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fe_nd.hpp
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11 
12 #ifndef MFEM_FE_ND
13 #define MFEM_FE_ND
14 
15 #include "fe_base.hpp"
16 #include "fe_h1.hpp"
17 
18 namespace mfem
19 {
20 
21 /// Arbitrary order Nedelec elements in 3D on a cube
22 class ND_HexahedronElement : public VectorTensorFiniteElement
23 {
24  static const double tk[18];
25 #ifndef MFEM_THREAD_SAFE
26  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
27  mutable Vector dshape_cx, dshape_cy, dshape_cz;
28 #endif
29  Array<int> dof2tk;
30  const double *cp;
31 
32 public:
33  /** @brief Construct the ND_HexahedronElement of order @a p and closed and
34  open BasisType @a cb_type and @a ob_type */
35  ND_HexahedronElement(const int p,
36  const int cb_type = BasisType::GaussLobatto,
37  const int ob_type = BasisType::GaussLegendre);
38 
39  virtual void CalcVShape(const IntegrationPoint &ip,
40  DenseMatrix &shape) const;
41 
42  virtual void CalcVShape(ElementTransformation &Trans,
43  DenseMatrix &shape) const
44  { CalcVShape_ND(Trans, shape); }
45 
46  virtual void CalcCurlShape(const IntegrationPoint &ip,
47  DenseMatrix &curl_shape) const;
48 
49  virtual void GetLocalInterpolation(ElementTransformation &Trans,
50  DenseMatrix &I) const
51  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
52 
53  virtual void GetLocalRestriction(ElementTransformation &Trans,
54  DenseMatrix &R) const
55  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
56 
57  virtual void GetTransferMatrix(const FiniteElement &fe,
58  ElementTransformation &Trans,
59  DenseMatrix &I) const
60  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
61 
62  using FiniteElement::Project;
63 
64  virtual void Project(VectorCoefficient &vc,
65  ElementTransformation &Trans, Vector &dofs) const
66  {
67  if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
68  else { Project_ND(tk, dof2tk, vc, Trans, dofs); }
69  }
70 
71  virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
72  Vector &dofs) const
73  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
74 
75  virtual void ProjectMatrixCoefficient(
76  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
77  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
78 
79  virtual void Project(const FiniteElement &fe,
80  ElementTransformation &Trans,
81  DenseMatrix &I) const
82  { Project_ND(tk, dof2tk, fe, Trans, I); }
83 
84  virtual void ProjectGrad(const FiniteElement &fe,
85  ElementTransformation &Trans,
86  DenseMatrix &grad) const
87  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
88 
89  virtual void ProjectCurl(const FiniteElement &fe,
90  ElementTransformation &Trans,
91  DenseMatrix &curl) const
92  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
93 
94 protected:
95  void ProjectIntegrated(VectorCoefficient &vc,
96  ElementTransformation &Trans,
97  Vector &dofs) const;
98 };
99 
100 
101 /// Arbitrary order Nedelec elements in 2D on a square
102 class ND_QuadrilateralElement : public VectorTensorFiniteElement
103 {
104  static const double tk[8];
105 
106 #ifndef MFEM_THREAD_SAFE
107  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
108  mutable Vector dshape_cx, dshape_cy;
109 #endif
110  Array<int> dof2tk;
111  const double *cp;
112 
113 public:
114  /** @brief Construct the ND_QuadrilateralElement of order @a p and closed and
115  open BasisType @a cb_type and @a ob_type */
116  ND_QuadrilateralElement(const int p,
117  const int cb_type = BasisType::GaussLobatto,
118  const int ob_type = BasisType::GaussLegendre);
119  virtual void CalcVShape(const IntegrationPoint &ip,
120  DenseMatrix &shape) const;
121  virtual void CalcVShape(ElementTransformation &Trans,
122  DenseMatrix &shape) const
123  { CalcVShape_ND(Trans, shape); }
124  virtual void CalcCurlShape(const IntegrationPoint &ip,
125  DenseMatrix &curl_shape) const;
126  virtual void GetLocalInterpolation(ElementTransformation &Trans,
127  DenseMatrix &I) const
128  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
129  virtual void GetLocalRestriction(ElementTransformation &Trans,
130  DenseMatrix &R) const
131  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
132  virtual void GetTransferMatrix(const FiniteElement &fe,
133  ElementTransformation &Trans,
134  DenseMatrix &I) const
135  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
136  using FiniteElement::Project;
137  virtual void Project(VectorCoefficient &vc,
138  ElementTransformation &Trans, Vector &dofs) const
139  {
140  if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
141  else { Project_ND(tk, dof2tk, vc, Trans, dofs); }
142  }
143  virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
144  Vector &dofs) const
145  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
146  virtual void ProjectMatrixCoefficient(
