MFEM  v3.1
Finite element discretization library
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fe.hpp
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1 // Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
2 // the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
3 // reserved. See file COPYRIGHT for details.
4 //
5 // This file is part of the MFEM library. For more information and source code
6 // availability see http://mfem.org.
7 //
8 // MFEM is free software; you can redistribute it and/or modify it under the
9 // terms of the GNU Lesser General Public License (as published by the Free
10 // Software Foundation) version 2.1 dated February 1999.
11 
12 #ifndef MFEM_FE
13 #define MFEM_FE
14 
15 #include "../config/config.hpp"
16 #include "../general/array.hpp"
17 #include "../linalg/linalg.hpp"
18 #include "intrules.hpp"
19 #include "geom.hpp"
20 
21 namespace mfem
22 {
23 
24 // Base and derived classes for finite elements
25 
27 class FunctionSpace
28 {
29 public:
30  enum
31  {
32  Pk, // polynomials of order k
33  Qk, // tensor products of polynomials of order k
34  rQk // refined tensor products of polynomials of order k
35  };
36 };
37 
38 class ElementTransformation;
39 class Coefficient;
40 class VectorCoefficient;
41 class KnotVector;
42 
44 class FiniteElement
45 {
46 protected:
47  int Dim, GeomType, Dof, Order, FuncSpace, RangeType, MapType;
48  IntegrationRule Nodes;
49 
50 public:
52  enum { SCALAR, VECTOR };
53 
71  enum { VALUE, INTEGRAL, H_DIV, H_CURL };
72 
79  FiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk);
80 
82  int GetDim() const { return Dim; }
83 
85  int GetGeomType() const { return GeomType; }
86 
88  int GetDof() const { return Dof; }
89 
91  int GetOrder() const { return Order; }
92 
94  int Space() const { return FuncSpace; }
95 
96  int GetRangeType() const { return RangeType; }
97 
98  int GetMapType() const { return MapType; }
99 
103  virtual void CalcShape(const IntegrationPoint &ip,
104  Vector &shape) const = 0;
105 
110  virtual void CalcDShape(const IntegrationPoint &ip,
111  DenseMatrix &dshape) const = 0;
112 
113  const IntegrationRule & GetNodes() const { return Nodes; }
114 
115  // virtual functions for finite elements on vector spaces
116 
121  virtual void CalcVShape(const IntegrationPoint &ip,
122  DenseMatrix &shape) const;
123 
124  virtual void CalcVShape(ElementTransformation &Trans,
125  DenseMatrix &shape) const;
126 
130  virtual void CalcDivShape(const IntegrationPoint &ip,
131  Vector &divshape) const;
132 
137  virtual void CalcCurlShape(const IntegrationPoint &ip,
138  DenseMatrix &curl_shape) const;
139 
140  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
141 
144  virtual void CalcHessian (const IntegrationPoint &ip,
145  DenseMatrix &h) const;
146 
150  virtual void GetLocalInterpolation (ElementTransformation &Trans,
151  DenseMatrix &I) const;
152 
156  virtual void Project (Coefficient &coeff,
157  ElementTransformation &Trans, Vector &dofs) const;
158 
162  virtual void Project (VectorCoefficient &vc,
163  ElementTransformation &Trans, Vector &dofs) const;
164 
167  virtual void ProjectDelta(int vertex, Vector &dofs) const;
168 
172  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
173  DenseMatrix &I) const;
174 
178  virtual void ProjectGrad(const FiniteElement &fe,
179  ElementTransformation &Trans,
180  DenseMatrix &grad) const;
181 
185  virtual void ProjectCurl(const FiniteElement &fe,
186  ElementTransformation &Trans,
187  DenseMatrix &curl) const;
188 
192  virtual void ProjectDiv(const FiniteElement &fe,
193  ElementTransformation &Trans,
194  DenseMatrix &div) const;
195 
196  virtual ~FiniteElement () { }
197 };
198 
199 class NodalFiniteElement : public FiniteElement
200 {
201 protected:
202  void NodalLocalInterpolation (ElementTransformation &Trans,
203  DenseMatrix &I,
204  const NodalFiniteElement &fine_fe) const;
205 
206  void ProjectCurl_2D(const FiniteElement &fe,
207  ElementTransformation &Trans,
208  DenseMatrix &curl) const;
209 
210 #ifndef MFEM_THREAD_SAFE
211  mutable Vector c_shape;
212 #endif
213 
214 public:
215  NodalFiniteElement(int D, int G, int Do, int O,
216  int F = FunctionSpace::Pk) :
217 #ifdef MFEM_THREAD_SAFE
218  FiniteElement(D, G, Do, O, F)
219 #else
220  FiniteElement(D, G, Do, O, F), c_shape(Do)
221 #endif
222  { }
223 
224  void SetMapType(int M)
225  {
226  MFEM_VERIFY(M == VALUE || M == INTEGRAL, "unknown MapType");
227  MapType = M;
228  }
229 
230  virtual void GetLocalInterpolation (ElementTransformation &Trans,
231  DenseMatrix &I) const
232  { NodalLocalInterpolation (Trans, I, *this); }
233 
234  virtual void Project (Coefficient &coeff,
235  ElementTransformation &Trans, Vector &dofs) const;
236 
237  virtual void Project (VectorCoefficient &vc,
238  ElementTransformation &Trans, Vector &dofs) const;
239 
240  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
241  DenseMatrix &I) const;
242 
243  virtual void ProjectGrad(const FiniteElement &fe,
244  ElementTransformation &Trans,
245  DenseMatrix &grad) const;
246 
247  virtual void ProjectDiv(const FiniteElement &fe,
248  ElementTransformation &Trans,
249  DenseMatrix &div) const;
250 };
251 
252 
253 class PositiveFiniteElement : public FiniteElement
254 {
255 public:
256  PositiveFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
257  : FiniteElement(D, G, Do, O, F) { }
258  using FiniteElement::Project;
259  virtual void Project(Coefficient &coeff,
260  ElementTransformation &Trans, Vector &dofs) const;
261  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
262  DenseMatrix &I) const;
263 };
264 
265 class VectorFiniteElement : public FiniteElement
266 {
267  // Hide the scalar functions CalcShape and CalcDShape.
268 private:
270  virtual void CalcShape(const IntegrationPoint &ip,
271  Vector &shape) const;
272 
274  virtual void CalcDShape(const IntegrationPoint &ip,
275  DenseMatrix &dshape) const;
276 
277 protected:
278 #ifndef MFEM_THREAD_SAFE
279  mutable DenseMatrix J, Jinv;
280  mutable DenseMatrix vshape, curlshape, curlshape_J;
281 #endif
282 
283  void CalcVShape_RT(ElementTransformation &Trans,
284  DenseMatrix &shape) const;
285 
286  void CalcVShape_ND(ElementTransformation &Trans,
287  DenseMatrix &shape) const;
288 
289  void Project_RT(const double *nk, const Array<int> &d2n,
290  VectorCoefficient &vc, ElementTransformation &Trans,
291  Vector &dofs) const;
292 
293  void Project_RT(const double *nk, const Array<int> &d2n,
294  const FiniteElement &fe, ElementTransformation &Trans,
295  DenseMatrix &I) const;
296 
297  // rotated gradient in 2D
298  void ProjectGrad_RT(const double *nk, const Array<int> &d2n,
299  const FiniteElement &fe, ElementTransformation &Trans,
300  DenseMatrix &grad) const;
301 
302  void ProjectCurl_ND(const double *tk, const Array<int> &d2t,
303  const FiniteElement &fe, ElementTransformation &Trans,
304  DenseMatrix &curl) const;
305 
306  void ProjectCurl_RT(const double *nk, const Array<int> &d2n,
307  const FiniteElement &fe, ElementTransformation &Trans,
308  DenseMatrix &curl) const;
309 
310  void Project_ND(const double *tk, const Array<int> &d2t,
311  VectorCoefficient &vc, ElementTransformation &Trans,
312  Vector &dofs) const;
313 
314  void Project_ND(const double *tk, const Array<int> &d2t,
315  const FiniteElement &fe, ElementTransformation &Trans,
316  DenseMatrix &I) const;
317 
318  void ProjectGrad_ND(const double *tk, const Array<int> &d2t,
319  const FiniteElement &fe, ElementTransformation &Trans,
320  DenseMatrix &grad) const;
321 
322  void LocalInterpolation_RT(const double *nk, const Array<int> &d2n,
323  ElementTransformation &Trans,
324  DenseMatrix &I) const;
325 
326  void LocalInterpolation_ND(const double *tk, const Array<int> &d2t,
327  ElementTransformation &Trans,
328  DenseMatrix &I) const;
329 
330 public:
331  VectorFiniteElement (int D, int G, int Do, int O, int M,
332  int F = FunctionSpace::Pk) :
333 #ifdef MFEM_THREAD_SAFE
334  FiniteElement(D, G, Do, O, F)
335  { RangeType = VECTOR; MapType = M; }
336 #else
337  FiniteElement(D, G, Do, O, F), Jinv(D), vshape(Do, D)
338  { RangeType = VECTOR; MapType = M; }
339 #endif
340 };
341 
342 class PointFiniteElement : public NodalFiniteElement
343 {
344 public:
345  PointFiniteElement();
346 
347  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
348 
349  virtual void CalcDShape(const IntegrationPoint &ip,
350  DenseMatrix &dshape) const;
351 };
352 
354 class Linear1DFiniteElement : public NodalFiniteElement
355 {
356 public:
358  Linear1DFiniteElement();
359 
363  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
364 
369  virtual void CalcDShape(const IntegrationPoint &ip,
370  DenseMatrix &dshape) const;
371 };
372 
374 class Linear2DFiniteElement : public NodalFiniteElement
375 {
376 public:
378  Linear2DFiniteElement();
379 
383  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
384 
389  virtual void CalcDShape(const IntegrationPoint &ip,
390  DenseMatrix &dshape) const;
391  virtual void ProjectDelta(int vertex, Vector &dofs) const
392  { dofs = 0.0; dofs(vertex) = 1.0; }
393 };
394 
396 class BiLinear2DFiniteElement : public NodalFiniteElement
397 {
398 public:
400  BiLinear2DFiniteElement();
401 
405  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
406 
411  virtual void CalcDShape(const IntegrationPoint &ip,
412  DenseMatrix &dshape) const;
413  virtual void CalcHessian (const IntegrationPoint &ip,
414  DenseMatrix &h) const;
415  virtual void ProjectDelta(int vertex, Vector &dofs) const
416  { dofs = 0.0; dofs(vertex) = 1.0; }
417  // { dofs = 1.0; }
418 };
419 
421 class GaussLinear2DFiniteElement : public NodalFiniteElement
422 {
423 public:
424  GaussLinear2DFiniteElement();
425  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
426  virtual void CalcDShape(const IntegrationPoint &ip,
427  DenseMatrix &dshape) const;
428  virtual void ProjectDelta(int vertex, Vector &dofs) const;
429 };
430 
432 class GaussBiLinear2DFiniteElement : public NodalFiniteElement
433 {
434 private:
435  static const double p[2];
436 
437 public:
438  GaussBiLinear2DFiniteElement();
439  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
440  virtual void CalcDShape(const IntegrationPoint &ip,
441  DenseMatrix &dshape) const;
442  virtual void ProjectDelta(int vertex, Vector &dofs) const;
443 };
444 
445 class P1OnQuadFiniteElement : public NodalFiniteElement
446 {
447 public:
448  P1OnQuadFiniteElement();
449  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
450  virtual void CalcDShape(const IntegrationPoint &ip,
451  DenseMatrix &dshape) const;
452  virtual void ProjectDelta(int vertex, Vector &dofs) const
453  { dofs = 1.0; }
454 };
455 
457 class Quad1DFiniteElement : public NodalFiniteElement
458 {
459 public:
461  Quad1DFiniteElement();
462 
466  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
467 
472  virtual void CalcDShape(const IntegrationPoint &ip,
473  DenseMatrix &dshape) const;
474 };
475 
476 class QuadPos1DFiniteElement : public FiniteElement
477 {
478 public:
479  QuadPos1DFiniteElement();
480  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
481  virtual void CalcDShape(const IntegrationPoint &ip,
482  DenseMatrix &dshape) const;
483 };
484 
486 class Quad2DFiniteElement : public NodalFiniteElement
487 {
488 public:
490  Quad2DFiniteElement();
491 
495  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
496 
501  virtual void CalcDShape(const IntegrationPoint &ip,
502  DenseMatrix &dshape) const;
503 
504  virtual void CalcHessian (const IntegrationPoint &ip,
505  DenseMatrix &h) const;
506  virtual void ProjectDelta(int vertex, Vector &dofs) const;
507 };
508 
