MFEM  v3.2
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; } // { dofs = 1.0; }
417 };
418 
420 class GaussLinear2DFiniteElement : public NodalFiniteElement
421 {
422 public:
423  GaussLinear2DFiniteElement();
424  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
425  virtual void CalcDShape(const IntegrationPoint &ip,
426  DenseMatrix &dshape) const;
427  virtual void ProjectDelta(int vertex, Vector &dofs) const;
428 };
429 
431 class GaussBiLinear2DFiniteElement : public NodalFiniteElement
432 {
433 private:
434  static const double p[2];
435 
436 public:
437  GaussBiLinear2DFiniteElement();
438  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
439  virtual void CalcDShape(const IntegrationPoint &ip,
440  DenseMatrix &dshape) const;
441  virtual void ProjectDelta(int vertex, Vector &dofs) const;
442 };
443 
444 class P1OnQuadFiniteElement : public NodalFiniteElement
445 {
446 public:
447  P1OnQuadFiniteElement();
448  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
449  virtual void CalcDShape(const IntegrationPoint &ip,
450  DenseMatrix &dshape) const;
451  virtual void ProjectDelta(int vertex, Vector &dofs) const
452  { dofs = 1.0; }
453 };
454 
456 class Quad1DFiniteElement : public NodalFiniteElement
457 {
458 public:
460  Quad1DFiniteElement();
461 
465  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
466 
471  virtual void CalcDShape(const IntegrationPoint &ip,
472  DenseMatrix &dshape) const;
473 };
474 
475 class QuadPos1DFiniteElement : public FiniteElement
476 {
477 public:
478  QuadPos1DFiniteElement();
479  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
480  virtual void CalcDShape(const IntegrationPoint &ip,
481  DenseMatrix &dshape) const;
482 };
483 
485 class Quad2DFiniteElement : public NodalFiniteElement
486 {
487 public:
489  Quad2DFiniteElement();
490 
494  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
495 
500  virtual void CalcDShape(const IntegrationPoint &ip,
501  DenseMatrix &dshape) const;
502 
503  virtual void CalcHessian (const IntegrationPoint &ip,
504  DenseMatrix &h) const;
505  virtual void ProjectDelta(int vertex, Vector &dofs) const;
506 };
507 
509 class GaussQuad2DFiniteElement : public NodalFiniteElement
510 {
511 private:
512  static const double p[2];
513  DenseMatrix A;
514  mutable DenseMatrix D;
515  mutable Vector pol;
516 public:
517  GaussQuad2DFiniteElement();
518  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
519  virtual void CalcDShape(const IntegrationPoint &ip,
520  DenseMatrix &dshape) const;
521  // virtual void ProjectDelta(int vertex, Vector &dofs) const;
522 };
523 
525 class BiQuad2DFiniteElement : public NodalFiniteElement
526 {
527 public:
529  BiQuad2DFiniteElement();
530 
534  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
535 
540  virtual void CalcDShape(const IntegrationPoint &ip,
541  DenseMatrix &dshape) const;
542  virtual void ProjectDelta(int vertex, Vector &dofs) const;
543 };
544 
545 class BiQuadPos2DFiniteElement : public FiniteElement
546 {
547 public:
548  BiQuadPos2DFiniteElement();
549  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
550  virtual void CalcDShape(const IntegrationPoint &ip,
551  DenseMatrix &dshape) const;
552  virtual void GetLocalInterpolation(ElementTransformation &Trans,
553  DenseMatrix &I) const;
554  using FiniteElement::Project;
555  virtual void Project(Coefficient &coeff, ElementTransformation &Trans,
556  Vector &dofs) const;
557  virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans,
558  Vector &dofs) const;
559  virtual void ProjectDelta(int vertex, Vector &dofs) const
560  { dofs = 0.; dofs(vertex) = 1.; }
561 };
562 
564 class GaussBiQuad2DFiniteElement : public NodalFiniteElement
565 {
566 public:
567  GaussBiQuad2DFiniteElement();
568  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
569  virtual void CalcDShape(const IntegrationPoint &ip,
570  DenseMatrix &dshape) const;
571  // virtual void ProjectDelta(int vertex, Vector &dofs) const { dofs = 1.; }
572 };
573 
574 class BiCubic2DFiniteElement : public NodalFiniteElement
575 {
576 public:
577  BiCubic2DFiniteElement();
578  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
579  virtual void CalcDShape(const IntegrationPoint &ip,
580  DenseMatrix &dshape) const;
581  virtual void CalcHessian (const IntegrationPoint &ip,
582  DenseMatrix &h) const;
583 };
584 
585 class Cubic1DFiniteElement : public NodalFiniteElement
586 {
587 public:
588  Cubic1DFiniteElement();
589 
590  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
591 
592  virtual void CalcDShape(const IntegrationPoint &ip,
593  DenseMatrix &dshape) const;
594 };
595 
596 class Cubic2DFiniteElement : public NodalFiniteElement
597 {
598 public:
599  Cubic2DFiniteElement();
600 