147  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
148  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
149  virtual void Project(const FiniteElement &fe,
150  ElementTransformation &Trans,
151  DenseMatrix &I) const
152  { Project_ND(tk, dof2tk, fe, Trans, I); }
153  virtual void ProjectGrad(const FiniteElement &fe,
154  ElementTransformation &Trans,
155  DenseMatrix &grad) const
156  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
157 
158 protected:
159  void ProjectIntegrated(VectorCoefficient &vc,
160  ElementTransformation &Trans,
161  Vector &dofs) const;
162 };
163 
164 
165 /// Arbitrary order Nedelec elements in 3D on a tetrahedron
166 class ND_TetrahedronElement : public VectorFiniteElement
167 {
168  static const double tk[18], c;
169 
170 #ifndef MFEM_THREAD_SAFE
171  mutable Vector shape_x, shape_y, shape_z, shape_l;
172  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
173  mutable DenseMatrix u;
174 #endif
175  Array<int> dof2tk;
176  DenseMatrixInverse Ti;
177 
178 public:
179  /// Construct the ND_TetrahedronElement of order @a p
180  ND_TetrahedronElement(const int p);
181  virtual void CalcVShape(const IntegrationPoint &ip,
182  DenseMatrix &shape) const;
183  virtual void CalcVShape(ElementTransformation &Trans,
184  DenseMatrix &shape) const
185  { CalcVShape_ND(Trans, shape); }
186  virtual void CalcCurlShape(const IntegrationPoint &ip,
187  DenseMatrix &curl_shape) const;
188  virtual void GetLocalInterpolation(ElementTransformation &Trans,
189  DenseMatrix &I) const
190  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
191  virtual void GetLocalRestriction(ElementTransformation &Trans,
192  DenseMatrix &R) const
193  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
194  virtual void GetTransferMatrix(const FiniteElement &fe,
195  ElementTransformation &Trans,
196  DenseMatrix &I) const
197  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
198  using FiniteElement::Project;
199  virtual void Project(VectorCoefficient &vc,
200  ElementTransformation &Trans, Vector &dofs) const
201  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
202  virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
203  Vector &dofs) const
204  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
205  virtual void ProjectMatrixCoefficient(
206  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
207  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
208  virtual void Project(const FiniteElement &fe,
209  ElementTransformation &Trans,
210  DenseMatrix &I) const
211  { Project_ND(tk, dof2tk, fe, Trans, I); }
212  virtual void ProjectGrad(const FiniteElement &fe,
213  ElementTransformation &Trans,
214  DenseMatrix &grad) const
215  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
216 
217  virtual void ProjectCurl(const FiniteElement &fe,
218  ElementTransformation &Trans,
219  DenseMatrix &curl) const
220  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
221 };
222 
223 /// Arbitrary order Nedelec elements in 2D on a triangle
224 class ND_TriangleElement : public VectorFiniteElement
225 {
226  static const double tk[8], c;
227 
228 #ifndef MFEM_THREAD_SAFE
229  mutable Vector shape_x, shape_y, shape_l;
230  mutable Vector dshape_x, dshape_y, dshape_l;
231  mutable DenseMatrix u;
232  mutable Vector curlu;
233 #endif
234  Array<int> dof2tk;
235  DenseMatrixInverse Ti;
236 
237 public:
238  /// Construct the ND_TriangleElement of order @a p
239  ND_TriangleElement(const int p);
240  virtual void CalcVShape(const IntegrationPoint &ip,
241  DenseMatrix &shape) const;
242  virtual void CalcVShape(ElementTransformation &Trans,
243  DenseMatrix &shape) const
244  { CalcVShape_ND(Trans, shape); }
245  virtual void CalcCurlShape(const IntegrationPoint &ip,
246  DenseMatrix &curl_shape) const;
247  virtual void GetLocalInterpolation(ElementTransformation &Trans,
248  DenseMatrix &I) const
249  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
250  virtual void GetLocalRestriction(ElementTransformation &Trans,
251  DenseMatrix &R) const
252  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
253  virtual void GetTransferMatrix(const FiniteElement &fe,
254  ElementTransformation &Trans,
255  DenseMatrix &I) const
256  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
257  using FiniteElement::Project;
258  virtual void Project(VectorCoefficient &vc,
259  ElementTransformation &Trans, Vector &dofs) const
260  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
261  virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
262  Vector &dofs) const
263  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
264  virtual void ProjectMatrixCoefficient(
265  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
266  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
267  virtual void Project(const FiniteElement &fe,
268  ElementTransformation &Trans,
