixedCrossGradIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1102
mfem::MixedVectorDivergenceIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:553
mfem::ScalarProductInterpolator::ScalarProductInterpolator
ScalarProductInterpolator(Coefficient &sc)
Definition: bilininteg.hpp:2339
mfem::MixedVectorWeakCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1523
mfem::MixedScalarWeakCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:651
mfem::VectorMassIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1038
mfem::MixedCrossCurlCurlIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:944
mfem::MixedVectorCurlIntegrator::MixedVectorCurlIntegrator
MixedVectorCurlIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:1471
mfem::MixedCurlCurlIntegrator::MixedCurlCurlIntegrator
MixedCurlCurlIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:884
mfem::MixedScalarWeakCurlIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:667
mfem::MixedScalarDivergenceIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:510
mfem::BoundaryMassIntegrator::BoundaryMassIntegrator
BoundaryMassIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1657
mfem::GroupConvectionIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &, ElementTransformation &, DenseMatrix &)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:903
mfem::MixedCurlCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:889
mfem::BilinearFormIntegrator::AssembleElementVector
virtual void AssembleElementVector(const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, Vector &elvect)
Perform the local action of the BilinearFormIntegrator.
Definition: bilininteg.cpp:56
mfem::MixedScalarWeakCurlCrossIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:1087
mfem::DiffusionIntegrator::AssembleElementVector
virtual void AssembleElementVector(const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, Vector &elvect)
Perform the local action of the BilinearFormIntegrator.
Definition: bilininteg.cpp:517
mfem::MixedWeakGradDotIntegrator::MixedWeakGradDotIntegrator
MixedWeakGradDotIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:731
mfem::ScalarVectorProductInterpolator::ScalarVectorProductInterpolator
ScalarVectorProductInterpolator(Coefficient &sc)
Definition: bilininteg.hpp:2356
mfem::MixedDotProductIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:717
mfem::MixedVectorDivergenceIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:558
mfem::BilinearFormIntegrator
Abstract base class BilinearFormIntegrator.
Definition: bilininteg.hpp:22
mfem::MixedGradDivIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:1346
mfem::MixedVectorIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:297
mfem::NormalInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:3024
mfem::VectorDivergenceIntegrator::VectorDivergenceIntegrator
VectorDivergenceIntegrator(Coefficient *_q)
Definition: bilininteg.hpp:1953
mfem::MixedVectorIntegrator::MixedVectorIntegrator
MixedVectorIntegrator(Coefficient &q)
Definition: bilininteg.hpp:264
mfem::DiffusionIntegrator::DiffusionIntegrator
DiffusionIntegrator(MatrixCoefficient &q)
Construct a diffusion integrator with a matrix coefficient q.
Definition: bilininteg.hpp:1598
mfem::MixedScalarCrossGradIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1208
mfem::MixedScalarWeakCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:660
mfem::MixedScalarCrossCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1174
mfem::MixedDivGradIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1360
mfem::MixedGradGradIntegrator::MixedGradGradIntegrator
MixedGradGradIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:798
mfem::ConvectionIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &, ElementTransformation &, DenseMatrix &)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:855
mfem::VectorFEMassIntegrator::VectorFEMassIntegrator
VectorFEMassIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:1927
mfem::MixedVectorMassIntegrator::MixedVectorMassIntegrator
MixedVectorMassIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:685
mfem::MixedScalarWeakCurlCrossIntegrator::MixedScalarWeakCurlCrossIntegrator
MixedScalarWeakCurlCrossIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1067
mfem::MixedScalarCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:610
mfem::MixedCrossGradCurlIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1023
mfem::Coefficient
Base class Coefficient that may optionally depend on time.
Definition: coefficient.hpp:31
mfem::BilinearFormIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:23
mfem::MixedVectorDivergenceIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:538
mfem::MixedCrossGradIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1122
mfem::VectorFECurlIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1246
mfem::MixedVectorWeakDivergenceIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1561
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:179
mfem::MixedScalarCrossProductIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1248
mfem::VectorScalarProductInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:3121
mfem::MixedScalarWeakDivergenceIntegrator::MixedScalarWeakDivergenceIntegrator
MixedScalarWeakDivergenceIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1394
mfem::DiffusionIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:437
mfem::DGDiffusionIntegrator::DGDiffusionIntegrator
DGDiffusionIntegrator(const double s, const double k)
Definition: bilininteg.hpp:2095
mfem::MixedWeakDivCrossIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:781
mfem::LumpedIntegrator::LumpedIntegrator
LumpedIntegrator(BilinearFormIntegrator *_bfi, int _own_bfi=1)
Definition: bilininteg.hpp:123
mfem::MixedCrossGradCurlIntegrator::MixedCrossGradCurlIntegrator
MixedCrossGradCurlIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:997
mfem::MixedVectorDivergenceIntegrator::MixedVectorDivergenceIntegrator
MixedVectorDivergenceIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:534
mfem::MassIntegrator::MassIntegrator
MassIntegrator(Coefficient &q, const IntegrationRule *ir=NULL)
Construct a mass integrator with coefficient q.