601  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
602 
603  virtual void CalcDShape(const IntegrationPoint &ip,
604  DenseMatrix &dshape) const;
605 
606  virtual void CalcHessian (const IntegrationPoint &ip,
607  DenseMatrix &h) const;
608 };
609 
611 class Cubic3DFiniteElement : public NodalFiniteElement
612 {
613 public:
615  Cubic3DFiniteElement();
616 
617  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
618 
619  virtual void CalcDShape(const IntegrationPoint &ip,
620  DenseMatrix &dshape) const;
621 };
622 
624 class P0TriangleFiniteElement : public NodalFiniteElement
625 {
626 public:
628  P0TriangleFiniteElement();
629 
631  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
632 
634  virtual void CalcDShape(const IntegrationPoint &ip,
635  DenseMatrix &dshape) const;
636  virtual void ProjectDelta(int vertex, Vector &dofs) const
637  { dofs(0) = 1.0; }
638 };
639 
640 
641 class P0QuadFiniteElement : public NodalFiniteElement
642 {
643 public:
644  P0QuadFiniteElement();
645  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
646  virtual void CalcDShape(const IntegrationPoint &ip,
647  DenseMatrix &dshape) const;
648  virtual void ProjectDelta(int vertex, Vector &dofs) const
649  { dofs(0) = 1.0; }
650 };
651 
652 
654 class Linear3DFiniteElement : public NodalFiniteElement
655 {
656 public:
658  Linear3DFiniteElement();
659 
663  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
664 
669  virtual void CalcDShape(const IntegrationPoint &ip,
670  DenseMatrix &dshape) const;
671 
672  virtual void ProjectDelta(int vertex, Vector &dofs) const
673  { dofs = 0.0; dofs(vertex) = 1.0; }
674 
675  virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;
676 };
677 
679 class Quadratic3DFiniteElement : public NodalFiniteElement
680 {
681 public:
683  Quadratic3DFiniteElement();
684 
685  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
686 
687  virtual void CalcDShape(const IntegrationPoint &ip,
688  DenseMatrix &dshape) const;
689 };
690 
692 class TriLinear3DFiniteElement : public NodalFiniteElement
693 {
694 public:
696  TriLinear3DFiniteElement();
697 
701  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
702 
707  virtual void CalcDShape(const IntegrationPoint &ip,
708  DenseMatrix &dshape) const;
709 
710  virtual void ProjectDelta(int vertex, Vector &dofs) const
711  { dofs = 0.0; dofs(vertex) = 1.0; }
712 };
713 
715 class CrouzeixRaviartFiniteElement : public NodalFiniteElement
716 {
717 public:
718  CrouzeixRaviartFiniteElement();
719  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
720  virtual void CalcDShape(const IntegrationPoint &ip,
721  DenseMatrix &dshape) const;
722  virtual void ProjectDelta(int vertex, Vector &dofs) const
723  { dofs = 1.0; }
724 };
725 
727 class CrouzeixRaviartQuadFiniteElement : public NodalFiniteElement
728 {
729 public:
730  CrouzeixRaviartQuadFiniteElement();
731  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
732  virtual void CalcDShape(const IntegrationPoint &ip,
733  DenseMatrix &dshape) const;
734 };
735 
736 class P0SegmentFiniteElement : public NodalFiniteElement
737 {
738 public:
739  P0SegmentFiniteElement(int Ord = 0);
740  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
741  virtual void CalcDShape(const IntegrationPoint &ip,
742  DenseMatrix &dshape) const;
743 };
744 
745 class RT0TriangleFiniteElement : public VectorFiniteElement
746 {
747 private:
748  static const double nk[3][2];
749 
750 public:
751  RT0TriangleFiniteElement();
752 
753  virtual void CalcVShape(const IntegrationPoint &ip,
754  DenseMatrix &shape) const;
755 
756  virtual void CalcVShape(ElementTransformation &Trans,
757  DenseMatrix &shape) const
758  { CalcVShape_RT(Trans, shape); }
759 
760  virtual void CalcDivShape(const IntegrationPoint &ip,
761  Vector &divshape) const;
762 
763  virtual void GetLocalInterpolation (ElementTransformation &Trans,
764  DenseMatrix &I) const;
765 
766  using FiniteElement::Project;
767 
768  virtual void Project (VectorCoefficient &vc,
769  ElementTransformation &Trans, Vector &dofs) const;
770 };
771 
772 class RT0QuadFiniteElement : public VectorFiniteElement
773 {
774 private:
775  static const double nk[4][2];
776 
777 public:
778  RT0QuadFiniteElement();
779 
780  virtual void CalcVShape(const IntegrationPoint &ip,
781  DenseMatrix &shape) const;
782 
783  virtual void CalcVShape(ElementTransformation &Trans,
784  DenseMatrix &shape) const
785  { CalcVShape_RT(Trans, shape); }
786 
787  virtual void CalcDivShape(const IntegrationPoint &ip,
788  Vector &divshape) const;
789 
790  virtual void GetLocalInterpolation (ElementTransformation &Trans,
791  DenseMatrix &I) const;
792 
793  using FiniteElement::Project;
794 
795  virtual void Project (VectorCoefficient &vc,