510 class GaussQuad2DFiniteElement : public NodalFiniteElement
511 {
512 private:
513  static const double p[2];
514  DenseMatrix A;
515  mutable DenseMatrix D;
516  mutable Vector pol;
517 public:
518  GaussQuad2DFiniteElement();
519  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
520  virtual void CalcDShape(const IntegrationPoint &ip,
521  DenseMatrix &dshape) const;
522  // virtual void ProjectDelta(int vertex, Vector &dofs) const;
523 };
524 
526 class BiQuad2DFiniteElement : public NodalFiniteElement
527 {
528 public:
530  BiQuad2DFiniteElement();
531 
535  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
536 
541  virtual void CalcDShape(const IntegrationPoint &ip,
542  DenseMatrix &dshape) const;
543  virtual void ProjectDelta(int vertex, Vector &dofs) const;
544 };
545 
546 class BiQuadPos2DFiniteElement : public FiniteElement
547 {
548 public:
549  BiQuadPos2DFiniteElement();
550  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
551  virtual void CalcDShape(const IntegrationPoint &ip,
552  DenseMatrix &dshape) const;
553  virtual void GetLocalInterpolation(ElementTransformation &Trans,
554  DenseMatrix &I) const;
555  using FiniteElement::Project;
556  virtual void Project(Coefficient &coeff, ElementTransformation &Trans,
557  Vector &dofs) const;
558  virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans,
559  Vector &dofs) const;
560  virtual void ProjectDelta(int vertex, Vector &dofs) const
561  { dofs = 0.; dofs(vertex) = 1.; }
562 };
563 
565 class GaussBiQuad2DFiniteElement : public NodalFiniteElement
566 {
567 public:
568  GaussBiQuad2DFiniteElement();
569  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
570  virtual void CalcDShape(const IntegrationPoint &ip,
571  DenseMatrix &dshape) const;
572  // virtual void ProjectDelta(int vertex, Vector &dofs) const { dofs = 1.; }
573 };
574 
575 class BiCubic2DFiniteElement : public NodalFiniteElement
576 {
577 public:
578  BiCubic2DFiniteElement();
579  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
580  virtual void CalcDShape(const IntegrationPoint &ip,
581  DenseMatrix &dshape) const;
582  virtual void CalcHessian (const IntegrationPoint &ip,
583  DenseMatrix &h) const;
584 };
585 
586 class Cubic1DFiniteElement : public NodalFiniteElement
587 {
588 public:
589  Cubic1DFiniteElement();
590 
591  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
592 
593  virtual void CalcDShape(const IntegrationPoint &ip,
594  DenseMatrix &dshape) const;
595 };
596 
597 class Cubic2DFiniteElement : public NodalFiniteElement
598 {
599 public:
600  Cubic2DFiniteElement();
601 
602  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
603 
604  virtual void CalcDShape(const IntegrationPoint &ip,
605  DenseMatrix &dshape) const;
606 
607  virtual void CalcHessian (const IntegrationPoint &ip,
608  DenseMatrix &h) const;
609 };
610 
612 class Cubic3DFiniteElement : public NodalFiniteElement
613 {
614 public:
616  Cubic3DFiniteElement();
617 
618  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
619 
620  virtual void CalcDShape(const IntegrationPoint &ip,
621  DenseMatrix &dshape) const;
622 };
623 
625 class P0TriangleFiniteElement : public NodalFiniteElement
626 {
627 public:
629  P0TriangleFiniteElement();
630 
632  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
633 
635  virtual void CalcDShape(const IntegrationPoint &ip,
636  DenseMatrix &dshape) const;
637  virtual void ProjectDelta(int vertex, Vector &dofs) const
638  { dofs(0) = 1.0; }
639 };
640 
641 
642 class P0QuadFiniteElement : public NodalFiniteElement
643 {
644 public:
645  P0QuadFiniteElement();
646  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
647  virtual void CalcDShape(const IntegrationPoint &ip,
648  DenseMatrix &dshape) const;
649  virtual void ProjectDelta(int vertex, Vector &dofs) const
650  { dofs(0) = 1.0; }
651 };
652 
653 
655 class Linear3DFiniteElement : public NodalFiniteElement
656 {
657 public:
659  Linear3DFiniteElement();
660 
664  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
665 
670  virtual void CalcDShape(const IntegrationPoint &ip,
671  DenseMatrix &dshape) const;
672 
673  virtual void ProjectDelta(int vertex, Vector &dofs) const
674  { dofs = 0.0; dofs(vertex) = 1.0; }
675 
676  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
677 };
678 
680 class Quadratic3DFiniteElement : public NodalFiniteElement
681 {
682 public:
684  Quadratic3DFiniteElement();
685 
686  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
687 
688  virtual void CalcDShape(const IntegrationPoint &ip,
689  DenseMatrix &dshape) const;
690 };
691 
693 class TriLinear3DFiniteElement : public NodalFiniteElement
694 {
695 public:
697  TriLinear3DFiniteElement();
698 
702  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
703 
708  virtual void CalcDShape(const IntegrationPoint &ip,
709  DenseMatrix &dshape) const;
710 
711  virtual void ProjectDelta(int vertex, Vector &dofs) const
712  { dofs = 0.0; dofs(vertex) = 1.0; }
713 };
714 
716 class CrouzeixRaviartFiniteElement : public NodalFiniteElement
717 {
718 public:
719  CrouzeixRaviartFiniteElement();
720  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
721  virtual void CalcDShape(const IntegrationPoint &ip,
722  DenseMatrix &dshape) const;
723  virtual void ProjectDelta(int vertex, Vector &dofs) const
724  { dofs = 1.0; }
725 };
726 
728 class CrouzeixRaviartQuadFiniteElement : public NodalFiniteElement
729 {
730 public:
731  CrouzeixRaviartQuadFiniteElement();
732  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
733  virtual void CalcDShape(const IntegrationPoint &ip,
734  DenseMatrix &dshape) const;
735 };
736 
737 class P0SegmentFiniteElement : public NodalFiniteElement
738 {
739 public:
740  P0SegmentFiniteElement(int Ord = 0);
741  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
742  virtual void CalcDShape(const IntegrationPoint &ip,
743  DenseMatrix &dshape) const;
744 };
745 
746 class RT0TriangleFiniteElement : public VectorFiniteElement
747 {
748 private:
749  static const double nk[3][2];
750 
751 public:
752  RT0TriangleFiniteElement();
753 
754  virtual void CalcVShape(const IntegrationPoint &ip,
755  DenseMatrix &shape) const;
756 
757  virtual void CalcVShape(ElementTransformation &Trans,
758  DenseMatrix &shape) const
759  { CalcVShape_RT(Trans, shape); }
760 
761  virtual void CalcDivShape(const IntegrationPoint &ip,
762  Vector &divshape) const;
763 
764  virtual void GetLocalInterpolation (ElementTransformation &Trans,
765  DenseMatrix &I) const;
766 
767  using FiniteElement::Project;
768 
769  virtual void Project (VectorCoefficient &vc,
770  ElementTransformation &Trans, Vector &dofs) const;
771 };
772 
773 class RT0QuadFiniteElement : public VectorFiniteElement
774 {
775 private:
776  static const double nk[4][2];
777 
778 public:
779  RT0QuadFiniteElement();
780 
781  virtual void CalcVShape(const IntegrationPoint &ip,
782  DenseMatrix &shape) const;
783 
784  virtual void CalcVShape(ElementTransformation &Trans,
785  DenseMatrix &shape) const
786  { CalcVShape_RT(Trans, shape); }
787 
788  virtual void CalcDivShape(const IntegrationPoint &ip,
789  Vector &divshape) const;
790 
791  virtual void GetLocalInterpolation (ElementTransformation &Trans,
792  DenseMatrix &I) const;
793 
794  using FiniteElement::Project;
795 
796  virtual void Project (VectorCoefficient &vc,
797  ElementTransformation &Trans, Vector &dofs) const;
798 };
799 
800 class RT1TriangleFiniteElement : public VectorFiniteElement
801 {
802 private:
803  static const double nk[8][2];
804 
805 public:
806  RT1TriangleFiniteElement();
807 
808  virtual void CalcVShape(const IntegrationPoint &ip,
809  DenseMatrix &shape) const;
810 
811  virtual void CalcVShape(ElementTransformation &Trans,
812  DenseMatrix &shape) const
813  { CalcVShape_RT(Trans, shape); }
814 
815  virtual void CalcDivShape(const IntegrationPoint &ip,
816  Vector &divshape) const;
817 
818  virtual void GetLocalInterpolation (ElementTransformation &Trans,
819  DenseMatrix &I) const;
820 
821  using FiniteElement::Project;
822 
823  virtual void Project (VectorCoefficient &vc,
824  ElementTransformation &Trans, Vector &dofs) const;
825 };
826 
827 class RT1QuadFiniteElement : public VectorFiniteElement
828 {
829 private:
830  static const double nk[12][2];
831 
832 public:
833  RT1QuadFiniteElement();
834 
835  virtual void CalcVShape(const IntegrationPoint &ip,
836  DenseMatrix &shape) const;
837 
838  virtual void CalcVShape(ElementTransformation &Trans,
839  DenseMatrix &shape) const
840  { CalcVShape_RT(Trans, shape); }
841 
842  virtual void CalcDivShape(const IntegrationPoint &ip,
843  Vector &divshape) const;
844 
845  virtual void GetLocalInterpolation (ElementTransformation &Trans,
846  DenseMatrix &I) const;
847 
848  using FiniteElement::Project;
849 
850  virtual void Project (VectorCoefficient &vc,
851  ElementTransformation &Trans, Vector &dofs) const;
852 };
853 
854 class RT2TriangleFiniteElement : public VectorFiniteElement
855 {
856 private:
857  static const double M[15][15];
858 public:
859  RT2TriangleFiniteElement();
860 
861  virtual void CalcVShape(const IntegrationPoint &ip,
862  DenseMatrix &shape) const;
863 
864  virtual void CalcVShape(ElementTransformation &Trans,
865  DenseMatrix &shape) const
866  { CalcVShape_RT(Trans, shape); }
867 
868  virtual void CalcDivShape(const IntegrationPoint &ip,
869  Vector &divshape) const;
870 };
871 
872 class RT2QuadFiniteElement : public VectorFiniteElement
873 {
874 private:
875  static const double nk[24][2];
876  static const double pt[4];
877  static const double dpt[3];
878 
879 public:
880  RT2QuadFiniteElement();
881 
882  virtual void CalcVShape(const IntegrationPoint &ip,
883  DenseMatrix &shape) const;
884 
885  virtual void CalcVShape(ElementTransformation &Trans,
886  DenseMatrix &shape) const
887  { CalcVShape_RT(Trans, shape); }
888 
889  virtual void CalcDivShape(const IntegrationPoint &ip,
890  Vector &divshape) const;
891 
892  virtual void GetLocalInterpolation (ElementTransformation &Trans,
893  DenseMatrix &I) const;
894 
895  using FiniteElement::Project;
896 
897  virtual void Project (VectorCoefficient &vc,
898  ElementTransformation &Trans, Vector &dofs) const;
899 };
900 
902 class P1SegmentFiniteElement : public NodalFiniteElement
903 {
904 public:
905  P1SegmentFiniteElement();
906  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
907  virtual void CalcDShape(const IntegrationPoint &ip,
908  DenseMatrix &dshape) const;
909 };
910 
912 class P2SegmentFiniteElement : public NodalFiniteElement
913 {
914 public:
915  P2SegmentFiniteElement();
916  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
917  virtual void CalcDShape(const IntegrationPoint &ip,
918  DenseMatrix &dshape) const;
919 };
920 
921 class Lagrange1DFiniteElement : public NodalFiniteElement
922 {
923 private:
924  Vector rwk;
925 #ifndef MFEM_THREAD_SAFE
926  mutable Vector rxxk;
927 #endif
928 public:
929  Lagrange1DFiniteElement (int degree);
930  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
931  virtual void CalcDShape(const IntegrationPoint &ip,
932  DenseMatrix &dshape) const;
933 };
934 
935 class P1TetNonConfFiniteElement : public NodalFiniteElement
936 {
937 public:
938  P1TetNonConfFiniteElement();
939  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
940  virtual void CalcDShape(const IntegrationPoint &ip,
941  DenseMatrix &dshape) const;
942 };
943 
944 class P0TetFiniteElement : public NodalFiniteElement
945 {
946 public:
947  P0TetFiniteElement ();
948  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
949  virtual void CalcDShape(const IntegrationPoint &ip,
950  DenseMatrix &dshape) const;