Definition: bilininteg.hpp:1640
mfem::DGDiffusionIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:2391
mfem::DerivativeIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:1343
mfem::MixedScalarIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:206
mfem::MixedCrossGradGradIntegrator::MixedCrossGradGradIntegrator
MixedCrossGradGradIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:844
mfem::MixedScalarDivergenceIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:517
mfem::MixedCrossCurlCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:926
mfem::MixedVectorIntegrator::MixedVectorIntegrator
MixedVectorIntegrator(VectorCoefficient &dq, bool diag=true)
Definition: bilininteg.hpp:266
mfem::MixedScalarCrossCurlIntegrator::MixedScalarCrossCurlIntegrator
MixedScalarCrossCurlIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1171
mfem::VectorCurlCurlIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Assemble an element matrix.
Definition: bilininteg.cpp:1604
mfem::BilinearFormIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:39
mfem::MixedScalarWeakGradientIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:583
mfem::MixedWeakGradDotIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:743
mfem::MixedWeakDivCrossIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:774
mfem::VectorMassIntegrator::VectorMassIntegrator
VectorMassIntegrator(Coefficient &q, int qo=0)
Definition: bilininteg.hpp:1726
mfem::VectorFEMassIntegrator::VectorFEMassIntegrator
VectorFEMassIntegrator(Coefficient *_q)
Definition: bilininteg.hpp:1922
mfem::DGElasticityIntegrator::DGElasticityIntegrator
DGElasticityIntegrator(double alpha_, double kappa_)
Definition: bilininteg.hpp:2171
mfem::MixedScalarDerivativeIntegrator::MixedScalarDerivativeIntegrator
MixedScalarDerivativeIntegrator(Coefficient &q)
Definition: bilininteg.hpp:425
mfem::CurlInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.hpp:2294
mfem::VectorFEMassIntegrator::VectorFEMassIntegrator
VectorFEMassIntegrator(MatrixCoefficient *_mq)
Definition: bilininteg.hpp:1926
mfem::MixedDotProductIntegrator::MixedDotProductIntegrator
MixedDotProductIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:706
mfem::MixedCrossGradCurlIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1018
mfem::MixedVectorCurlIntegrator::MixedVectorCurlIntegrator
MixedVectorCurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1467
mfem::MixedWeakCurlCrossIntegrator::MixedWeakCurlCrossIntegrator
MixedWeakCurlCrossIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1035
mfem::MixedVectorCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1475
mfem::MixedScalarCrossGradIntegrator::CalcVShape
virtual void CalcVShape(const FiniteElement &vector_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1225
mfem::MixedScalarWeakDerivativeIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:473
mfem::MixedVectorWeakDivergenceIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1568
mfem::MixedScalarCrossProductIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1239
mfem::MassIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:767
mfem::MixedCrossCurlIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1142
mfem::MixedGradDivIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1324
mfem::VectorCrossProductInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &nd_fe, const FiniteElement &rt_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:3159
mfem::MixedVectorIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:188
mfem::VectorMassIntegrator::VectorMassIntegrator
VectorMassIntegrator(MatrixCoefficient &q, int qo=0)
Construct an integrator with matrix coefficient q.
Definition: bilininteg.hpp:1735
mfem::MixedScalarWeakCrossProductIntegrator::MixedScalarWeakCrossProductIntegrator
MixedScalarWeakCrossProductIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1261
mfem::MixedCrossGradIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1105
mfem::ElasticityIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &, ElementTransformation &, DenseMatrix &)
Given a particular Finite Element computes the element matrix elmat.