796  ElementTransformation &Trans, Vector &dofs) const;
797 };
798 
799 class RT1TriangleFiniteElement : public VectorFiniteElement
800 {
801 private:
802  static const double nk[8][2];
803 
804 public:
805  RT1TriangleFiniteElement();
806 
807  virtual void CalcVShape(const IntegrationPoint &ip,
808  DenseMatrix &shape) const;
809 
810  virtual void CalcVShape(ElementTransformation &Trans,
811  DenseMatrix &shape) const
812  { CalcVShape_RT(Trans, shape); }
813 
814  virtual void CalcDivShape(const IntegrationPoint &ip,
815  Vector &divshape) const;
816 
817  virtual void GetLocalInterpolation (ElementTransformation &Trans,
818  DenseMatrix &I) const;
819 
820  using FiniteElement::Project;
821 
822  virtual void Project (VectorCoefficient &vc,
823  ElementTransformation &Trans, Vector &dofs) const;
824 };
825 
826 class RT1QuadFiniteElement : public VectorFiniteElement
827 {
828 private:
829  static const double nk[12][2];
830 
831 public:
832  RT1QuadFiniteElement();
833 
834  virtual void CalcVShape(const IntegrationPoint &ip,
835  DenseMatrix &shape) const;
836 
837  virtual void CalcVShape(ElementTransformation &Trans,
838  DenseMatrix &shape) const
839  { CalcVShape_RT(Trans, shape); }
840 
841  virtual void CalcDivShape(const IntegrationPoint &ip,
842  Vector &divshape) const;
843 
844  virtual void GetLocalInterpolation (ElementTransformation &Trans,
845  DenseMatrix &I) const;
846 
847  using FiniteElement::Project;
848 
849  virtual void Project (VectorCoefficient &vc,
850  ElementTransformation &Trans, Vector &dofs) const;
851 };
852 
853 class RT2TriangleFiniteElement : public VectorFiniteElement
854 {
855 private:
856  static const double M[15][15];
857 public:
858  RT2TriangleFiniteElement();
859 
860  virtual void CalcVShape(const IntegrationPoint &ip,
861  DenseMatrix &shape) const;
862 
863  virtual void CalcVShape(ElementTransformation &Trans,
864  DenseMatrix &shape) const
865  { CalcVShape_RT(Trans, shape); }
866 
867  virtual void CalcDivShape(const IntegrationPoint &ip,
868  Vector &divshape) const;
869 };
870 
871 class RT2QuadFiniteElement : public VectorFiniteElement
872 {
873 private:
874  static const double nk[24][2];
875  static const double pt[4];
876  static const double dpt[3];
877 
878 public:
879  RT2QuadFiniteElement();
880 
881  virtual void CalcVShape(const IntegrationPoint &ip,
882  DenseMatrix &shape) const;
883 
884  virtual void CalcVShape(ElementTransformation &Trans,
885  DenseMatrix &shape) const
886  { CalcVShape_RT(Trans, shape); }
887 
888  virtual void CalcDivShape(const IntegrationPoint &ip,
889  Vector &divshape) const;
890 
891  virtual void GetLocalInterpolation (ElementTransformation &Trans,
892  DenseMatrix &I) const;
893 
894  using FiniteElement::Project;
895 
896  virtual void Project (VectorCoefficient &vc,
897  ElementTransformation &Trans, Vector &dofs) const;
898 };
899 
901 class P1SegmentFiniteElement : public NodalFiniteElement
902 {
903 public:
904  P1SegmentFiniteElement();
905  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
906  virtual void CalcDShape(const IntegrationPoint &ip,
907  DenseMatrix &dshape) const;
908 };
909 
911 class P2SegmentFiniteElement : public NodalFiniteElement
912 {
913 public:
914  P2SegmentFiniteElement();
915  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
916  virtual void CalcDShape(const IntegrationPoint &ip,
917  DenseMatrix &dshape) const;
918 };
919 
920 class Lagrange1DFiniteElement : public NodalFiniteElement
921 {
922 private:
923  Vector rwk;
924 #ifndef MFEM_THREAD_SAFE
925  mutable Vector rxxk;
926 #endif
927 public:
928  Lagrange1DFiniteElement (int degree);
929  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
930  virtual void CalcDShape(const IntegrationPoint &ip,
931  DenseMatrix &dshape) const;
932 };
933 
934 class P1TetNonConfFiniteElement : public NodalFiniteElement
935 {
936 public:
937  P1TetNonConfFiniteElement();
938  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
939  virtual void CalcDShape(const IntegrationPoint &ip,
940  DenseMatrix &dshape) const;
941 };
942 
943 class P0TetFiniteElement : public NodalFiniteElement
944 {
945 public:
946  P0TetFiniteElement ();
947  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
948  virtual void CalcDShape(const IntegrationPoint &ip,
949  DenseMatrix &dshape) const;
950  virtual void ProjectDelta(int vertex, Vector &dofs) const
951  { dofs(0) = 1.0; }
952 };
953 
954 class P0HexFiniteElement : public NodalFiniteElement
955 {
956 public:
957  P0HexFiniteElement ();
958  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
959  virtual void CalcDShape(const IntegrationPoint &ip,
960  DenseMatrix &dshape) const;
961  virtual void ProjectDelta(int vertex, Vector &dofs) const
962  { dofs(0) = 1.0; }
963 };
964 