269  DenseMatrix &I) const
270  { Project_ND(tk, dof2tk, fe, Trans, I); }
271  virtual void ProjectGrad(const FiniteElement &fe,
272  ElementTransformation &Trans,
273  DenseMatrix &grad) const
274  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
275 };
276 
277 
278 /// Arbitrary order Nedelec elements in 1D on a segment
279 class ND_SegmentElement : public VectorTensorFiniteElement
280 {
281  static const double tk[1];
282 
283  Array<int> dof2tk;
284 
285 public:
286  /** @brief Construct the ND_SegmentElement of order @a p and open
287  BasisType @a ob_type */
288  ND_SegmentElement(const int p, const int ob_type = BasisType::GaussLegendre);
289  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
290  { obasis1d.Eval(ip.x, shape); }
291  virtual void CalcVShape(const IntegrationPoint &ip,
292  DenseMatrix &shape) const;
293  virtual void CalcVShape(ElementTransformation &Trans,
294  DenseMatrix &shape) const
295  { CalcVShape_ND(Trans, shape); }
296  // virtual void CalcCurlShape(const IntegrationPoint &ip,
297  // DenseMatrix &curl_shape) const;
298  virtual void GetLocalInterpolation(ElementTransformation &Trans,
299  DenseMatrix &I) const
300  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
301  virtual void GetLocalRestriction(ElementTransformation &Trans,
302  DenseMatrix &R) const
303  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
304  virtual void GetTransferMatrix(const FiniteElement &fe,
305  ElementTransformation &Trans,
306  DenseMatrix &I) const
307  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
308  using FiniteElement::Project;
309  virtual void Project(VectorCoefficient &vc,
310  ElementTransformation &Trans, Vector &dofs) const
311  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
312  virtual void ProjectMatrixCoefficient(
313  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
314  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
315  virtual void Project(const FiniteElement &fe,
316  ElementTransformation &Trans,
317  DenseMatrix &I) const
318  { Project_ND(tk, dof2tk, fe, Trans, I); }
319  virtual void ProjectGrad(const FiniteElement &fe,
320  ElementTransformation &Trans,
321  DenseMatrix &grad) const
322  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
323 };
324 
325 class ND_WedgeElement : public VectorFiniteElement
326 {
327 private:
328  static const double tk[15];
329 
330 #ifndef MFEM_THREAD_SAFE
331  mutable Vector t1_shape, s1_shape;
332  mutable DenseMatrix tn_shape, sn_shape;
333  mutable DenseMatrix t1_dshape, s1_dshape, tn_dshape;
334 #endif
335  Array<int> dof2tk, t_dof, s_dof;
336 
337  H1_TriangleElement H1TriangleFE;
338  ND_TriangleElement NDTriangleFE;
339  H1_SegmentElement H1SegmentFE;
340  ND_SegmentElement NDSegmentFE;
341 
342 public:
343  ND_WedgeElement(const int p,
344  const int cb_type = BasisType::GaussLobatto,
345  const int ob_type = BasisType::GaussLegendre);
346 
347  virtual void CalcVShape(const IntegrationPoint &ip,
348  DenseMatrix &shape) const;
349 
350  virtual void CalcVShape(ElementTransformation &Trans,
351  DenseMatrix &shape) const
352  { CalcVShape_ND(Trans, shape); }
353 
354  virtual void CalcCurlShape(const IntegrationPoint &ip,
355  DenseMatrix &curl_shape) const;
356 
357  virtual void GetLocalInterpolation(ElementTransformation &Trans,
358  DenseMatrix &I) const
359  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
360  virtual void GetLocalRestriction(ElementTransformation &Trans,
361  DenseMatrix &R) const
362  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
363  virtual void GetTransferMatrix(const FiniteElement &fe,
364  ElementTransformation &Trans,
365  DenseMatrix &I) const
366  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
367 
368  using FiniteElement::Project;
369 
370  virtual void Project(VectorCoefficient &vc,
371  ElementTransformation &Trans, Vector &dofs) const
372  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
373 
374  virtual void ProjectMatrixCoefficient(
375  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
376  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
377 
378  virtual void Project(const FiniteElement &fe,
379  ElementTransformation &Trans,
380  DenseMatrix &I) const
381  { Project_ND(tk, dof2tk, fe, Trans, I); }
382 
383  virtual void ProjectGrad(const FiniteElement &fe,
384  ElementTransformation &Trans,
385  DenseMatrix &grad) const
386  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
387 
388  virtual void ProjectCurl(const FiniteElement &fe,
389  ElementTransformation &Trans,
390  DenseMatrix &curl) const
391  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
392 };
393 
394 
395 /// A 0D Nedelec finite element for the boundary of a 1D domain
396 /** ND_R1D_PointElement provides a representation of the trace of a three
397  component Nedelec basis restricted to 1D.