951  virtual void ProjectDelta(int vertex, Vector &dofs) const
952  { dofs(0) = 1.0; }
953 };
954 
955 class P0HexFiniteElement : public NodalFiniteElement
956 {
957 public:
958  P0HexFiniteElement ();
959  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
960  virtual void CalcDShape(const IntegrationPoint &ip,
961  DenseMatrix &dshape) const;
962  virtual void ProjectDelta(int vertex, Vector &dofs) const
963  { dofs(0) = 1.0; }
964 };
965 
967 class LagrangeHexFiniteElement : public NodalFiniteElement
968 {
969 private:
970  Lagrange1DFiniteElement * fe1d;
971  int dof1d;
972  int *I, *J, *K;
973 #ifndef MFEM_THREAD_SAFE
974  mutable Vector shape1dx, shape1dy, shape1dz;
975  mutable DenseMatrix dshape1dx, dshape1dy, dshape1dz;
976 #endif
977 
978 public:
979  LagrangeHexFiniteElement (int degree);
980  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
981  virtual void CalcDShape(const IntegrationPoint &ip,
982  DenseMatrix &dshape) const;
983  ~LagrangeHexFiniteElement ();
984 };
985 
986 
988 class RefinedLinear1DFiniteElement : public NodalFiniteElement
989 {
990 public:
992  RefinedLinear1DFiniteElement();
993 
997  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
998 
1003  virtual void CalcDShape(const IntegrationPoint &ip,
1004  DenseMatrix &dshape) const;
1005 };
1006 
1008 class RefinedLinear2DFiniteElement : public NodalFiniteElement
1009 {
1010 public:
1012  RefinedLinear2DFiniteElement();
1013 
1017  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1018 
1023  virtual void CalcDShape(const IntegrationPoint &ip,
1024  DenseMatrix &dshape) const;
1025 };
1026 
1028 class RefinedLinear3DFiniteElement : public NodalFiniteElement
1029 {
1030 public:
1032  RefinedLinear3DFiniteElement();
1033 
1034  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1035 
1036  virtual void CalcDShape(const IntegrationPoint &ip,
1037  DenseMatrix &dshape) const;
1038 };
1039 
1041 class RefinedBiLinear2DFiniteElement : public NodalFiniteElement
1042 {
1043 public:
1045  RefinedBiLinear2DFiniteElement();
1046 
1050  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1051 
1056  virtual void CalcDShape(const IntegrationPoint &ip,
1057  DenseMatrix &dshape) const;
1058 };
1059 
1061 class RefinedTriLinear3DFiniteElement : public NodalFiniteElement
1062 {
1063 public:
1065  RefinedTriLinear3DFiniteElement();
1066 
1070  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1071 
1076  virtual void CalcDShape(const IntegrationPoint &ip,
1077  DenseMatrix &dshape) const;
1078 };
1079 
1080 
1081 class Nedelec1HexFiniteElement : public VectorFiniteElement
1082 {
1083 private:
1084  static const double tk[12][3];
1085 
1086 public:
1087  Nedelec1HexFiniteElement();
1088  virtual void CalcVShape(const IntegrationPoint &ip,
1089  DenseMatrix &shape) const;
1090  virtual void CalcVShape(ElementTransformation &Trans,
1091  DenseMatrix &shape) const
1092  { CalcVShape_ND(Trans, shape); }
1093  virtual void CalcCurlShape(const IntegrationPoint &ip,
1094  DenseMatrix &curl_shape) const;
1095  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1096  DenseMatrix &I) const;
1097  using FiniteElement::Project;
1098  virtual void Project (VectorCoefficient &vc,
1099  ElementTransformation &Trans, Vector &dofs) const;
1100 };
1101 
1102 
1103 class Nedelec1TetFiniteElement : public VectorFiniteElement
1104 {
1105 private:
1106  static const double tk[6][3];
1107 
1108 public:
1109  Nedelec1TetFiniteElement();
1110  virtual void CalcVShape(const IntegrationPoint &ip,
1111  DenseMatrix &shape) const;
1112  virtual void CalcVShape(ElementTransformation &Trans,
1113  DenseMatrix &shape) const
1114  { CalcVShape_ND(Trans, shape); }
1115  virtual void CalcCurlShape(const IntegrationPoint &ip,
1116  DenseMatrix &curl_shape) const;
1117  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1118  DenseMatrix &I) const;
1119  using FiniteElement::Project;
1120  virtual void Project (VectorCoefficient &vc,
1121  ElementTransformation &Trans, Vector &dofs) const;
1122 };
1123 
1124 
1125 class RT0HexFiniteElement : public VectorFiniteElement
1126 {
1127 private:
1128  static const double nk[6][3];
1129 
1130 public:
1131  RT0HexFiniteElement();
1132 
1133  virtual void CalcVShape(const IntegrationPoint &ip,
1134  DenseMatrix &shape) const;
1135 
1136  virtual void CalcVShape(ElementTransformation &Trans,
1137  DenseMatrix &shape) const
1138  { CalcVShape_RT(Trans, shape); }
1139 
1140  virtual void CalcDivShape(const IntegrationPoint &ip,
1141  Vector &divshape) const;
1142 
1143  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1144  DenseMatrix &I) const;
1145 
1146  using FiniteElement::Project;
1147 
1148  virtual void Project (VectorCoefficient &vc,
1149  ElementTransformation &Trans, Vector &dofs) const;
1150 };
1151 
1152 
1153 class RT1HexFiniteElement : public VectorFiniteElement
1154 {
1155 private:
1156  static const double nk[36][3];
1157 
1158 public:
1159  RT1HexFiniteElement();
1160 
1161  virtual void CalcVShape(const IntegrationPoint &ip,
1162  DenseMatrix &shape) const;
1163 
1164  virtual void CalcVShape(ElementTransformation &Trans,
1165  DenseMatrix &shape) const
1166  { CalcVShape_RT(Trans, shape); }
1167 
1168  virtual void CalcDivShape(const IntegrationPoint &ip,
1169  Vector &divshape) const;
1170 
1171  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1172  DenseMatrix &I) const;
1173 
1174  using FiniteElement::Project;
1175 
1176  virtual void Project (VectorCoefficient &vc,
1177  ElementTransformation &Trans, Vector &dofs) const;
1178 };
1179 
1180 
1181 class RT0TetFiniteElement : public VectorFiniteElement
1182 {
1183 private:
1184  static const double nk[4][3];
1185 
1186 public:
1187  RT0TetFiniteElement();
1188 
1189  virtual void CalcVShape(const IntegrationPoint &ip,
1190  DenseMatrix &shape) const;
1191 
1192  virtual void CalcVShape(ElementTransformation &Trans,
1193  DenseMatrix &shape) const
1194  { CalcVShape_RT(Trans, shape); }
1195 
1196  virtual void CalcDivShape(const IntegrationPoint &ip,
1197  Vector &divshape) const;
1198 
1199  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1200  DenseMatrix &I) const;
1201 
1202  using FiniteElement::Project;
1203 
1204  virtual void Project (VectorCoefficient &vc,
1205  ElementTransformation &Trans, Vector &dofs) const;
1206 };
1207 
1208 
1209 class RotTriLinearHexFiniteElement : public NodalFiniteElement
1210 {
1211 public:
1212  RotTriLinearHexFiniteElement();
1213  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1214  virtual void CalcDShape(const IntegrationPoint &ip,
1215  DenseMatrix &dshape) const;
1216 };
1217 
1218 
1219 class Poly_1D
1220 {
1221 public:
1222  class Basis
1223  {
1224  private:
1225  int mode; // 0 - use change of basis, O(p^2) Evals
1226  // 1 - use barycentric Lagrangian interpolation, O(p) Evals
1227  DenseMatrixInverse Ai;
1228  mutable Vector x, w;
1229 
1230  public:
1231  Basis(const int p, const double *nodes, const int _mode = 1);
1232  void Eval(const double x, Vector &u) const;
1233  void Eval(const double x, Vector &u, Vector &d) const;
1234  };
1235 
1236 private:
1237  Array<double *> open_pts, closed_pts;
1238  Array<Basis *> open_basis, closed_basis;
1239 
1240  static Array2D<int> binom;
1241 
1242  static void CalcMono(const int p, const double x, double *u);
1243  static void CalcMono(const int p, const double x, double *u, double *d);
1244 
1245  static void CalcLegendre(const int p, const double x, double *u);
1246  static void CalcLegendre(const int p, const double x, double *u, double *d);
1247 
1248  static void CalcChebyshev(const int p, const double x, double *u);
1249  static void CalcChebyshev(const int p, const double x, double *u, double *d);
1250 
1251 public:
1252  Poly_1D() { }
1253 
1254  static const int *Binom(const int p);
1255 
1256  const double *OpenPoints(const int p);
1257  const double *ClosedPoints(const int p);
1258 
1259  Basis &OpenBasis(const int p);
1260  Basis &ClosedBasis(const int p);
1261 
1262  // Evaluate the values of a hierarchical 1D basis at point x
1263  // hierarchical = k-th basis function is degree k polynomial
1264  static void CalcBasis(const int p, const double x, double *u)
1265  // { CalcMono(p, x, u); }
1266  // Bernstein basis is not hierarchical --> does not work for triangles
1267  // and tetrahedra
1268  // { CalcBernstein(p, x, u); }
1269  // { CalcLegendre(p, x, u); }
1270  { CalcChebyshev(p, x, u); }
1271 
1272  // Evaluate the values and derivatives of a hierarchical 1D basis at point x
1273  static void CalcBasis(const int p, const double x, double *u, double *d)
1274  // { CalcMono(p, x, u, d); }
1275  // { CalcBernstein(p, x, u, d); }
1276  // { CalcLegendre(p, x, u, d); }
1277  { CalcChebyshev(p, x, u, d); }
1278 
1279  // Evaluate a representation of a Delta function at point x
1280  static double CalcDelta(const int p, const double x)
1281  { return pow(x, (double) p); }
1282 
1283  static void UniformPoints(const int p, double *x);
1284  static void GaussPoints(const int p, double *x);
1285  static void GaussLobattoPoints(const int p, double *x);
1286  static void ChebyshevPoints(const int p, double *x);
1287 
1289  static void CalcBinomTerms(const int p, const double x, const double y,
1290  double *u);
1293  static void CalcBinomTerms(const int p, const double x, const double y,
1294  double *u, double *d);
1297  static void CalcDBinomTerms(const int p, const double x, const double y,
1298  double *d);
1299  static void CalcBernstein(const int p, const double x, double *u)
1300  { CalcBinomTerms(p, x, 1. - x, u); }
1301  static void CalcBernstein(const int p, const double x, double *u, double *d)
1302  { CalcBinomTerms(p, x, 1. - x, u, d); }
1303 
1304  ~Poly_1D();
1305 };
1306 
1307 extern Poly_1D poly1d;
1308 
1309 
1310 class H1_SegmentElement : public NodalFiniteElement
1311 {
1312 private:
1313  Poly_1D::Basis &basis1d;
1314 #ifndef MFEM_THREAD_SAFE
1315  mutable Vector shape_x, dshape_x;
1316 #endif
1317 
1318 public:
1319  H1_SegmentElement(const int p);
1320  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1321  virtual void CalcDShape(const IntegrationPoint &ip,
1322  DenseMatrix &dshape) const;
1323  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1324 };
1325 
1326 
1327 class H1_QuadrilateralElement : public NodalFiniteElement
1328 {
1329 private:
1330  Poly_1D::Basis &basis1d;
1331 #ifndef MFEM_THREAD_SAFE
1332  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1333 #endif
1334  Array<int> dof_map;
1335 
1336 public:
1337  H1_QuadrilateralElement(const int p);
1338  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1339  virtual void CalcDShape(const IntegrationPoint &ip,
1340  DenseMatrix &dshape) const;
1341  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1342  const Array<int> &GetDofMap() const { return dof_map; }
1343 };
1344 
1345 
1346 class H1_HexahedronElement : public NodalFiniteElement
1347 {
1348 private:
1349  Poly_1D::Basis &basis1d;
1350 #ifndef MFEM_THREAD_SAFE
1351  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1352 #endif
1353  Array<int> dof_map;
1354 
1355 public:
1356  H1_HexahedronElement(const int p);
1357  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1358  virtual void CalcDShape(const IntegrationPoint &ip,
1359  DenseMatrix &dshape) const;
1360  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1361  const Array<int> &GetDofMap() const { return dof_map; }
1362 };
1363 
1364 class H1Pos_SegmentElement : public PositiveFiniteElement
1365 {
1366 private:
1367 #ifndef MFEM_THREAD_SAFE
1368  // This is to share scratch space between invocations, which helps
1369  // speed things up, but with OpenMP, we need one copy per thread.