966 class LagrangeHexFiniteElement : public NodalFiniteElement
967 {
968 private:
969  Lagrange1DFiniteElement * fe1d;
970  int dof1d;
971  int *I, *J, *K;
972 #ifndef MFEM_THREAD_SAFE
973  mutable Vector shape1dx, shape1dy, shape1dz;
974  mutable DenseMatrix dshape1dx, dshape1dy, dshape1dz;
975 #endif
976 
977 public:
978  LagrangeHexFiniteElement (int degree);
979  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
980  virtual void CalcDShape(const IntegrationPoint &ip,
981  DenseMatrix &dshape) const;
982  ~LagrangeHexFiniteElement ();
983 };
984 
985 
987 class RefinedLinear1DFiniteElement : public NodalFiniteElement
988 {
989 public:
991  RefinedLinear1DFiniteElement();
992 
996  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
997 
1002  virtual void CalcDShape(const IntegrationPoint &ip,
1003  DenseMatrix &dshape) const;
1004 };
1005 
1007 class RefinedLinear2DFiniteElement : public NodalFiniteElement
1008 {
1009 public:
1011  RefinedLinear2DFiniteElement();
1012 
1016  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1017 
1022  virtual void CalcDShape(const IntegrationPoint &ip,
1023  DenseMatrix &dshape) const;
1024 };
1025 
1027 class RefinedLinear3DFiniteElement : public NodalFiniteElement
1028 {
1029 public:
1031  RefinedLinear3DFiniteElement();
1032 
1033  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1034 
1035  virtual void CalcDShape(const IntegrationPoint &ip,
1036  DenseMatrix &dshape) const;
1037 };
1038 
1040 class RefinedBiLinear2DFiniteElement : public NodalFiniteElement
1041 {
1042 public:
1044  RefinedBiLinear2DFiniteElement();
1045 
1049  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1050 
1055  virtual void CalcDShape(const IntegrationPoint &ip,
1056  DenseMatrix &dshape) const;
1057 };
1058 
1060 class RefinedTriLinear3DFiniteElement : public NodalFiniteElement
1061 {
1062 public:
1064  RefinedTriLinear3DFiniteElement();
1065 
1069  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1070 
1075  virtual void CalcDShape(const IntegrationPoint &ip,
1076  DenseMatrix &dshape) const;
1077 };
1078 
1079 
1080 class Nedelec1HexFiniteElement : public VectorFiniteElement
1081 {
1082 private:
1083  static const double tk[12][3];
1084 
1085 public:
1086  Nedelec1HexFiniteElement();
1087  virtual void CalcVShape(const IntegrationPoint &ip,
1088  DenseMatrix &shape) const;
1089  virtual void CalcVShape(ElementTransformation &Trans,
1090  DenseMatrix &shape) const
1091  { CalcVShape_ND(Trans, shape); }
1092  virtual void CalcCurlShape(const IntegrationPoint &ip,
1093  DenseMatrix &curl_shape) const;
1094  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1095  DenseMatrix &I) const;
1096  using FiniteElement::Project;
1097  virtual void Project (VectorCoefficient &vc,
1098  ElementTransformation &Trans, Vector &dofs) const;
1099 };
1100 
1101 
1102 class Nedelec1TetFiniteElement : public VectorFiniteElement
1103 {
1104 private:
1105  static const double tk[6][3];
1106 
1107 public:
1108  Nedelec1TetFiniteElement();
1109  virtual void CalcVShape(const IntegrationPoint &ip,
1110  DenseMatrix &shape) const;
1111  virtual void CalcVShape(ElementTransformation &Trans,
1112  DenseMatrix &shape) const
1113  { CalcVShape_ND(Trans, shape); }
1114  virtual void CalcCurlShape(const IntegrationPoint &ip,
1115  DenseMatrix &curl_shape) const;
1116  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1117  DenseMatrix &I) const;
1118  using FiniteElement::Project;
1119  virtual void Project (VectorCoefficient &vc,
1120  ElementTransformation &Trans, Vector &dofs) const;
1121 };
1122 
1123 
1124 class RT0HexFiniteElement : public VectorFiniteElement
1125 {
1126 private:
1127  static const double nk[6][3];
1128 
1129 public:
1130  RT0HexFiniteElement();
1131 
1132  virtual void CalcVShape(const IntegrationPoint &ip,
1133  DenseMatrix &shape) const;
1134 
1135  virtual void CalcVShape(ElementTransformation &Trans,
1136  DenseMatrix &shape) const
1137  { CalcVShape_RT(Trans, shape); }
1138 
1139  virtual void CalcDivShape(const IntegrationPoint &ip,
1140  Vector &divshape) const;
1141 
1142  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1143  DenseMatrix &I) const;
1144 
1145  using FiniteElement::Project;
1146 
1147  virtual void Project (VectorCoefficient &vc,
1148  ElementTransformation &Trans, Vector &dofs) const;
1149 };
1150 
1151 
1152 class RT1HexFiniteElement : public VectorFiniteElement
1153 {
1154 private:
1155  static const double nk[36][3];
1156 
1157 public:
1158  RT1HexFiniteElement();
1159 
1160  virtual void CalcVShape(const IntegrationPoint &ip,
1161  DenseMatrix &shape) const;
1162 
1163  virtual void CalcVShape(ElementTransformation &Trans,
1164  DenseMatrix &shape) const
1165  { CalcVShape_RT(Trans, shape); }
1166 
1167  virtual void CalcDivShape(const IntegrationPoint &ip,