398 */
399 class ND_R1D_PointElement : public VectorFiniteElement
400 {
401  static const double tk[9];
402 
403 public:
404  /** @brief Construct the ND_R1D_PointElement */
405  ND_R1D_PointElement(int p);
406 
407  using FiniteElement::CalcVShape;
408 
409  virtual void CalcVShape(const IntegrationPoint &ip,
410  DenseMatrix &shape) const;
411 
412  virtual void CalcVShape(ElementTransformation &Trans,
413  DenseMatrix &shape) const;
414 };
415 
416 /// Arbitrary order, three component, Nedelec elements in 1D on a segment
417 /** ND_R1D_SegmentElement provides a representation of a three component Nedelec
418  basis where the vector components vary along only one dimension.
419 */
420 class ND_R1D_SegmentElement : public VectorFiniteElement
421 {
422  static const double tk[9];
423 #ifndef MFEM_THREAD_SAFE
424  mutable Vector shape_cx, shape_ox;
425  mutable Vector dshape_cx;
426 #endif
427  Array<int> dof_map, dof2tk;
428 
429  Poly_1D::Basis &cbasis1d, &obasis1d;
430 
431 public:
432  /** @brief Construct the ND_R1D_SegmentElement of order @a p and closed and
433  open BasisType @a cb_type and @a ob_type */
434  ND_R1D_SegmentElement(const int p,
435  const int cb_type = BasisType::GaussLobatto,
436  const int ob_type = BasisType::GaussLegendre);
437 
438  using FiniteElement::CalcVShape;
439  using FiniteElement::CalcPhysCurlShape;
440 
441  virtual void CalcVShape(const IntegrationPoint &ip,
442  DenseMatrix &shape) const;
443 
444  virtual void CalcVShape(ElementTransformation &Trans,
445  DenseMatrix &shape) const;
446 
447  virtual void CalcCurlShape(const IntegrationPoint &ip,
448  DenseMatrix &curl_shape) const;
449 
450  virtual void CalcPhysCurlShape(ElementTransformation &Trans,
451  DenseMatrix &curl_shape) const;
452 
453  virtual void GetLocalInterpolation(ElementTransformation &Trans,
454  DenseMatrix &I) const
455  { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
456 
457  virtual void GetLocalRestriction(ElementTransformation &Trans,
458  DenseMatrix &R) const
459  { LocalRestriction_ND(tk, dof2tk, Trans, R); }
460 
461  virtual void GetTransferMatrix(const FiniteElement &fe,
462  ElementTransformation &Trans,
463  DenseMatrix &I) const
464  { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
465 
466  using FiniteElement::Project;
467 
468  virtual void Project(VectorCoefficient &vc,
469  ElementTransformation &Trans, Vector &dofs) const;
470 
471  virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
472  Vector &dofs) const
473  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
474 
475  virtual void ProjectMatrixCoefficient(
476  MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
477  { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
478 
479  virtual void Project(const FiniteElement &fe,
480  ElementTransformation &Trans,
481  DenseMatrix &I) const;
482 
483  virtual void ProjectGrad(const FiniteElement &fe,
484  ElementTransformation &Trans,
485  DenseMatrix &grad) const
486  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
487 
488  virtual void ProjectCurl(const FiniteElement &fe,
489  ElementTransformation &Trans,
490  DenseMatrix &curl) const
491  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
492 };
493 
494 
495 /** ND_R2D_SegmentElement provides a representation of a 3D Nedelec
496  basis where the vector field is assumed constant in the third dimension.