1370  // Right now, we solve this by allocating this space within each function
1371  // call every time we call it. Alternatively, we should do some sort
1372  // thread private thing. Brunner, Jan 2014
1373  mutable Vector shape_x, dshape_x;
1374 #endif
1375 
1376 public:
1377  H1Pos_SegmentElement(const int p);
1378  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1379  virtual void CalcDShape(const IntegrationPoint &ip,
1380  DenseMatrix &dshape) const;
1381  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1382 };
1383 
1384 
1385 class H1Pos_QuadrilateralElement : public PositiveFiniteElement
1386 {
1387 private:
1388 #ifndef MFEM_THREAD_SAFE
1389  // See comment in H1Pos_SegmentElement
1390  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1391 #endif
1392  Array<int> dof_map;
1393 
1394 public:
1395  H1Pos_QuadrilateralElement(const int p);
1396  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1397  virtual void CalcDShape(const IntegrationPoint &ip,
1398  DenseMatrix &dshape) const;
1399  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1400 };
1401 
1402 
1403 class H1Pos_HexahedronElement : public PositiveFiniteElement
1404 {
1405 private:
1406 #ifndef MFEM_THREAD_SAFE
1407  // See comment in H1Pos_SegementElement.
1408  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1409 #endif
1410  Array<int> dof_map;
1411 
1412 public:
1413  H1Pos_HexahedronElement(const int p);
1414  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1415  virtual void CalcDShape(const IntegrationPoint &ip,
1416  DenseMatrix &dshape) const;
1417  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1418 };
1419 
1420 
1421 class H1_TriangleElement : public NodalFiniteElement
1422 {
1423 private:
1424 #ifndef MFEM_THREAD_SAFE
1425  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1426  mutable DenseMatrix du;
1427 #endif
1428  DenseMatrixInverse Ti;
1429 
1430 public:
1431  H1_TriangleElement(const int p);
1432  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1433  virtual void CalcDShape(const IntegrationPoint &ip,
1434  DenseMatrix &dshape) const;
1435 };
1436 
1437 
1438 class H1_TetrahedronElement : public NodalFiniteElement
1439 {
1440 private:
1441 #ifndef MFEM_THREAD_SAFE
1442  mutable Vector shape_x, shape_y, shape_z, shape_l;
1443  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1444  mutable DenseMatrix du;
1445 #endif
1446  DenseMatrixInverse Ti;
1447 
1448 public:
1449  H1_TetrahedronElement(const int p);
1450  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1451  virtual void CalcDShape(const IntegrationPoint &ip,
1452  DenseMatrix &dshape) const;
1453 };
1454 
1455 
1456 // TODO: define H1Pos_ FEs on triangle and tetrahedron
1457 
1458 
1459 class L2_SegmentElement : public NodalFiniteElement
1460 {
1461 private:
1462  int type;
1463  Poly_1D::Basis *basis1d;
1464 #ifndef MFEM_THREAD_SAFE
1465  mutable Vector shape_x, dshape_x;
1466 #endif
1467 
1468 public:
1469  L2_SegmentElement(const int p, const int _type = 0);
1470  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1471  virtual void CalcDShape(const IntegrationPoint &ip,
1472  DenseMatrix &dshape) const;
1473  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1474 };
1475 
1476 
1477 class L2Pos_SegmentElement : public PositiveFiniteElement
1478 {
1479 private:
1480 #ifndef MFEM_THREAD_SAFE
1481  mutable Vector shape_x, dshape_x;
1482 #endif
1483 
1484 public:
1485  L2Pos_SegmentElement(const int p);
1486  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1487  virtual void CalcDShape(const IntegrationPoint &ip,
1488  DenseMatrix &dshape) const;
1489  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1490 };
1491 
1492 
1493 class L2_QuadrilateralElement : public NodalFiniteElement
1494 {
1495 private:
1496  int type;
1497  Poly_1D::Basis *basis1d;
1498 #ifndef MFEM_THREAD_SAFE
1499  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1500 #endif
1501 
1502 public:
1503  L2_QuadrilateralElement(const int p, const int _type = 0);
1504  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1505  virtual void CalcDShape(const IntegrationPoint &ip,
1506  DenseMatrix &dshape) const;
1507  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1508  virtual void ProjectCurl(const FiniteElement &fe,
1509  ElementTransformation &Trans,
1510  DenseMatrix &curl) const
1511  { ProjectCurl_2D(fe, Trans, curl); }
1512 };
1513 
1514 
1515 class L2Pos_QuadrilateralElement : public PositiveFiniteElement
1516 {
1517 private:
1518 #ifndef MFEM_THREAD_SAFE
1519  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1520 #endif
1521 
1522 public:
1523  L2Pos_QuadrilateralElement(const int p);
1524  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1525  virtual void CalcDShape(const IntegrationPoint &ip,
1526  DenseMatrix &dshape) const;
1527  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1528 };
1529 
1530 
1531 class L2_HexahedronElement : public NodalFiniteElement
1532 {
1533 private:
1534  int type;
1535  Poly_1D::Basis *basis1d;
1536 #ifndef MFEM_THREAD_SAFE
1537  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1538 #endif
1539 
1540 public:
1541  L2_HexahedronElement(const int p, const int _type = 0);
1542  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1543  virtual void CalcDShape(const IntegrationPoint &ip,
1544  DenseMatrix &dshape) const;
1545  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1546 };
1547 
1548 
1549 class L2Pos_HexahedronElement : public PositiveFiniteElement
1550 {
1551 private:
1552 #ifndef MFEM_THREAD_SAFE
1553  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1554 #endif
1555 
1556 public:
1557  L2Pos_HexahedronElement(const int p);
1558  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1559  virtual void CalcDShape(const IntegrationPoint &ip,
1560  DenseMatrix &dshape) const;
1561  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1562 };
1563 
1564 
1565 class L2_TriangleElement : public NodalFiniteElement
1566 {
1567 private:
1568  int type;
1569 #ifndef MFEM_THREAD_SAFE
1570  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1571  mutable DenseMatrix du;
1572 #endif
1573  DenseMatrixInverse Ti;
1574 
1575 public:
1576  L2_TriangleElement(const int p, const int _type = 0);
1577  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1578  virtual void CalcDShape(const IntegrationPoint &ip,
1579  DenseMatrix &dshape) const;
1580  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1581  virtual void ProjectCurl(const FiniteElement &fe,
1582  ElementTransformation &Trans,
1583  DenseMatrix &curl) const
1584  { ProjectCurl_2D(fe, Trans, curl); }
1585 };
1586 
1587 
1588 class L2Pos_TriangleElement : public PositiveFiniteElement
1589 {
1590 private:
1591 #ifndef MFEM_THREAD_SAFE
1592  mutable Vector dshape_1d;
1593 #endif
1594 
1595 public:
1596  L2Pos_TriangleElement(const int p);
1597  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1598  virtual void CalcDShape(const IntegrationPoint &ip,
1599  DenseMatrix &dshape) const;
1600  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1601 };
1602 
1603 
1604 class L2_TetrahedronElement : public NodalFiniteElement
1605 {
1606 private:
1607  int type;
1608 #ifndef MFEM_THREAD_SAFE
1609  mutable Vector shape_x, shape_y, shape_z, shape_l;
1610  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1611  mutable DenseMatrix du;
1612 #endif
1613  DenseMatrixInverse Ti;
1614 
1615 public:
1616  L2_TetrahedronElement(const int p, const int _type = 0);
1617  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1618  virtual void CalcDShape(const IntegrationPoint &ip,
1619  DenseMatrix &dshape) const;
1620  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1621 };
1622 
1623 
1624 class L2Pos_TetrahedronElement : public PositiveFiniteElement
1625 {
1626 private:
1627 #ifndef MFEM_THREAD_SAFE
1628  mutable Vector dshape_1d;
1629 #endif
1630 
1631 public:
1632  L2Pos_TetrahedronElement(const int p);
1633  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1634  virtual void CalcDShape(const IntegrationPoint &ip,
1635  DenseMatrix &dshape) const;
1636  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1637 };
1638 
1639 
1640 class RT_QuadrilateralElement : public VectorFiniteElement
1641 {
1642 private:
1643  static const double nk[8];
1644 
1645  Poly_1D::Basis &cbasis1d, &obasis1d;
1646 #ifndef MFEM_THREAD_SAFE
1647  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
1648  mutable Vector dshape_cx, dshape_cy;
1649 #endif
1650  Array<int> dof_map, dof2nk;
1651 
1652 public:
1653  RT_QuadrilateralElement(const int p);
1654  virtual void CalcVShape(const IntegrationPoint &ip,
1655  DenseMatrix &shape) const;
1656  virtual void CalcVShape(ElementTransformation &Trans,
1657  DenseMatrix &shape) const
1658  { CalcVShape_RT(Trans, shape); }
1659  virtual void CalcDivShape(const IntegrationPoint &ip,
1660  Vector &divshape) const;
1661  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1662  DenseMatrix &I) const
1663  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1664  using FiniteElement::Project;
1665  virtual void Project(VectorCoefficient &vc,
1666  ElementTransformation &Trans, Vector &dofs) const
1667  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1668  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1669  DenseMatrix &I) const
1670  { Project_RT(nk, dof2nk, fe, Trans, I); }
1671  virtual void ProjectGrad(const FiniteElement &fe,
1672  ElementTransformation &Trans,
1673  DenseMatrix &grad) const
1674  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1675 };
1676 
1677 
1678 class RT_HexahedronElement : public VectorFiniteElement
1679 {
1680  static const double nk[18];
1681 
1682  Poly_1D::Basis &cbasis1d, &obasis1d;
1683 #ifndef MFEM_THREAD_SAFE
1684  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
1685  mutable Vector dshape_cx, dshape_cy, dshape_cz;
1686 #endif
1687  Array<int> dof_map, dof2nk;
1688 
1689 public:
1690  RT_HexahedronElement(const int p);
1691  virtual void CalcVShape(const IntegrationPoint &ip,
1692  DenseMatrix &shape) const;
1693  virtual void CalcVShape(ElementTransformation &Trans,
1694  DenseMatrix &shape) const
1695  { CalcVShape_RT(Trans, shape); }
1696  virtual void CalcDivShape(const IntegrationPoint &ip,
1697  Vector &divshape) const;
1698  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1699  DenseMatrix &I) const
1700  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1701  using FiniteElement::Project;
1702  virtual void Project(VectorCoefficient &vc,
1703  ElementTransformation &Trans, Vector &dofs) const
1704  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1705  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1706  DenseMatrix &I) const
1707  { Project_RT(nk, dof2nk, fe, Trans, I); }
1708  virtual void ProjectCurl(const FiniteElement &fe,
1709  ElementTransformation &Trans,
1710  DenseMatrix &curl) const
1711  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
1712 };
1713 
1714 
1715 class RT_TriangleElement : public VectorFiniteElement
1716 {
1717  static const double nk[6], c;
1718 