1168  Vector &divshape) const;
1169 
1170  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1171  DenseMatrix &I) const;
1172 
1173  using FiniteElement::Project;
1174 
1175  virtual void Project (VectorCoefficient &vc,
1176  ElementTransformation &Trans, Vector &dofs) const;
1177 };
1178 
1179 
1180 class RT0TetFiniteElement : public VectorFiniteElement
1181 {
1182 private:
1183  static const double nk[4][3];
1184 
1185 public:
1186  RT0TetFiniteElement();
1187 
1188  virtual void CalcVShape(const IntegrationPoint &ip,
1189  DenseMatrix &shape) const;
1190 
1191  virtual void CalcVShape(ElementTransformation &Trans,
1192  DenseMatrix &shape) const
1193  { CalcVShape_RT(Trans, shape); }
1194 
1195  virtual void CalcDivShape(const IntegrationPoint &ip,
1196  Vector &divshape) const;
1197 
1198  virtual void GetLocalInterpolation (ElementTransformation &Trans,
1199  DenseMatrix &I) const;
1200 
1201  using FiniteElement::Project;
1202 
1203  virtual void Project (VectorCoefficient &vc,
1204  ElementTransformation &Trans, Vector &dofs) const;
1205 };
1206 
1207 
1208 class RotTriLinearHexFiniteElement : public NodalFiniteElement
1209 {
1210 public:
1211  RotTriLinearHexFiniteElement();
1212  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1213  virtual void CalcDShape(const IntegrationPoint &ip,
1214  DenseMatrix &dshape) const;
1215 };
1216 
1217 
1218 class Poly_1D
1219 {
1220 public:
1221  class Basis
1222  {
1223  private:
1224  int mode; // 0 - use change of basis, O(p^2) Evals
1225  // 1 - use barycentric Lagrangian interpolation, O(p) Evals
1226  DenseMatrixInverse Ai;
1227  mutable Vector x, w;
1228 
1229  public:
1230  Basis(const int p, const double *nodes, const int _mode = 1);
1231  void Eval(const double x, Vector &u) const;
1232  void Eval(const double x, Vector &u, Vector &d) const;
1233  };
1234 
1235 private:
1236  Array<double *> open_pts, closed_pts;
1237  Array<Basis *> open_basis, closed_basis;
1238 
1239  static Array2D<int> binom;
1240 
1241  static void CalcMono(const int p, const double x, double *u);
1242  static void CalcMono(const int p, const double x, double *u, double *d);
1243 
1244  static void CalcLegendre(const int p, const double x, double *u);
1245  static void CalcLegendre(const int p, const double x, double *u, double *d);
1246 
1247  static void CalcChebyshev(const int p, const double x, double *u);
1248  static void CalcChebyshev(const int p, const double x, double *u, double *d);
1249 
1250 public:
1251  Poly_1D() { }
1252 
1253  static const int *Binom(const int p);
1254 
1255  const double *OpenPoints(const int p);
1256  const double *ClosedPoints(const int p);
1257 
1258  Basis &OpenBasis(const int p);
1259  Basis &ClosedBasis(const int p);
1260 
1261  // Evaluate the values of a hierarchical 1D basis at point x
1262  // hierarchical = k-th basis function is degree k polynomial
1263  static void CalcBasis(const int p, const double x, double *u)
1264  // { CalcMono(p, x, u); }
1265  // Bernstein basis is not hierarchical --> does not work for triangles
1266  // and tetrahedra
1267  // { CalcBernstein(p, x, u); }
1268  // { CalcLegendre(p, x, u); }
1269  { CalcChebyshev(p, x, u); }
1270 
1271  // Evaluate the values and derivatives of a hierarchical 1D basis at point x
1272  static void CalcBasis(const int p, const double x, double *u, double *d)
1273  // { CalcMono(p, x, u, d); }
1274  // { CalcBernstein(p, x, u, d); }
1275  // { CalcLegendre(p, x, u, d); }
1276  { CalcChebyshev(p, x, u, d); }
1277 
1278  // Evaluate a representation of a Delta function at point x
1279  static double CalcDelta(const int p, const double x)
1280  { return pow(x, (double) p); }
1281 
1282  static void UniformPoints(const int p, double *x);
1283  static void GaussPoints(const int p, double *x);
1284  static void GaussLobattoPoints(const int p, double *x);
1285  static void ChebyshevPoints(const int p, double *x);
1286 
1288  static void CalcBinomTerms(const int p, const double x, const double y,
1289  double *u);
1292  static void CalcBinomTerms(const int p, const double x, const double y,
1293  double *u, double *d);
1296  static void CalcDBinomTerms(const int p, const double x, const double y,
1297  double *d);
1298  static void CalcBernstein(const int p, const double x, double *u)
1299  { CalcBinomTerms(p, x, 1. - x, u); }
1300  static void CalcBernstein(const int p, const double x, double *u, double *d)
1301  { CalcBinomTerms(p, x, 1. - x, u, d); }
1302 
1303  ~Poly_1D();
1304 };
1305 
1306 extern Poly_1D poly1d;
1307 
1308 
1309 class H1_SegmentElement : public NodalFiniteElement
1310 {
1311 private:
1312  Poly_1D::Basis &basis1d;
1313 #ifndef MFEM_THREAD_SAFE
1314  mutable Vector shape_x, dshape_x;
1315 #endif
1316  Array<int> dof_map;