497 */
498 class ND_R2D_SegmentElement : public VectorFiniteElement
499 {
500  static const double tk[4];
501 #ifndef MFEM_THREAD_SAFE
502  mutable Vector shape_cx, shape_ox;
503  mutable Vector dshape_cx;
504 #endif
505  Array<int> dof_map, dof2tk;
506 
507  Poly_1D::Basis &cbasis1d, &obasis1d;
508 
509 private:
510  void LocalInterpolation(const VectorFiniteElement &cfe,
511  ElementTransformation &Trans,
512  DenseMatrix &I) const;
513 
514 public:
515  /** @brief Construct the ND_R2D_SegmentElement of order @a p and closed and
516  open BasisType @a cb_type and @a ob_type */
517  ND_R2D_SegmentElement(const int p,
518  const int cb_type = BasisType::GaussLobatto,
519  const int ob_type = BasisType::GaussLegendre);
520 
521  virtual void CalcVShape(const IntegrationPoint &ip,
522  DenseMatrix &shape) const;
523 
524  virtual void CalcVShape(ElementTransformation &Trans,
525  DenseMatrix &shape) const;
526 
527  virtual void CalcCurlShape(const IntegrationPoint &ip,
528  DenseMatrix &curl_shape) const;
529 
530  virtual void GetLocalInterpolation(ElementTransformation &Trans,
531  DenseMatrix &I) const
532  { LocalInterpolation(*this, Trans, I); }
533 
534  virtual void GetLocalRestriction(ElementTransformation &Trans,
535  DenseMatrix &R) const
536  { MFEM_ABORT("method is not overloaded"); }
537 
538  virtual void GetTransferMatrix(const FiniteElement &fe,
539  ElementTransformation &Trans,
540  DenseMatrix &I) const
541  { LocalInterpolation(CheckVectorFE(fe), Trans, I); }
542 
543  using FiniteElement::Project;
544 
545  virtual void Project(VectorCoefficient &vc,
546  ElementTransformation &Trans, Vector &dofs) const;
547 };
548 
549 class ND_R2D_FiniteElement : public VectorFiniteElement
550 {
551 protected:
552  const double *tk;
553  Array<int> dof_map, dof2tk;
554 
555  ND_R2D_FiniteElement(int p, Geometry::Type G, int Do, const double *tk_fe);
556 
557 private:
558  void LocalInterpolation(const VectorFiniteElement &cfe,
559  ElementTransformation &Trans,
560  DenseMatrix &I) const;
561 
562 public:
563  using FiniteElement::CalcVShape;
564  using FiniteElement::CalcPhysCurlShape;
565 
566  virtual void CalcVShape(ElementTransformation &Trans,
567  DenseMatrix &shape) const;
568 
569  virtual void CalcPhysCurlShape(ElementTransformation &Trans,
570  DenseMatrix &curl_shape) const;
571 
572  virtual void GetLocalInterpolation(ElementTransformation &Trans,
573  DenseMatrix &I) const
574  { LocalInterpolation(*this, Trans, I); }
575 
576  virtual void GetLocalRestriction(ElementTransformation &Trans,
577  DenseMatrix &R) const;
578 
579  virtual void GetTransferMatrix(const FiniteElement &fe,
580  ElementTransformation &Trans,
581  DenseMatrix &I) const
582  { LocalInterpolation(CheckVectorFE(fe), Trans, I); }
583 
584  using FiniteElement::Project;
585 
586  virtual void Project(VectorCoefficient &vc,
587  ElementTransformation &Trans, Vector &dofs) const;
588 
589  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
590  DenseMatrix &I) const;
591 
592  virtual void ProjectGrad(const FiniteElement &fe,
593  ElementTransformation &Trans,
594  DenseMatrix &grad) const;
595 };
596 
597 /// Arbitrary order Nedelec 3D elements in 2D on a triangle
598 class ND_R2D_TriangleElement : public ND_R2D_FiniteElement
599 {
600 private:
601  static const double tk_t[15];
602 
603 #ifndef MFEM_THREAD_SAFE
604  mutable DenseMatrix nd_shape;
605  mutable Vector h1_shape;
606  mutable DenseMatrix nd_dshape;
607  mutable DenseMatrix h1_dshape;
608 #endif
609 
610  ND_TriangleElement ND_FE;
611  H1_TriangleElement H1_FE;
612 
613 public:
614  /// Construct the ND_R2D_TriangleElement of order @a p
615  ND_R2D_TriangleElement(const int p,
616  const int cb_type = BasisType::GaussLobatto);
617 
618  using ND_R2D_FiniteElement::CalcVShape;
619  using ND_R2D_FiniteElement::CalcPhysCurlShape;
620 
621  virtual void CalcVShape(const IntegrationPoint &ip,
622  DenseMatrix &shape) const;
623  virtual void CalcCurlShape(const IntegrationPoint &ip,
624  DenseMatrix &curl_shape) const;
625 };
626 
627 
628 /// Arbitrary order Nedelec 3D elements in 2D on a square
629 class ND_R2D_QuadrilateralElement : public ND_R2D_FiniteElement
630 {
631  static const double tk_q[15];
632 
633 #ifndef MFEM_THREAD_SAFE
634  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
635  mutable Vector dshape_cx, dshape_cy;
636 #endif
637 
638  Poly_1D::Basis &cbasis1d, &obasis1d;
639 
640 public:
641  /** @brief Construct the ND_R2D_QuadrilateralElement of order @a p and
642  closed and open BasisType @a cb_type and @a ob_type */
643  ND_R2D_QuadrilateralElement(const int p,
644  const int cb_type = BasisType::GaussLobatto,
645  const int ob_type = BasisType::GaussLegendre);
646 
647  using ND_R2D_FiniteElement::CalcVShape;
648  using ND_R2D_FiniteElement::CalcPhysCurlShape;
649 
650  virtual void CalcVShape(const IntegrationPoint &ip,
651  DenseMatrix &shape) const;
652  virtual void CalcCurlShape(const IntegrationPoint &ip,
653  DenseMatrix &curl_shape) const;
654 };
655 
656 
657 } // namespace mfem
658 
659 #endif
mfem::FiniteElement
Abstract class for all finite elements.