1719 #ifndef MFEM_THREAD_SAFE
1720  mutable Vector shape_x, shape_y, shape_l;
1721  mutable Vector dshape_x, dshape_y, dshape_l;
1722  mutable DenseMatrix u;
1723  mutable Vector divu;
1724 #endif
1725  Array<int> dof2nk;
1726  DenseMatrixInverse Ti;
1727 
1728 public:
1729  RT_TriangleElement(const int p);
1730  virtual void CalcVShape(const IntegrationPoint &ip,
1731  DenseMatrix &shape) const;
1732  virtual void CalcVShape(ElementTransformation &Trans,
1733  DenseMatrix &shape) const
1734  { CalcVShape_RT(Trans, shape); }
1735  virtual void CalcDivShape(const IntegrationPoint &ip,
1736  Vector &divshape) const;
1737  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1738  DenseMatrix &I) const
1739  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1740  using FiniteElement::Project;
1741  virtual void Project(VectorCoefficient &vc,
1742  ElementTransformation &Trans, Vector &dofs) const
1743  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1744  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1745  DenseMatrix &I) const
1746  { Project_RT(nk, dof2nk, fe, Trans, I); }
1747  virtual void ProjectGrad(const FiniteElement &fe,
1748  ElementTransformation &Trans,
1749  DenseMatrix &grad) const
1750  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1751 };
1752 
1753 
1754 class RT_TetrahedronElement : public VectorFiniteElement
1755 {
1756  static const double nk[12], c;
1757 
1758 #ifndef MFEM_THREAD_SAFE
1759  mutable Vector shape_x, shape_y, shape_z, shape_l;
1760  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
1761  mutable DenseMatrix u;
1762  mutable Vector divu;
1763 #endif
1764  Array<int> dof2nk;
1765  DenseMatrixInverse Ti;
1766 
1767 public:
1768  RT_TetrahedronElement(const int p);
1769  virtual void CalcVShape(const IntegrationPoint &ip,
1770  DenseMatrix &shape) const;
1771  virtual void CalcVShape(ElementTransformation &Trans,
1772  DenseMatrix &shape) const
1773  { CalcVShape_RT(Trans, shape); }
1774  virtual void CalcDivShape(const IntegrationPoint &ip,
1775  Vector &divshape) const;
1776  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1777  DenseMatrix &I) const
1778  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1779  using FiniteElement::Project;
1780  virtual void Project(VectorCoefficient &vc,
1781  ElementTransformation &Trans, Vector &dofs) const
1782  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1783  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1784  DenseMatrix &I) const
1785  { Project_RT(nk, dof2nk, fe, Trans, I); }
1786  virtual void ProjectCurl(const FiniteElement &fe,
1787  ElementTransformation &Trans,
1788  DenseMatrix &curl) const
1789  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
1790 };
1791 
1792 
1793 class ND_HexahedronElement : public VectorFiniteElement
1794 {
1795  static const double tk[18];
1796 
1797  Poly_1D::Basis &cbasis1d, &obasis1d;
1798 #ifndef MFEM_THREAD_SAFE
1799  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
1800  mutable Vector dshape_cx, dshape_cy, dshape_cz;
1801 #endif
1802  Array<int> dof_map, dof2tk;
1803 
1804 public:
1805  ND_HexahedronElement(const int p);
1806 
1807  virtual void CalcVShape(const IntegrationPoint &ip,
1808  DenseMatrix &shape) const;
1809 
1810  virtual void CalcVShape(ElementTransformation &Trans,
1811  DenseMatrix &shape) const
1812  { CalcVShape_ND(Trans, shape); }
1813 
1814  virtual void CalcCurlShape(const IntegrationPoint &ip,
1815  DenseMatrix &curl_shape) const;
1816 
1817  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1818  DenseMatrix &I) const
1819  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1820 
1821  using FiniteElement::Project;
1822 
1823  virtual void Project(VectorCoefficient &vc,
1824  ElementTransformation &Trans, Vector &dofs) const
1825  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1826 
1827  virtual void Project(const FiniteElement &fe,
1828  ElementTransformation &Trans,
1829  DenseMatrix &I) const
1830  { Project_ND(tk, dof2tk, fe, Trans, I); }
1831 
1832  virtual void ProjectGrad(const FiniteElement &fe,
1833  ElementTransformation &Trans,
1834  DenseMatrix &grad) const
1835  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1836 
1837  virtual void ProjectCurl(const FiniteElement &fe,
1838  ElementTransformation &Trans,
1839  DenseMatrix &curl) const
1840  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
1841 };
1842 
1843 
1844 class ND_QuadrilateralElement : public VectorFiniteElement
1845 {
1846  static const double tk[8];
1847 
1848  Poly_1D::Basis &cbasis1d, &obasis1d;
1849 #ifndef MFEM_THREAD_SAFE
1850  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
1851  mutable Vector dshape_cx, dshape_cy;
1852 #endif
1853  Array<int> dof_map, dof2tk;
1854 
1855 public:
1856  ND_QuadrilateralElement(const int p);
1857  virtual void CalcVShape(const IntegrationPoint &ip,
1858  DenseMatrix &shape) const;
1859  virtual void CalcVShape(ElementTransformation &Trans,
1860  DenseMatrix &shape) const
1861  { CalcVShape_ND(Trans, shape); }
1862  virtual void CalcCurlShape(const IntegrationPoint &ip,
1863  DenseMatrix &curl_shape) const;
1864  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1865  DenseMatrix &I) const
1866  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1867  using FiniteElement::Project;
1868  virtual void Project(VectorCoefficient &vc,
1869  ElementTransformation &Trans, Vector &dofs) const
1870  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1871  virtual void Project(const FiniteElement &fe,
1872  ElementTransformation &Trans,
1873  DenseMatrix &I) const
1874  { Project_ND(tk, dof2tk, fe, Trans, I); }
1875  virtual void ProjectGrad(const FiniteElement &fe,
1876  ElementTransformation &Trans,
1877  DenseMatrix &grad) const
1878  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1879 };
1880 
1881 
1882 class ND_TetrahedronElement : public VectorFiniteElement
1883 {
1884  static const double tk[18], c;
1885 
1886 #ifndef MFEM_THREAD_SAFE
1887  mutable Vector shape_x, shape_y, shape_z, shape_l;
1888  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
1889  mutable DenseMatrix u;
1890 #endif
1891  Array<int> dof2tk;
1892  DenseMatrixInverse Ti;
1893 
1894 public:
1895  ND_TetrahedronElement(const int p);
1896  virtual void CalcVShape(const IntegrationPoint &ip,
1897  DenseMatrix &shape) const;
1898  virtual void CalcVShape(ElementTransformation &Trans,
1899  DenseMatrix &shape) const
1900  { CalcVShape_ND(Trans, shape); }
1901  virtual void CalcCurlShape(const IntegrationPoint &ip,
1902  DenseMatrix &curl_shape) const;
1903  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1904  DenseMatrix &I) const
1905  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1906  using FiniteElement::Project;
1907  virtual void Project(VectorCoefficient &vc,
1908  ElementTransformation &Trans, Vector &dofs) const
1909  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1910  virtual void Project(const FiniteElement &fe,
1911  ElementTransformation &Trans,
1912  DenseMatrix &I) const
1913  { Project_ND(tk, dof2tk, fe, Trans, I); }
1914  virtual void ProjectGrad(const FiniteElement &fe,
1915  ElementTransformation &Trans,
1916  DenseMatrix &grad) const
1917  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1918 
1919  virtual void ProjectCurl(const FiniteElement &fe,
1920  ElementTransformation &Trans,
1921  DenseMatrix &curl) const
1922  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
1923 };
1924 
1925 class ND_TriangleElement : public VectorFiniteElement
1926 {
1927  static const double tk[8], c;
1928 
1929 #ifndef MFEM_THREAD_SAFE
1930  mutable Vector shape_x, shape_y, shape_l;
1931  mutable Vector dshape_x, dshape_y, dshape_l;
1932  mutable DenseMatrix u;
1933  mutable Vector curlu;
1934 #endif
1935  Array<int> dof2tk;
1936  DenseMatrixInverse Ti;
1937 
1938 public:
1939  ND_TriangleElement(const int p);
1940  virtual void CalcVShape(const IntegrationPoint &ip,
1941  DenseMatrix &shape) const;
1942  virtual void CalcVShape(ElementTransformation &Trans,
1943  DenseMatrix &shape) const
1944  { CalcVShape_ND(Trans, shape); }
1945  virtual void CalcCurlShape(const IntegrationPoint &ip,
1946  DenseMatrix &curl_shape) const;
1947  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1948  DenseMatrix &I) const
1949  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1950  using FiniteElement::Project;
1951  virtual void Project(VectorCoefficient &vc,
1952  ElementTransformation &Trans, Vector &dofs) const
1953  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1954  virtual void Project(const FiniteElement &fe,
1955  ElementTransformation &Trans,
1956  DenseMatrix &I) const
1957  { Project_ND(tk, dof2tk, fe, Trans, I); }
1958  virtual void ProjectGrad(const FiniteElement &fe,
1959  ElementTransformation &Trans,
1960  DenseMatrix &grad) const
1961  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1962 };
1963 
1964 
1965 class ND_SegmentElement : public VectorFiniteElement
1966 {
1967  static const double tk[1];
1968 
1969  Poly_1D::Basis &obasis1d;
1970  Array<int> dof2tk;
1971 
1972 public:
1973  ND_SegmentElement(const int p);
1974  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
1975  { obasis1d.Eval(ip.x, shape); }
1976  virtual void CalcVShape(const IntegrationPoint &ip,
1977  DenseMatrix &shape) const;
1978  virtual void CalcVShape(ElementTransformation &Trans,
1979  DenseMatrix &shape) const
1980  { CalcVShape_ND(Trans, shape); }
1981  // virtual void CalcCurlShape(const IntegrationPoint &ip,
1982  // DenseMatrix &curl_shape) const;
1983  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1984  DenseMatrix &I) const
1985  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1986  using FiniteElement::Project;
1987  virtual void Project(VectorCoefficient &vc,
1988  ElementTransformation &Trans, Vector &dofs) const
1989  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1990  virtual void Project(const FiniteElement &fe,
1991  ElementTransformation &Trans,
1992  DenseMatrix &I) const
1993  { Project_ND(tk, dof2tk, fe, Trans, I); }
1994  virtual void ProjectGrad(const FiniteElement &fe,
1995  ElementTransformation &Trans,
1996  DenseMatrix &grad) const
1997  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1998 };
1999 
2000 
2001 class NURBSFiniteElement : public FiniteElement
2002 {
2003 protected:
2004  mutable Array <KnotVector*> kv;
2005  mutable int *ijk, patch, elem;
2006  mutable Vector weights;
2007 
2008 public:
2009  NURBSFiniteElement(int D, int G, int Do, int O, int F)
2010  : FiniteElement(D, G, Do, O, F)
2011  {
2012  ijk = NULL;
2013  patch = elem = -1;
2014  kv.SetSize(Dim);
2015  weights.SetSize(Dof);
2016  weights = 1.0;
2017  }
2018 
2019  void Reset () const { patch = elem = -1; }
2020  void SetIJK (int *IJK) const { ijk = IJK; }
2021  int GetPatch () const { return patch; }
2022  void SetPatch (int p) const { patch = p; }
2023  int GetElement () const { return elem; }
2024  void SetElement (int e) const { elem = e; }
2025  Array <KnotVector*> &KnotVectors() const { return kv; }
2026  Vector &Weights () const { return weights; }