Definition: bilininteg.cpp:2176
mfem::MixedVectorIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:286
mfem::GroupConvectionIntegrator::GroupConvectionIntegrator
GroupConvectionIntegrator(VectorCoefficient &q, double a=1.0)
Definition: bilininteg.hpp:1696
mfem::MixedScalarVectorIntegrator::CalcVShape
virtual void CalcVShape(const FiniteElement &vector_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:373
mfem::MixedDirectionalDerivativeIntegrator::CalcVShape
virtual void CalcVShape(const FiniteElement &vector_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:1310
mfem::MixedCrossGradGradIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:869
mfem::MixedVectorGradientIntegrator::MixedVectorGradientIntegrator
MixedVectorGradientIntegrator(VectorCoefficient &dq)
Definition: bilininteg.hpp:1428
mfem::DGElasticityIntegrator::AssembleBlock
static void AssembleBlock(const int dim, const int row_ndofs, const int col_ndofs, const int row_offset, const int col_offset, const double jmatcoef, const Vector &col_nL, const Vector &col_nM, const Vector &row_shape, const Vector &col_shape, const Vector &col_dshape_dnM, const DenseMatrix &col_dshape, DenseMatrix &elmat, DenseMatrix &jmat)
Definition: bilininteg.cpp:2626
mfem::MixedScalarWeakCrossProductIntegrator::CalcShape
virtual void CalcShape(const FiniteElement &scalar_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:1280
mfem::SumIntegrator::~SumIntegrator
virtual ~SumIntegrator()
Definition: bilininteg.cpp:118
mfem::MixedScalarWeakCrossProductIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1273
mfem::VectorDiffusionIntegrator::AssembleElementVector
virtual void AssembleElementVector(const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, Vector &elvect)
Perform the local action of the BilinearFormIntegrator.
Definition: bilininteg.cpp:2125
mfem::MixedVectorWeakDivergenceIntegrator::MixedVectorWeakDivergenceIntegrator
MixedVectorWeakDivergenceIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:1549
mfem::MixedScalarWeakCurlCrossIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1070
mfem::VectorInnerProductInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &rt_fe, const FiniteElement &l2_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:3213
mfem::MixedVectorWeakDivergenceIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:1553
mfem::MixedScalarDerivativeIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:438
mfem::MixedCurlCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:900
mfem::MixedScalarWeakCurlCrossIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1080
mfem::DGDiffusionIntegrator::DGDiffusionIntegrator
DGDiffusionIntegrator(MatrixCoefficient &q, const double s, const double k)
Definition: bilininteg.hpp:2099
mfem::MixedScalarCurlIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:631
mfem::VectorCurlCurlIntegrator::GetElementEnergy
virtual double GetElementEnergy(const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun)
Compute element energy: (1/2) (curl u, curl u)_E.
Definition: bilininteg.cpp:1652
mfem::BilinearFormIntegrator::AssembleFaceGrad
virtual void AssembleFaceGrad(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, DenseMatrix &elmat)
Assemble the local action of the gradient of the NonlinearFormIntegrator resulting from a face integr...
Definition: bilininteg.hpp:66
mfem::MixedCrossCurlIntegrator::MixedCrossCurlIntegrator
MixedCrossCurlIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1139
mfem::Vector
Vector data type.
Definition: vector.hpp:48
mfem::FiniteElement::GetDerivType
int GetDerivType() const
Definition: fe.hpp:239
mfem::ScalarVectorProductInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:3086
mfem::MixedVectorDivergenceIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:546
mfem::MixedVectorProductIntegrator::MixedVectorProductIntegrator
MixedVectorProductIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:415
mfem::VectorScalarProductInterpolator::VectorScalarProductInterpolator
VectorScalarProductInterpolator(VectorCoefficient &vc)
Definition: bilininteg.hpp:2373
mfem::MixedCrossGradCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1011
mfem::ConvectionIntegrator::ConvectionIntegrator
ConvectionIntegrator(VectorCoefficient &q, double a=1.0)
Definition: bilininteg.hpp:1679
mfem::DGTraceIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:2257
mfem::MixedScalarCurlIntegrator::MixedScalarCurlIntegrator
MixedScalarCurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:606
mfem::BilinearFormIntegrator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:31
mfem::MixedCrossCurlCurlIntegrator::CalcTestShape
virtual void CalcTestShape(const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &shape)
Definition: bilininteg.hpp:949
mfem::DerivativeIntegrator::DerivativeIntegrator
DerivativeIntegrator(Coefficient &q, int i)
Definition: bilininteg.hpp:1832
mfem::DGTraceIntegrator::DGTraceIntegrator
DGTraceIntegrator(Coefficient &_rho, VectorCoefficient &_u, double a, double b)
Definition: bilininteg.hpp:2060
mfem::MixedDotProductIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:709
mfem::CurlCurlIntegrator::CurlCurlIntegrator
CurlCurlIntegrator(Coefficient &q)
Construct a bilinear form integrator for Nedelec elements.