Definition: fe_base.hpp:235
mfem::ND_R1D_PointElement
A 0D Nedelec finite element for the boundary of a 1D domain.
Definition: fe_nd.hpp:399
mfem::ND_SegmentElement
Arbitrary order Nedelec elements in 1D on a segment.
Definition: fe_nd.hpp:279
mfem::ND_SegmentElement::ND_SegmentElement
ND_SegmentElement(const int p, const int ob_type=BasisType::GaussLegendre)
Construct the ND_SegmentElement of order p and open BasisType ob_type.
Definition: fe_nd.cpp:1194
mfem::ND_R2D_FiniteElement::CalcPhysCurlShape
virtual 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_nd.cpp:2035
mfem::ND_TetrahedronElement::ProjectFromNodes
virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition: fe_nd.hpp:202
mfem::ND_QuadrilateralElement::ProjectIntegrated
void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe_nd.cpp:574
mfem::ND_R1D_SegmentElement::ProjectFromNodes
virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition: fe_nd.hpp:471
mfem::VectorFiniteElement::ProjectMatrixCoefficient_ND
void ProjectMatrixCoefficient_ND(const double *tk, const Array< int > &d2t, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Project the rows of the matrix coefficient in an ND space.
Definition: fe_base.cpp:1180
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_base.cpp:39
mfem::ND_WedgeElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.hpp:350
mfem::ND_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:153
mfem::ND_SegmentElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:301
mfem::Poly_1D::Basis::IsIntegratedType
bool IsIntegratedType() const
Returns true if the basis is &quot;integrated&quot;, false otherwise.
Definition: fe_base.hpp:1021
mfem::ND_WedgeElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:383
mfem::VectorCoefficient
Base class for vector Coefficients that optionally depend on time and space.
Definition: coefficient.hpp:432
mfem::ND_R2D_SegmentElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:534
mfem::ND_R2D_QuadrilateralElement
Arbitrary order Nedelec 3D elements in 2D on a square.
Definition: fe_nd.hpp:629
mfem::ND_WedgeElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:363
mfem::FiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Given a coefficient and a transformation, compute its projection (approximation) in the local finite ...
Definition: fe_base.cpp:125
mfem::ND_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:217
mfem::ND_R1D_PointElement::ND_R1D_PointElement
ND_R1D_PointElement(int p)
Construct the ND_R1D_PointElement.
Definition: fe_nd.cpp:1509
mfem::ND_TriangleElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:250
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.hpp:42
mfem::ND_TriangleElement::ProjectFromNodes
virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition: fe_nd.hpp:261
mfem::ND_R1D_SegmentElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:488
mfem::ND_R2D_SegmentElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:538
mfem::ND_QuadrilateralElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.hpp:121
mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition: densemat.hpp:23
mfem::ND_R2D_TriangleElement::ND_R2D_TriangleElement
ND_R2D_TriangleElement(const int p, const int cb_type=BasisType::GaussLobatto)
Construct the ND_R2D_TriangleElement of order p.
Definition: fe_nd.cpp:2280
mfem::ND_R2D_SegmentElement::ND_R2D_SegmentElement
ND_R2D_SegmentElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the ND_R2D_SegmentElement of order p and closed and open BasisType cb_type and ob_type...
Definition: fe_nd.cpp:1815
mfem::ND_R2D_SegmentElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:1864
mfem::ND_TetrahedronElement
Arbitrary order Nedelec elements in 3D on a tetrahedron.
Definition: fe_nd.hpp:166
mfem::VectorFiniteElement::ProjectCurl_ND
void ProjectCurl_ND(const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe_base.cpp:1093
mfem::ND_R2D_FiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.cpp:2018
mfem::ND_R1D_SegmentElement
Arbitrary order, three component, Nedelec elements in 1D on a segment.
Definition: fe_nd.hpp:420
mfem::VectorFiniteElement
Intermediate class for finite elements whose basis functions return vector values.
Definition: fe_base.hpp:785
mfem::ND_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:89
mfem::ND_HexahedronElement::ProjectFromNodes
virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition: fe_nd.hpp:71
mfem::ND_R2D_TriangleElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:2359
mfem::ND_R1D_SegmentElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:1602
mfem::ND_R2D_FiniteElement::dof2tk
Array< int > dof2tk
Definition: fe_nd.hpp:553
mfem::ND_TriangleElement
Arbitrary order Nedelec elements in 2D on a triangle.