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  const Array<int> &GetDofMap() const { return dof_map; }
1325 };
1326 
1327 
1328 class H1_QuadrilateralElement : public NodalFiniteElement
1329 {
1330 private:
1331  Poly_1D::Basis &basis1d;
1332 #ifndef MFEM_THREAD_SAFE
1333  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1334 #endif
1335  Array<int> dof_map;
1336 
1337 public:
1338  H1_QuadrilateralElement(const int p);
1339  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1340  virtual void CalcDShape(const IntegrationPoint &ip,
1341  DenseMatrix &dshape) const;
1342  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1343  const Array<int> &GetDofMap() const { return dof_map; }
1344 };
1345 
1346 
1347 class H1_HexahedronElement : public NodalFiniteElement
1348 {
1349 private:
1350  Poly_1D::Basis &basis1d;
1351 #ifndef MFEM_THREAD_SAFE
1352  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1353 #endif
1354  Array<int> dof_map;
1355 
1356 public:
1357  H1_HexahedronElement(const int p);
1358  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1359  virtual void CalcDShape(const IntegrationPoint &ip,
1360  DenseMatrix &dshape) const;
1361  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1362  const Array<int> &GetDofMap() const { return dof_map; }
1363 };
1364 
1365 class H1Pos_SegmentElement : public PositiveFiniteElement
1366 {
1367 private:
1368 #ifndef MFEM_THREAD_SAFE
1369  // This is to share scratch space between invocations, which helps
1370  // speed things up, but with OpenMP, we need one copy per thread.
1371  // Right now, we solve this by allocating this space within each function
1372  // call every time we call it. Alternatively, we should do some sort
1373  // thread private thing. Brunner, Jan 2014
1374  mutable Vector shape_x, dshape_x;
1375 #endif
1376  Array<int> dof_map;
1377 
1378 public:
1379  H1Pos_SegmentElement(const int p);
1380  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1381  virtual void CalcDShape(const IntegrationPoint &ip,
1382  DenseMatrix &dshape) const;
1383  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1384  const Array<int> &GetDofMap() const { return dof_map; }
1385 };
1386 
1387 
1388 class H1Pos_QuadrilateralElement : public PositiveFiniteElement
1389 {
1390 private:
1391 #ifndef MFEM_THREAD_SAFE
1392  // See comment in H1Pos_SegmentElement
1393  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1394 #endif
1395  Array<int> dof_map;
1396 
1397 public:
1398  H1Pos_QuadrilateralElement(const int p);
1399  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1400  virtual void CalcDShape(const IntegrationPoint &ip,
1401  DenseMatrix &dshape) const;
1402  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1403  const Array<int> &GetDofMap() const { return dof_map; }
1404 };
1405 
1406 
1407 class H1Pos_HexahedronElement : public PositiveFiniteElement
1408 {
1409 private:
1410 #ifndef MFEM_THREAD_SAFE
1411  // See comment in H1Pos_SegementElement.
1412  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1413 #endif
1414  Array<int> dof_map;
1415 
1416 public:
1417  H1Pos_HexahedronElement(const int p);
1418  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1419  virtual void CalcDShape(const IntegrationPoint &ip,
1420  DenseMatrix &dshape) const;
1421  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1422  const Array<int> &GetDofMap() const { return dof_map; }
1423 };
1424 
1425 
1426 class H1_TriangleElement : public NodalFiniteElement
1427 {
1428 private:
1429 #ifndef MFEM_THREAD_SAFE
1430  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1431  mutable DenseMatrix du;
1432 #endif
1433  DenseMatrixInverse Ti;
1434 
1435 public:
1436  H1_TriangleElement(const int p);
1437  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1438  virtual void CalcDShape(const IntegrationPoint &ip,
1439  DenseMatrix &dshape) const;
1440 };
1441 
1442 
1443 class H1_TetrahedronElement : public NodalFiniteElement
1444 {
1445 private:
1446 #ifndef MFEM_THREAD_SAFE
1447  mutable Vector shape_x, shape_y, shape_z, shape_l;
1448  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1449  mutable DenseMatrix du;
1450 #endif
1451  DenseMatrixInverse Ti;
1452 
1453 public:
1454  H1_TetrahedronElement(const int p);
1455  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1456  virtual void CalcDShape(const IntegrationPoint &ip,
1457  DenseMatrix &dshape) const;
1458 };
1459 
1460 
1461 class H1Pos_TriangleElement : public PositiveFiniteElement
1462 {
1463 protected:
1464 #ifndef MFEM_THREAD_SAFE
1465  mutable Vector m_shape, dshape_1d;
1466  mutable DenseMatrix m_dshape;
1467 #endif
1468  Array<int> dof_map;
1469 
1470 public:
1471  H1Pos_TriangleElement(const int p);
1472 
1473  // The size of shape is (p+1)(p+2)/2 (dof).