2027 };
2028 
2029 class NURBS1DFiniteElement : public NURBSFiniteElement
2030 {
2031 protected:
2032  mutable Vector shape_x;
2033 
2034 public:
2035  NURBS1DFiniteElement(int p)
2036  : NURBSFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
2037  shape_x(p + 1) { }
2038 
2039  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2040  virtual void CalcDShape(const IntegrationPoint &ip,
2041  DenseMatrix &dshape) const;
2042 };
2043 
2044 class NURBS2DFiniteElement : public NURBSFiniteElement
2045 {
2046 protected:
2047  mutable Vector u, shape_x, shape_y, dshape_x, dshape_y;
2048 
2049 public:
2050  NURBS2DFiniteElement(int p)
2051  : NURBSFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
2052  FunctionSpace::Qk), u(Dof),
2053  shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1), dshape_y(p + 1) { }
2054 
2055  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2056  virtual void CalcDShape(const IntegrationPoint &ip,
2057  DenseMatrix &dshape) const;
2058 };
2059 
2060 class NURBS3DFiniteElement : public NURBSFiniteElement
2061 {
2062 protected:
2063  mutable Vector u, shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
2064 
2065 public:
2066  NURBS3DFiniteElement(int p)
2067  : NURBSFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
2068  FunctionSpace::Qk), u(Dof),
2069  shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
2070  dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1) { }
2071 
2072  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2073  virtual void CalcDShape(const IntegrationPoint &ip,
2074  DenseMatrix &dshape) const;
2075 };
2076 
2077 }
2078 
2079 #endif
mfem::FiniteElement
Abstract class for Finite Elements.
Definition: fe.hpp:44
mfem::RefinedLinear3DFiniteElement::RefinedLinear3DFiniteElement
RefinedLinear3DFiniteElement()
Construct a quadratic FE on tetrahedron.
Definition: fe.cpp:4073
mfem::RT0TetFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1192
mfem::BiQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1189
mfem::L2_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7896
mfem::ND_SegmentElement
Definition: fe.hpp:1965
mfem::RT_QuadrilateralElement::RT_QuadrilateralElement
RT_QuadrilateralElement(const int p)
Definition: fe.cpp:8875
mfem::VectorFiniteElement::curlshape_J
DenseMatrix curlshape_J
Definition: fe.hpp:280
mfem::RT0TetFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5872
mfem::RT_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1702
mfem::FiniteElement::GetDim
int GetDim() const
Returns the space dimension for the finite element.
Definition: fe.hpp:82
mfem::H1Pos_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7163
mfem::L2_TetrahedronElement::L2_TetrahedronElement
L2_TetrahedronElement(const int p, const int _type=0)
Definition: fe.cpp:8564
mfem::RT1TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2714
mfem::RT1HexFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1164
mfem::P1TetNonConfFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3651
mfem::P1OnQuadFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:937
mfem::Poly_1D::CalcBernstein
static void CalcBernstein(const int p, const double x, double *u, double *d)
Definition: fe.hpp:1301
mfem::IntegrationRule
Class for integration rule.
Definition: intrules.hpp:83
mfem::P1SegmentFiniteElement
Linear 1D element with nodes 1/3 and 2/3 (trace of RT1)
Definition: fe.hpp:902
mfem::P2SegmentFiniteElement
Quadratic 1D element with nodes the Gaussian points in [0,1] (trace of RT2)
Definition: fe.hpp:912
mfem::L2Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8316
mfem::NURBS2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:10783
mfem::Linear3DFiniteElement::Linear3DFiniteElement
Linear3DFiniteElement()
Construct a linear FE on tetrahedron.
Definition: fe.cpp:2112
mfem::Poly_1D::CalcDelta
static double CalcDelta(const int p, const double x)
Definition: fe.hpp:1280
mfem::RT1QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2896
mfem::RT_TriangleElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1732
mfem::RT_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1776
mfem::H1_HexahedronElement::H1_HexahedronElement
H1_HexahedronElement(const int p)
Definition: fe.cpp:6847
mfem::L2Pos_TriangleElement
Definition: fe.hpp:1588
mfem::L2Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8055
mfem::RT_TetrahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:9646
mfem::FiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:30
mfem::RefinedBiLinear2DFiniteElement::RefinedBiLinear2DFiniteElement
RefinedBiLinear2DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:4305
mfem::ND_QuadrilateralElement::ND_QuadrilateralElement
ND_QuadrilateralElement(const int p)
Definition: fe.cpp:10097
mfem::GaussBiQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1507
mfem::L2Pos_TriangleElement::L2Pos_TriangleElement
L2Pos_TriangleElement(const int p)
Definition: fe.cpp:8468
mfem::ND_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1875
mfem::RT0TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:757
mfem::H1Pos_SegmentElement::H1Pos_SegmentElement
H1Pos_SegmentElement(const int p)
Definition: fe.cpp:7105
mfem::NURBSFiniteElement::GetPatch
int GetPatch() const
Definition: fe.hpp:2021
mfem::RT_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1786
mfem::FiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:116
mfem::L2_TriangleElement
Definition: fe.hpp:1565
mfem::P0QuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:649
mfem::Nedelec1HexFiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:4917
mfem::FiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:75
mfem::BiQuadPos2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:560
mfem::P0SegmentFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2350
mfem::Linear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2129
mfem::Poly_1D::Poly_1D
Poly_1D()
Definition: fe.hpp:1252
mfem::L2Pos_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8552
mfem::ND_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1919
mfem::RT1TriangleFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:2668
mfem::RT1QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2948
mfem::BiQuadPos2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1303
mfem::H1Pos_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7143
mfem::L2_HexahedronElement
Definition: fe.hpp:1531
mfem::VectorFiniteElement::FiniteElement
FiniteElement(D, G, Do, O, F)
mfem::L2Pos_TetrahedronElement::L2Pos_TetrahedronElement
L2Pos_TetrahedronElement(const int p)
Definition: fe.cpp:8715
mfem::NURBSFiniteElement::kv
Array< KnotVector * > kv
Definition: fe.hpp:2004
mfem::VectorFiniteElement::CalcVShape_RT
void CalcVShape_RT(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:372
mfem::Vector::SetSize
void SetSize(int s)
Resizes the vector if the new size is different.
Definition: vector.hpp:259
mfem::RT_QuadrilateralElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9033
mfem::Nedelec1HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:4979
mfem::P1SegmentFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3438
mfem::GaussLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:858
mfem::NodalFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:177
mfem::BiQuadPos2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1327
mfem::VectorFiniteElement::LocalInterpolation_ND
void LocalInterpolation_ND(const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:687
mfem::BiCubic2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1685
mfem::BiCubic2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1596
mfem::RT0TriangleFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:2433
mfem::Poly_1D::UniformPoints
static void UniformPoints(const int p, double *x)
Definition: fe.cpp:6150
mfem::P0TriangleFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
evaluate derivatives of shape function - constant 0
Definition: fe.cpp:2083
mfem::Nedelec1TetFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1112
mfem::L2Pos_SegmentElement
Definition: fe.hpp:1477
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1810
mfem::Linear1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:747
mfem::H1_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6675
mfem::NURBS1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:10731
mfem::L2_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7915
mfem::RT_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1661
mfem::LagrangeHexFiniteElement::LagrangeHexFiniteElement
LagrangeHexFiniteElement(int degree)
Definition: fe.cpp:3703
mfem::FiniteElement::GetOrder
int GetOrder() const
Returns the order of the finite element.
Definition: fe.hpp:91
mfem::H1_QuadrilateralElement
Definition: fe.hpp:1327
mfem::RT0TriangleFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:2446
mfem::Lagrange1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3559
mfem::LagrangeHexFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3865
mfem::ND_QuadrilateralElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1859
mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition: densemat.hpp:22
mfem::Lagrange1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3513
mfem::NodalFiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:259
mfem::NURBSFiniteElement::Reset
void Reset() const
Definition: fe.hpp:2019
mfem::RT_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1741
mfem::Quad2DFiniteElement
Class for quadratic FE on triangle.
Definition: fe.hpp:486
mfem::NURBS1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:10745
mfem::Poly_1D::OpenBasis
Basis & OpenBasis(const int p)
Definition: fe.cpp:6548
mfem::Poly_1D::ClosedPoints
const double * ClosedPoints(const int p)
Definition: fe.cpp:6523
mfem::PositiveFiniteElement::PositiveFiniteElement
PositiveFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:256
mfem::Quad1DFiniteElement
Class for quadratic FE on interval.
Definition: fe.hpp:457
mfem::RT_QuadrilateralElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1656
mfem::RT_TriangleElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9503
mfem::ND_TetrahedronElement
Definition: fe.hpp:1882
mfem::Nedelec1TetFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5145
mfem::VectorFiniteElement::ProjectCurl_ND
void ProjectCurl_ND(const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:509
mfem::P0QuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2098
mfem::FiniteElement::Space
int Space() const
Returns the type of space on each element.
Definition: fe.hpp:94
mfem::Cubic1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1756
mfem::FiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:69
mfem::RT_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1705
mfem::RefinedTriLinear3DFiniteElement::RefinedTriLinear3DFiniteElement
RefinedTriLinear3DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:4452
mfem::P0HexFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3690
mfem::Quadratic3DFiniteElement::Quadratic3DFiniteElement
Quadratic3DFiniteElement()
Construct a quadratic FE on tetrahedron.