Definition: fe_nd.hpp:224
mfem::ND_R2D_SegmentElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:1907
mfem::ND_WedgeElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:357
mfem::ND_R1D_PointElement::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_nd.cpp:1520
mfem::ND_WedgeElement::ND_WedgeElement
ND_WedgeElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Definition: fe_nd.cpp:1222
mfem::ND_WedgeElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.hpp:370
mfem::ND_R1D_SegmentElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:1655
mfem::ND_TriangleElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:264
mfem::ND_TriangleElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:1115
mfem::FiniteElement::CalcPhysCurlShape
virtual 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_base.cpp:70
mfem::ND_TriangleElement::ND_TriangleElement
ND_TriangleElement(const int p)
Construct the ND_TriangleElement of order p.
Definition: fe_nd.cpp:1034
mfem::ND_SegmentElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:304
mfem::ND_R2D_QuadrilateralElement::ND_R2D_QuadrilateralElement
ND_R2D_QuadrilateralElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the ND_R2D_QuadrilateralElement of order p and closed and open BasisType cb_type and ob_typ...
Definition: fe_nd.cpp:2421
mfem::ND_R2D_SegmentElement
Definition: fe_nd.hpp:498
mfem::ND_SegmentElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:319
mfem::ND_HexahedronElement::ND_HexahedronElement
ND_HexahedronElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the ND_HexahedronElement of order p and closed and open BasisType cb_type and ob_type...
Definition: fe_nd.cpp:25
mfem::ND_R1D_SegmentElement::CalcPhysCurlShape
virtual 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_nd.cpp:1695
mfem::ND_R2D_FiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.cpp:2144
mfem::ND_R2D_FiniteElement::ND_R2D_FiniteElement
ND_R2D_FiniteElement(int p, Geometry::Type G, int Do, const double *tk_fe)
Definition: fe_nd.cpp:2000
mfem::ND_TetrahedronElement::ND_TetrahedronElement
ND_TetrahedronElement(const int p)
Construct the ND_TetrahedronElement of order p.
Definition: fe_nd.cpp:772
mfem::ND_R1D_SegmentElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:483
mfem::ND_TetrahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.hpp:183
mfem::ND_R1D_SegmentElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:453
mfem::ND_QuadrilateralElement::ProjectFromNodes
virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector of values at the finite element nodes and a transformation, compute its projection (ap...
Definition: fe_nd.hpp:143
mfem::ND_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:188
mfem::ND_R2D_FiniteElement::tk
const double * tk
Definition: fe_nd.hpp:552
mfem::ND_WedgeElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:388
mfem::ND_WedgeElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:360
mfem::ND_WedgeElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
Definition: fe_nd.hpp:378
mfem::ND_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.hpp:199
mfem::ND_R1D_SegmentElement::ND_R1D_SegmentElement
ND_R1D_SegmentElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the ND_R1D_SegmentElement of order p and closed and open BasisType cb_type and ob_type...
Definition: fe_nd.cpp:1538
mfem::ND_R1D_SegmentElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:461
mfem::ND_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:247
mfem::ND_TetrahedronElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:194
mfem::ND_R2D_TriangleElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:2388
mfem::ND_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:126
mfem::VectorFiniteElement::ProjectGrad_ND
void ProjectGrad_ND(const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe_base.cpp:1279
mfem::ND_QuadrilateralElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:710
mfem::ND_SegmentElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
Definition: fe_nd.hpp:315
mfem::ND_TriangleElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:1149
mfem::VectorFiniteElement::LocalInterpolation_ND
void LocalInterpolation_ND(const VectorFiniteElement &cfe, const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe_base.cpp:1434
p
double p(const Vector &x, double t)
Definition: navier_mms.cpp:53
mfem::ND_QuadrilateralElement::ND_QuadrilateralElement
ND_QuadrilateralElement(const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
Construct the ND_QuadrilateralElement of order p and closed and open BasisType cb_type and ob_type...
Definition: fe_nd.cpp:483
mfem::ND_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Overrides the scalar CalcShape function to print an error.
Definition: fe_nd.hpp:289
mfem::VectorFiniteElement::CalcVShape_ND
void CalcVShape_ND(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe_base.cpp:915
mfem::ND_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.hpp:309
mfem::ND_R2D_FiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:572
mfem::ND_SegmentElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:312
mfem::ND_HexahedronElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:53
mfem::ND_R2D_FiniteElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:579
mfem::MatrixCoefficient
Base class for Matrix Coefficients that optionally depend on time and space.