1474  static void CalcShape(const int p, const double x, const double y,
1475  double *shape);
1476 
1477  // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
1478  static void CalcDShape(const int p, const double x, const double y,
1479  double *dshape_1d, double *dshape);
1480 
1481  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1482  virtual void CalcDShape(const IntegrationPoint &ip,
1483  DenseMatrix &dshape) const;
1484 };
1485 
1486 
1487 class H1Pos_TetrahedronElement : public PositiveFiniteElement
1488 {
1489 protected:
1490 #ifndef MFEM_THREAD_SAFE
1491  mutable Vector m_shape, dshape_1d;
1492  mutable DenseMatrix m_dshape;
1493 #endif
1494  Array<int> dof_map;
1495 
1496 public:
1497  H1Pos_TetrahedronElement(const int p);
1498 
1499  // The size of shape is (p+1)(p+2)(p+3)/6 (dof).
1500  static void CalcShape(const int p, const double x, const double y,
1501  const double z, double *shape);
1502 
1503  // The size of dshape_1d is p+1; the size of dshape is (dof x dim).
1504  static void CalcDShape(const int p, const double x, const double y,
1505  const double z, double *dshape_1d, double *dshape);
1506 
1507  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1508  virtual void CalcDShape(const IntegrationPoint &ip,
1509  DenseMatrix &dshape) const;
1510 };
1511 
1512 
1513 class L2_SegmentElement : public NodalFiniteElement
1514 {
1515 private:
1516  int type;
1517  Poly_1D::Basis *basis1d;
1518 #ifndef MFEM_THREAD_SAFE
1519  mutable Vector shape_x, dshape_x;
1520 #endif
1521 
1522 public:
1523  L2_SegmentElement(const int p, const int _type = 0);
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 L2Pos_SegmentElement : public PositiveFiniteElement
1532 {
1533 private:
1534 #ifndef MFEM_THREAD_SAFE
1535  mutable Vector shape_x, dshape_x;
1536 #endif
1537 
1538 public:
1539  L2Pos_SegmentElement(const int p);
1540  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1541  virtual void CalcDShape(const IntegrationPoint &ip,
1542  DenseMatrix &dshape) const;
1543  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1544 };
1545 
1546 
1547 class L2_QuadrilateralElement : public NodalFiniteElement
1548 {
1549 private:
1550  int type;
1551  Poly_1D::Basis *basis1d;
1552 #ifndef MFEM_THREAD_SAFE
1553  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1554 #endif
1555 
1556 public:
1557  L2_QuadrilateralElement(const int p, const int _type = 0);
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  virtual void ProjectCurl(const FiniteElement &fe,
1563  ElementTransformation &Trans,
1564  DenseMatrix &curl) const
1565  { ProjectCurl_2D(fe, Trans, curl); }
1566 };
1567 
1568 
1569 class L2Pos_QuadrilateralElement : public PositiveFiniteElement
1570 {
1571 private:
1572 #ifndef MFEM_THREAD_SAFE
1573  mutable Vector shape_x, shape_y, dshape_x, dshape_y;
1574 #endif
1575 
1576 public:
1577  L2Pos_QuadrilateralElement(const int p);
1578  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1579  virtual void CalcDShape(const IntegrationPoint &ip,
1580  DenseMatrix &dshape) const;
1581  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1582 };
1583 
1584 
1585 class L2_HexahedronElement : public NodalFiniteElement
1586 {
1587 private:
1588  int type;
1589  Poly_1D::Basis *basis1d;
1590 #ifndef MFEM_THREAD_SAFE
1591  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1592 #endif
1593 
1594 public:
1595  L2_HexahedronElement(const int p, const int _type = 0);
1596  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1597  virtual void CalcDShape(const IntegrationPoint &ip,
1598  DenseMatrix &dshape) const;
1599  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1600 };
1601 
1602 
1603 class L2Pos_HexahedronElement : public PositiveFiniteElement
1604 {
1605 private:
1606 #ifndef MFEM_THREAD_SAFE
1607  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
1608 #endif
1609 
1610 public:
1611  L2Pos_HexahedronElement(const int p);
1612  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1613  virtual void CalcDShape(const IntegrationPoint &ip,
1614  DenseMatrix &dshape) const;
1615  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1616 };
1617 
1618 
1619 class L2_TriangleElement : public NodalFiniteElement
1620 {
1621 private:
1622  int type;
1623 #ifndef MFEM_THREAD_SAFE
1624  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
1625  mutable DenseMatrix du;
1626 #endif
1627  DenseMatrixInverse Ti;
1628 
1629 public:
1630  L2_TriangleElement(const int p, const int _type = 0);