Definition: fe.cpp:2168
mfem::FiniteElement::GetMapType
int GetMapType() const
Definition: fe.hpp:98
mfem::L2_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7769
mfem::RT1HexFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:5495
mfem::RT1HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5682
mfem::L2Pos_TetrahedronElement
Definition: fe.hpp:1624
mfem::RT0QuadFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:2545
mfem::H1_HexahedronElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1361
mfem::L2_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8680
mfem::ND_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1837
mfem::Cubic2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1808
mfem::L2Pos_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8770
mfem::CrouzeixRaviartFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2375
mfem::CrouzeixRaviartFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2367
mfem::L2Pos_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7839
mfem::H1_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:6759
mfem::P0HexFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:962
mfem::VectorFiniteElement::ProjectCurl_RT
void ProjectCurl_RT(const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:547
mfem::H1Pos_HexahedronElement::H1Pos_HexahedronElement
H1Pos_HexahedronElement(const int p)
Definition: fe.cpp:7273
mfem::FiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:100
mfem::ND_TriangleElement
Definition: fe.hpp:1925
mfem::L2_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8622
mfem::RT_HexahedronElement::RT_HexahedronElement
RT_HexahedronElement(const int p)
Definition: fe.cpp:9083
mfem::BiLinear2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:819
mfem::NURBSFiniteElement::GetElement
int GetElement() const
Definition: fe.hpp:2023
mfem::H1Pos_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7245
mfem::Linear2DFiniteElement::Linear2DFiniteElement
Linear2DFiniteElement()
Construct a linear FE on triangle.
Definition: fe.cpp:761
mfem::RT_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1665
mfem::Quadratic3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2225
mfem::RefinedBiLinear2DFiniteElement
Class for refined bi-linear FE on quadrilateral.
Definition: fe.hpp:1041
mfem::RT0TetFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5817
mfem::RefinedTriLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4641
mfem::ND_TriangleElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:10628
mfem::PointFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:728
mfem::L2_SegmentElement::L2_SegmentElement
L2_SegmentElement(const int p, const int _type=0)
Definition: fe.cpp:7740
mfem::Cubic2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1828
mfem::L2Pos_HexahedronElement::L2Pos_HexahedronElement
L2Pos_HexahedronElement(const int p)
Definition: fe.cpp:8243
mfem::ND_TriangleElement::ND_TriangleElement
ND_TriangleElement(const int p)
Definition: fe.cpp:10548
mfem::L2_TriangleElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1581
mfem::RT_TetrahedronElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9682
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u)
Definition: fe.hpp:1264
mfem::RT0QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:784
mfem::P0TriangleFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
evaluate shape function - constant 1
Definition: fe.cpp:2077
mfem::Cubic2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1856
mfem::Poly_1D::CalcBinomTerms
static void CalcBinomTerms(const int p, const double x, const double y, double *u)
Compute the terms in the expansion of the binomial (x + y)^p.
Definition: fe.cpp:6333
mfem::FiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:63
mfem::RT2QuadFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:3150
mfem::Cubic3DFiniteElement::Cubic3DFiniteElement
Cubic3DFiniteElement()
Construct a cubic FE on tetrahedron.
Definition: fe.cpp:1903
mfem::Linear1DFiniteElement::Linear1DFiniteElement
Linear1DFiniteElement()
Construct a linear FE on interval.
Definition: fe.cpp:740
mfem::RefinedLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4014
mfem::RT0TetFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:5805
mfem::BiQuadPos2DFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:1376
mfem::FiniteElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:108
mfem::QuadPos1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:994
mfem::RT_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1698
mfem::CrouzeixRaviartQuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2399
mfem::Cubic3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1996
mfem::P2SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3456
mfem::P1OnQuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:452
mfem::L2Pos_QuadrilateralElement
Definition: fe.hpp:1515
mfem::GaussBiLinear2DFiniteElement
Class for bilinear FE on quad with nodes at the 4 Gaussian points.
Definition: fe.hpp:432
mfem::RefinedLinear1DFiniteElement
Class for refined linear FE on interval.
Definition: fe.hpp:988
mfem::L2_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7775
mfem::RefinedLinear2DFiniteElement
Class for refined linear FE on triangle.
Definition: fe.hpp:1008
mfem::RefinedLinear3DFiniteElement
Class for refined linear FE on tetrahedron.
Definition: fe.hpp:1028
mfem::L2_SegmentElement
Definition: fe.hpp:1459
mfem::NURBSFiniteElement::SetPatch
void SetPatch(int p) const
Definition: fe.hpp:2022
mfem::Quad1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:954
mfem::Quad1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:965
mfem::BiQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1213
mfem::P0TriangleFiniteElement
Class for constant FE on triangle.
Definition: fe.hpp:625
mfem::ND_SegmentElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1994
mfem::ND_SegmentElement::ND_SegmentElement
ND_SegmentElement(const int p)
Definition: fe.cpp:10707
mfem::H1_TriangleElement::H1_TriangleElement
H1_TriangleElement(const int p)
Definition: fe.cpp:7451
mfem::RefinedLinear1DFiniteElement::RefinedLinear1DFiniteElement
RefinedLinear1DFiniteElement()
Construct a quadratic FE on interval.
Definition: fe.cpp:3903
mfem::H1_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7020
mfem::H1Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7266
mfem::GaussBiQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1480
mfem::L2_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8410
mfem::H1_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7518
mfem::RT_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1708
mfem::RefinedLinear1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3930
mfem::VectorFiniteElement::VectorFiniteElement
VectorFiniteElement(int D, int G, int Do, int O, int M, int F=FunctionSpace::Pk)
Definition: fe.hpp:331
mfem::VectorFiniteElement::LocalInterpolation_RT
void LocalInterpolation_RT(const double *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:651
mfem::RT2TriangleFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:3089
mfem::Poly_1D::ChebyshevPoints
static void ChebyshevPoints(const int p, double *x)
Definition: fe.cpp:6301
mfem::NURBSFiniteElement::NURBSFiniteElement
NURBSFiniteElement(int D, int G, int Do, int O, int F)
Definition: fe.hpp:2009
mfem::RotTriLinearHexFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:5942
mfem::H1_QuadrilateralElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1342
mfem::P0TetFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3675
mfem::RT0TetFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:5783
mfem::RefinedTriLinear3DFiniteElement
Class for refined trilinear FE on a hexahedron.
Definition: fe.hpp:1061
mfem::ND_TetrahedronElement::ND_TetrahedronElement
ND_TetrahedronElement(const int p)
Definition: fe.cpp:10286
mfem::L2Pos_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8516
mfem::Poly_1D
Definition: fe.hpp:1219
mfem::Quadratic3DFiniteElement
Class for quadratic FE on tetrahedron.
Definition: fe.hpp:680
mfem::FiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const =0
mfem::ND_TetrahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1898
mfem::PointFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:734
mfem::RT_TetrahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1771
mfem::Cubic1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1771
mfem::ND_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1903
mfem::FiniteElement::GetNodes
const IntegrationRule & GetNodes() const
Definition: fe.hpp:113
mfem::Nedelec1HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5032
mfem::Quad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1035
mfem::L2_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8151
mfem::VectorFiniteElement::vshape
DenseMatrix vshape
Definition: fe.hpp:280
mfem::Quadratic3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2203
mfem::RT_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1671
mfem::L2Pos_QuadrilateralElement::L2Pos_QuadrilateralElement
L2Pos_QuadrilateralElement(const int p)
Definition: fe.cpp:7991
mfem::P0SegmentFiniteElement::P0SegmentFiniteElement
P0SegmentFiniteElement(int Ord=0)
Definition: fe.cpp:2338
mfem::H1_TetrahedronElement
Definition: fe.hpp:1438
mfem::RT1TriangleFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:2691
mfem::NURBS3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:10818
mfem::VectorFiniteElement::curlshape
DenseMatrix curlshape
Definition: fe.hpp:280
mfem::ND_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1907
mfem::RT2TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:864
mfem::Linear3DFiniteElement
Class for linear FE on tetrahedron.
Definition: fe.hpp:655
mfem::Linear1DFiniteElement
Class for linear FE on interval.
Definition: fe.hpp:354
mfem::RT_HexahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:9244
mfem::Nedelec1TetFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:5083
mfem::CrouzeixRaviartQuadFiniteElement
Crouzeix-Raviart finite element on quadrilateral.
Definition: fe.hpp:728
mfem::Linear2DFiniteElement
Class for linear FE on triangle.
Definition: fe.hpp:374
mfem::GaussQuad2DFiniteElement
Class for quadratic FE on triangle with nodes at the &quot;Gaussian&quot; points.
Definition: fe.hpp:510
mfem::L2_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8388
mfem::RT_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:8986
mfem::ND_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1947
mfem::BiCubic2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1635
mfem::RT2QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:3348
mfem::ND_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1864
mfem::BiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:810
mfem::Linear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2138
mfem::RT_HexahedronElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9318
mfem::H1_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7681
mfem::Quad2DFiniteElement::CalcHessian
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &h) const
Definition: fe.cpp:1059
mfem::NURBSFiniteElement::SetElement
void SetElement(int e) const
Definition: fe.hpp:2024
mfem::GaussQuad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1137
mfem::VectorFiniteElement::ProjectGrad_ND
void ProjectGrad_ND(const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:630
mfem::L2Pos_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8490
mfem::RT_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1783
mfem::RT1TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:811
mfem::L2_QuadrilateralElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1508
mfem::NURBS3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:10842
mfem::GaussQuad2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:1151
mfem::FiniteElement::GetGeomType
int GetGeomType() const
Returns the geometry type:
Definition: fe.hpp:85
mfem::ND_QuadrilateralElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:10232
mfem::L2Pos_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8016
mfem::ND_HexahedronElement::ND_HexahedronElement
ND_HexahedronElement(const int p)
Definition: fe.cpp:9728
mfem::FiniteElement::Nodes
IntegrationRule Nodes
Definition: fe.hpp:48
mfem::ND_SegmentElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1990
mfem::L2_TetrahedronElement
Definition: fe.hpp:1604
mfem::Quad2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1021
mfem::L2Pos_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8271
mfem::H1Pos_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7123
mfem::H1Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7444
mfem::RT2QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:3400
mfem::ND_TriangleElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:10662
mfem::RT0QuadFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:2560
mfem::RefinedBiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4328
mfem::RT_TetrahedronElement
Definition: fe.hpp:1754
mfem::FiniteElement::~FiniteElement
virtual ~FiniteElement()
Definition: fe.hpp:196
mfem::H1_QuadrilateralElement::H1_QuadrilateralElement
H1_QuadrilateralElement(const int p)
Definition: fe.cpp:6703
mfem::RT0TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2457
mfem::ND_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Overrides the scalar CalcShape function to print an error.
Definition: fe.hpp:1974
mfem::VectorFiniteElement::CalcVShape_ND
void CalcVShape_ND(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:385
mfem::VectorFiniteElement::Jinv
DenseMatrix Jinv
Definition: fe.hpp:279
mfem::RT0HexFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1136
mfem::ND_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1987
mfem::L2_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7786
mfem::FiniteElement::GetDof
int GetDof() const
Returns the degrees of freedom in the FE space.
Definition: fe.hpp:88
mfem::H1_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7706
mfem::BiQuad2DFiniteElement
Class for bi-quadratic FE on quadrilateral.
Definition: fe.hpp:526
mfem::H1Pos_HexahedronElement
Definition: fe.hpp:1403
mfem::TriLinear3DFiniteElement
Class for tri-linear FE on cube.