Definition: bilininteg.hpp:1858
mfem::MixedVectorCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:1484
mfem::MixedGradGradIntegrator::MixedGradGradIntegrator
MixedGradGradIntegrator(Coefficient &q)
Definition: bilininteg.hpp:794
mfem::MixedVectorGradientIntegrator::MixedVectorGradientIntegrator
MixedVectorGradientIntegrator(MatrixCoefficient &mq)
Definition: bilininteg.hpp:1430
mfem::MixedGradGradIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:818
mfem::TraceJumpIntegrator::AssembleFaceMatrix
virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe, const FiniteElement &test_fe1, const FiniteElement &test_fe2, FaceElementTransformations &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:2847
mfem::FiniteElement::GetRangeType
int GetRangeType() const
Definition: fe.hpp:233
mfem::MixedScalarDivergenceIntegrator::CalcTrialShape
virtual void CalcTrialShape(const FiniteElement &trial_fe, ElementTransformation &Trans, Vector &shape)
Definition: bilininteg.hpp:522
mfem::DivergenceInterpolator::AssembleElementMatrix2
virtual void AssembleElementMatrix2(const FiniteElement &dom_fe, const FiniteElement &ran_fe, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.hpp:2313
mfem::DiffusionIntegrator::AssembleElementMatrix
virtual void AssembleElementMatrix(const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
Definition: bilininteg.cpp:365
mfem::MixedCrossCurlGradIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:974
mfem::MixedCrossCurlCurlIntegrator::FiniteElementTypeFailureMessage
virtual const char * FiniteElementTypeFailureMessage() const
Definition: bilininteg.hpp:937
mfem::MassIntegrator::MassIntegrator
MassIntegrator(const IntegrationRule *ir=NULL)
Definition: bilininteg.hpp:1637
mfem::CurlCurlIntegrator::ComputeElementFlux
virtual void ComputeElementFlux(const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, int with_coef)
Definition: bilininteg.cpp:1483
mfem::MixedScalarIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:212
mfem::DiffusionIntegrator::ComputeFluxEnergy
virtual double ComputeFluxEnergy(const FiniteElement &fluxelem, ElementTransformation &Trans, Vector &flux, Vector *d_energy=NULL)
Definition: bilininteg.cpp:653
mfem::VectorFEMassIntegrator
Integrator for (Q u, v) for VectorFiniteElements.
Definition: bilininteg.hpp:1903
mfem::MixedVectorWeakCurlIntegrator::MixedVectorWeakCurlIntegrator
MixedVectorWeakCurlIntegrator(Coefficient &q)
Definition: bilininteg.hpp:1506
mfem::MixedCrossGradGradIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:847
mfem::TransposeIntegrator::TransposeIntegrator
TransposeIntegrator(BilinearFormIntegrator *_bfi, int _own_bfi=1)
Definition: bilininteg.hpp:95
mfem::MixedDivGradIntegrator::MixedDivGradIntegrator
MixedDivGradIntegrator(VectorCoefficient &vq)
Definition: bilininteg.hpp:1357
mfem::MixedScalarDerivativeIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:429
mfem::MixedScalarCurlIntegrator::GetIntegrationOrder
virtual int GetIntegrationOrder(const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans)
Definition: bilininteg.hpp:626
mfem::MixedScalarIntegrator::MixedScalarIntegrator
MixedScalarIntegrator(Coefficient &q)
Definition: bilininteg.hpp:196
mfem::DGElasticityIntegrator::DGElasticityIntegrator
DGElasticityIntegrator(Coefficient &lambda_, Coefficient &mu_, double alpha_, double kappa_)
Definition: bilininteg.hpp:2174
mfem::DerivativeIntegrator
Class for integrating (Q D_i(u), v); u and v are scalars.
Definition: bilininteg.hpp:1824
mfem::InverseIntegrator::InverseIntegrator
InverseIntegrator(BilinearFormIntegrator *integ, int own_integ=1)
Definition: bilininteg.hpp:141
mfem::MixedScalarVectorIntegrator::VerifyFiniteElementTypes
virtual bool VerifyFiniteElementTypes(const FiniteElement &trial_fe, const FiniteElement &test_fe) const
Definition: bilininteg.hpp:338
mfem::ConvectionIntegrator
alpha (q . grad u, v)
Definition: bilininteg.hpp:1668
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