Definition: coefficient.hpp:876
mfem::ND_R1D_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.cpp:1706
mfem::ND_R2D_FiniteElement
Definition: fe_nd.hpp:549
mfem::ND_HexahedronElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:57
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:309
mfem::ND_R2D_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.cpp:1975
mfem::ND_WedgeElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:1471
mfem::ND_R2D_QuadrilateralElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:2608
mfem::ND_QuadrilateralElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:129
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.hpp:293
mfem::ND_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:49
mfem::ND_WedgeElement
Definition: fe_nd.hpp:325
mfem::VectorFiniteElement::LocalRestriction_ND
void LocalRestriction_ND(const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &R) const
Definition: fe_base.cpp:1516
mfem::ND_QuadrilateralElement
Arbitrary order Nedelec elements in 2D on a square.
Definition: fe_nd.hpp:102
mfem::ND_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.hpp:258
mfem::ND_TetrahedronElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:205
mfem::IntegrationPoint
Class for integration point with weight.
Definition: intrules.hpp:25
mfem::ND_WedgeElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:374
mfem::ND_TetrahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:920
mfem::ND_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:650
mfem::ND_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:271
mfem::H1_TriangleElement
Arbitrary order H1 elements in 2D on a triangle.
Definition: fe_h1.hpp:83
mfem::ND_QuadrilateralElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:146
mfem::ND_R2D_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:2548
mfem::H1_SegmentElement
Arbitrary order H1 elements in 1D.
Definition: fe_h1.hpp:21
mfem::ND_WedgeElement::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_nd.cpp:1437
mfem::ND_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.hpp:137
mfem::ND_HexahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:84
mfem::Poly_1D::Basis
Class for evaluating 1D nodal, positive (Bernstein), or integrated (Gerritsma) bases.
Definition: fe_base.hpp:976
mfem::ND_R2D_TriangleElement
Arbitrary order Nedelec 3D elements in 2D on a triangle.
Definition: fe_nd.hpp:598
mfem::ND_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
Definition: fe_nd.hpp:267
mfem::ND_HexahedronElement
Arbitrary order Nedelec elements in 3D on a cube.
Definition: fe_nd.hpp:22
mfem::ND_R2D_FiniteElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.cpp:2098
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in reference space at the given...
Definition: fe_nd.cpp:1211
mfem::ND_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Given a vector coefficient and a transformation, compute its projection (approximation) in the local ...
Definition: fe_nd.hpp:64
mfem::ND_HexahedronElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:75
mfem::ND_HexahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:396
mfem::Poly_1D::Basis::Eval
void Eval(const double x, Vector &u) const
Evaluate the basis functions at point x in [0,1].
Definition: fe_base.cpp:1622
mfem::Vector
Vector data type.
Definition: vector.hpp:60
mfem::ND_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
Definition: fe_nd.hpp:79
mfem::ND_R2D_SegmentElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:530
mfem::ND_R2D_FiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.cpp:2256
mfem::ND_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
Definition: fe_nd.hpp:149
fe_h1.hpp
fe_base.hpp
mfem::ND_TetrahedronElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:191
mfem::ND_SegmentElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base g...
Definition: fe_nd.hpp:298
mfem::VectorFiniteElement::CheckVectorFE
static const VectorFiniteElement & CheckVectorFE(const FiniteElement &fe)
Definition: fe_base.hpp:946
mfem::ND_R1D_SegmentElement::ProjectMatrixCoefficient
virtual void ProjectMatrixCoefficient(MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
Given a matrix coefficient and a transformation, compute an approximation (&quot;projection&quot;) in the local...
Definition: fe_nd.hpp:475
mfem::ND_TetrahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Evaluate the curl of all shape functions of a vector finite element in reference space at the given p...
Definition: fe_nd.cpp:962
mfem::ND_R2D_FiniteElement::dof_map
Array< int > dof_map
Definition: fe_nd.hpp:553
mfem::ND_TriangleElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:253
mfem::ND_QuadrilateralElement::GetTransferMatrix
virtual void GetTransferMatrix(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this f...
Definition: fe_nd.hpp:132
mfem::ND_TetrahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Compute the discrete gradient matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
Definition: fe_nd.hpp:212
mfem::VectorFiniteElement::Project_ND
void Project_ND(const double *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Project a vector coefficient onto the ND basis functions.
Definition: fe_base.cpp:1150
mfem::ND_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto &#39;this&#39; FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
Definition: fe_nd.hpp:208
mfem::ND_HexahedronElement::ProjectIntegrated
void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe_nd.cpp:244
mfem::ND_R1D_SegmentElement::GetLocalRestriction
virtual void GetLocalRestriction(ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. ...
Definition: fe_nd.hpp:457
mfem::ND_TriangleElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Evaluate the values of all shape functions of a vector finite element in physical space at the point ...
Definition: fe_nd.hpp:242
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