Definition: fe.hpp:693
mfem::Coefficient
Base class Coefficient that may optionally depend on time.
Definition: coefficient.hpp:31
mfem::GaussBiLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:905
mfem::P0TetFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:951
mfem::Nedelec1TetFiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:5113
mfem::L2Pos_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8738
mfem::CrouzeixRaviartFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:723
mfem::Linear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:772
mfem::RefinedTriLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4498
mfem::RefinedLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4195
mfem::P0TriangleFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:637
mfem::Poly_1D::Binom
static const int * Binom(const int p)
Definition: fe.cpp:6133
mfem::RT2QuadFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:3250
mfem::H1_HexahedronElement
Definition: fe.hpp:1346
mfem::FiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:44
mfem::GaussLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:840
mfem::RT_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1668
mfem::Poly_1D::GaussLobattoPoints
static void GaussLobattoPoints(const int p, double *x)
Definition: fe.cpp:6225
mfem::Nedelec1HexFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1090
mfem::L2_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8647
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:9944
mfem::RT_TriangleElement
Definition: fe.hpp:1715
mfem::RT0QuadFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2624
mfem::FiniteElement::FiniteElement
FiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.cpp:22
mfem::BiQuad2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1262
mfem::TriLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2283
mfem::BiLinear2DFiniteElement
Class for bilinear FE on quadrilateral.
Definition: fe.hpp:396
mfem::Quad1DFiniteElement::Quad1DFiniteElement
Quad1DFiniteElement()
Construct a quadratic FE on interval.
Definition: fe.cpp:946
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1978
mfem::H1Pos_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7399
mfem::FiniteElement::GetFaceDofs
virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const
Definition: fe.cpp:58
mfem::GaussLinear2DFiniteElement
Class for linear FE on triangle with nodes at the 3 &quot;Gaussian&quot; points.
Definition: fe.hpp:421
mfem::GaussBiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:894
mfem::ND_HexahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1817
mfem::RT2QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:885
mfem::BiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:801
mfem::FiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:51
mfem::H1Pos_QuadrilateralElement::H1Pos_QuadrilateralElement
H1Pos_QuadrilateralElement(const int p)
Definition: fe.cpp:7170
mfem::ND_QuadrilateralElement
Definition: fe.hpp:1844
mfem::ND_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1951
mfem::NURBSFiniteElement::KnotVectors
Array< KnotVector * > & KnotVectors() const
Definition: fe.hpp:2025
mfem::IntegrationPoint
Class for integration point with weight.
Definition: intrules.hpp:25
mfem::Linear1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:754
mfem::L2_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8439
mfem::H1Pos_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7420
mfem::L2Pos_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7845
mfem::NodalFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:230
mfem::P0QuadFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2104
mfem::RT_QuadrilateralElement
Definition: fe.hpp:1640
mfem::GaussBiQuad2DFiniteElement
Bi-quadratic element on quad with nodes at the 9 Gaussian points.
Definition: fe.hpp:565
mfem::RT1QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:838
mfem::L2Pos_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8292
mfem::VectorFiniteElement::Project_RT
void Project_RT(const double *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:404
mfem::H1_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:6975
mfem::P1OnQuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:929
mfem::RT2TriangleFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:3064
mfem::ND_TetrahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:10434
mfem::RT1QuadFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:2824
mfem::ND_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:10183
mfem::Linear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:391
mfem::ND_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1958
mfem::NodalFiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:288
mfem::H1_TriangleElement
Definition: fe.hpp:1421
mfem::RT0QuadFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2572
mfem::L2Pos_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7856
mfem::RefinedLinear2DFiniteElement::RefinedLinear2DFiniteElement
RefinedLinear2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:3949
mfem::L2_QuadrilateralElement
Definition: fe.hpp:1493
mfem::NodalFiniteElement::NodalLocalInterpolation
void NodalLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I, const NodalFiniteElement &fine_fe) const
Definition: fe.cpp:125
mfem::H1_SegmentElement
Definition: fe.hpp:1310
mfem::RT1HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5737
mfem::NodalFiniteElement::ProjectCurl_2D
void ProjectCurl_2D(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.cpp:158
mfem::NURBSFiniteElement::SetIJK
void SetIJK(int *IJK) const
Definition: fe.hpp:2020
mfem::ND_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1868
mfem::ND_HexahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1832
mfem::RefinedLinear1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3911
mfem::P1TetNonConfFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3639
mfem::RT_TetrahedronElement::RT_TetrahedronElement
RT_TetrahedronElement(const int p)
Definition: fe.cpp:9545
mfem::Poly_1D::Basis
Definition: fe.hpp:1222
mfem::L2_TriangleElement::L2_TriangleElement
L2_TriangleElement(const int p, const int _type=0)
Definition: fe.cpp:8335
mfem::RT0HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5293
mfem::H1Pos_SegmentElement
Definition: fe.hpp:1364
mfem::LagrangeHexFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3844
mfem::NURBSFiniteElement::Weights
Vector & Weights() const
Definition: fe.hpp:2026
mfem::H1_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:6656
mfem::H1_TetrahedronElement::H1_TetrahedronElement
H1_TetrahedronElement(const int p)
Definition: fe.cpp:7570
mfem::BiQuad2DFiniteElement::BiQuad2DFiniteElement
BiQuad2DFiniteElement()
Construct a biquadratic FE on quadrilateral.
Definition: fe.cpp:1166
mfem::Linear3DFiniteElement::GetFaceDofs
virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const
Definition: fe.cpp:2158
mfem::LagrangeHexFiniteElement
Tensor products of 1D FEs (only degree 2 is functional)
Definition: fe.hpp:967
mfem::Poly_1D::ClosedBasis
Basis & ClosedBasis(const int p)
Definition: fe.cpp:6571
mfem::RT1QuadFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:2861
mfem::P0TriangleFiniteElement::P0TriangleFiniteElement
P0TriangleFiniteElement()
Construct P0 triangle finite element.
Definition: fe.cpp:2070
mfem::ND_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1954
mfem::ND_HexahedronElement
Definition: fe.hpp:1793
mfem::H1Pos_QuadrilateralElement
Definition: fe.hpp:1385
mfem::P0SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2344
mfem::L2Pos_HexahedronElement
Definition: fe.hpp:1549
mfem::RT_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1744
mfem::RT_TriangleElement::RT_TriangleElement
RT_TriangleElement(const int p)
Definition: fe.cpp:9393
mfem::H1_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:6637
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:10722
mfem::ND_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1823
mfem::ND_HexahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:10018
mfem::Poly_1D::Basis::Eval
void Eval(const double x, Vector &u) const
Definition: fe.cpp:6023
mfem::L2Pos_SegmentElement::L2Pos_SegmentElement
L2Pos_SegmentElement(const int p)
Definition: fe.cpp:7818
mfem::RefinedLinear3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:4108
mfem::RT0HexFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5348
mfem::Cubic3DFiniteElement
Class for cubic FE on tetrahedron.
Definition: fe.hpp:612
mfem::Vector
Vector data type.
Definition: vector.hpp:33
mfem::RT0HexFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:5279
mfem::Poly_1D::CalcBernstein
static void CalcBernstein(const int p, const double x, double *u)
Definition: fe.hpp:1299
mfem::ND_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1827
mfem::H1Pos_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7225
mfem::L2_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8127
mfem::Quad2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:1087
mfem::RT_TriangleElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:9470
mfem::Quad2DFiniteElement::Quad2DFiniteElement
Quad2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:1004
mfem::ND_QuadrilateralElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1871
mfem::RT_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1780
mfem::FunctionSpace
Describes the space on each element.
Definition: fe.hpp:27
mfem::TriLinear3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2299
mfem::Poly_1D::OpenPoints
const double * OpenPoints(const int p)
Definition: fe.cpp:6498
mfem::ND_SegmentElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1983
mfem::Nedelec1TetFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:5198
mfem::L2Pos_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8035
mfem::Poly_1D::GaussPoints
static void GaussPoints(const int p, double *x)
Definition: fe.cpp:6165
mfem::ND_TetrahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:10476
mfem::P0HexFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3696
mfem::BiQuadPos2DFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:1405
mfem::Linear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:780
mfem::H1_SegmentElement::H1_SegmentElement
H1_SegmentElement(const int p)
Definition: fe.cpp:6618
mfem::Cubic3DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:1968
mfem::NodalFiniteElement::NodalFiniteElement
NodalFiniteElement(int D, int G, int Do, int O, int F=FunctionSpace::Pk)
Definition: fe.hpp:215
mfem::CrouzeixRaviartQuadFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:2410
mfem::H1_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:6798
mfem::L2_HexahedronElement::L2_HexahedronElement
L2_HexahedronElement(const int p, const int _type=0)
Definition: fe.cpp:8070
mfem::TriLinear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:711
mfem::RT0HexFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:5249
mfem::P2SegmentFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:3468
mfem::BiLinear2DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:415
mfem::RefinedBiLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:4379
mfem::FiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const =0
mfem::RT_HexahedronElement
Definition: fe.hpp:1678
mfem::NURBS2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:10764
mfem::RT_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1737
mfem::ND_TetrahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1914
mfem::VectorFiniteElement::Project_ND
void Project_ND(const double *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:566
mfem::FiniteElement::GetRangeType
int GetRangeType() const
Definition: fe.hpp:96
mfem::GaussBiLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:883
mfem::RT1TriangleFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2766
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u, double *d)
Definition: fe.hpp:1273
mfem::ND_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1910
mfem::P0TetFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3669
mfem::H1_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:6996
mfem::RT_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1747
mfem::H1_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:6778
mfem::Poly_1D::Basis::Basis
Basis(const int p, const double *nodes, const int _mode=1)
Definition: fe.cpp:5977
mfem::Poly_1D::CalcDBinomTerms
static void CalcDBinomTerms(const int p, const double x, const double y, double *d)
Definition: fe.cpp:6397
mfem::Nedelec1HexFiniteElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:4862
mfem::TriLinear3DFiniteElement::TriLinear3DFiniteElement
TriLinear3DFiniteElement()
Construct a tri-linear FE on cube.
Definition: fe.cpp:2247
mfem::FiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:87
mfem::QuadPos1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:984
mfem::L2_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8106
mfem::RT_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1693
mfem::RefinedLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3966
mfem::P1SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3429
mfem::BiLinear2DFiniteElement::BiLinear2DFiniteElement
BiLinear2DFiniteElement()
Construct a bilinear FE on quadrilateral.
Definition: fe.cpp:788
mfem::ND_TriangleElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1942
mfem::poly1d
Poly_1D poly1d
Definition: fe.cpp:6614
mfem::CrouzeixRaviartFiniteElement
Crouzeix-Raviart finite element on triangle.
Definition: fe.hpp:716
mfem::L2_QuadrilateralElement::L2_QuadrilateralElement
L2_QuadrilateralElement(const int p, const int _type=0)
Definition: fe.cpp:7863
mfem::RotTriLinearHexFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:5925
mfem::Lagrange1DFiniteElement::Lagrange1DFiniteElement
Lagrange1DFiniteElement(int degree)
Definition: fe.cpp:3481
mfem::Poly_1D::~Poly_1D
~Poly_1D()
Definition: fe.cpp:6594
mfem::RT0TriangleFiniteElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:2509
mfem::RT1HexFiniteElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:5618
mfem::L2Pos_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8859
mfem::L2_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7935
mfem::GaussLinear2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:850
mfem::Linear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:673
mfem::H1_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7540
mfem::VectorFiniteElement::ProjectGrad_RT
void ProjectGrad_RT(const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:482
mfem::PositiveFiniteElement::Project
virtual void Project(Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.cpp:320
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