1631  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1632  virtual void CalcDShape(const IntegrationPoint &ip,
1633  DenseMatrix &dshape) const;
1634  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1635  virtual void ProjectCurl(const FiniteElement &fe,
1636  ElementTransformation &Trans,
1637  DenseMatrix &curl) const
1638  { ProjectCurl_2D(fe, Trans, curl); }
1639 };
1640 
1641 
1642 class L2Pos_TriangleElement : public PositiveFiniteElement
1643 {
1644 private:
1645 #ifndef MFEM_THREAD_SAFE
1646  mutable Vector dshape_1d;
1647 #endif
1648 
1649 public:
1650  L2Pos_TriangleElement(const int p);
1651  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1652  virtual void CalcDShape(const IntegrationPoint &ip,
1653  DenseMatrix &dshape) const;
1654  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1655 };
1656 
1657 
1658 class L2_TetrahedronElement : public NodalFiniteElement
1659 {
1660 private:
1661  int type;
1662 #ifndef MFEM_THREAD_SAFE
1663  mutable Vector shape_x, shape_y, shape_z, shape_l;
1664  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
1665  mutable DenseMatrix du;
1666 #endif
1667  DenseMatrixInverse Ti;
1668 
1669 public:
1670  L2_TetrahedronElement(const int p, const int _type = 0);
1671  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1672  virtual void CalcDShape(const IntegrationPoint &ip,
1673  DenseMatrix &dshape) const;
1674  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1675 };
1676 
1677 
1678 class L2Pos_TetrahedronElement : public PositiveFiniteElement
1679 {
1680 private:
1681 #ifndef MFEM_THREAD_SAFE
1682  mutable Vector dshape_1d;
1683 #endif
1684 
1685 public:
1686  L2Pos_TetrahedronElement(const int p);
1687  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
1688  virtual void CalcDShape(const IntegrationPoint &ip,
1689  DenseMatrix &dshape) const;
1690  virtual void ProjectDelta(int vertex, Vector &dofs) const;
1691 };
1692 
1693 
1694 class RT_QuadrilateralElement : public VectorFiniteElement
1695 {
1696 private:
1697  static const double nk[8];
1698 
1699  Poly_1D::Basis &cbasis1d, &obasis1d;
1700 #ifndef MFEM_THREAD_SAFE
1701  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
1702  mutable Vector dshape_cx, dshape_cy;
1703 #endif
1704  Array<int> dof_map, dof2nk;
1705 
1706 public:
1707  RT_QuadrilateralElement(const int p);
1708  virtual void CalcVShape(const IntegrationPoint &ip,
1709  DenseMatrix &shape) const;
1710  virtual void CalcVShape(ElementTransformation &Trans,
1711  DenseMatrix &shape) const
1712  { CalcVShape_RT(Trans, shape); }
1713  virtual void CalcDivShape(const IntegrationPoint &ip,
1714  Vector &divshape) const;
1715  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1716  DenseMatrix &I) const
1717  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1718  using FiniteElement::Project;
1719  virtual void Project(VectorCoefficient &vc,
1720  ElementTransformation &Trans, Vector &dofs) const
1721  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1722  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1723  DenseMatrix &I) const
1724  { Project_RT(nk, dof2nk, fe, Trans, I); }
1725  virtual void ProjectGrad(const FiniteElement &fe,
1726  ElementTransformation &Trans,
1727  DenseMatrix &grad) const
1728  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1729 };
1730 
1731 
1732 class RT_HexahedronElement : public VectorFiniteElement
1733 {
1734  static const double nk[18];
1735 
1736  Poly_1D::Basis &cbasis1d, &obasis1d;
1737 #ifndef MFEM_THREAD_SAFE
1738  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
1739  mutable Vector dshape_cx, dshape_cy, dshape_cz;
1740 #endif
1741  Array<int> dof_map, dof2nk;
1742 
1743 public:
1744  RT_HexahedronElement(const int p);
1745  virtual void CalcVShape(const IntegrationPoint &ip,
1746  DenseMatrix &shape) const;
1747  virtual void CalcVShape(ElementTransformation &Trans,
1748  DenseMatrix &shape) const
1749  { CalcVShape_RT(Trans, shape); }
1750  virtual void CalcDivShape(const IntegrationPoint &ip,
1751  Vector &divshape) const;
1752  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1753  DenseMatrix &I) const
1754  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1755  using FiniteElement::Project;
1756  virtual void Project(VectorCoefficient &vc,
1757  ElementTransformation &Trans, Vector &dofs) const
1758  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1759  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1760  DenseMatrix &I) const
1761  { Project_RT(nk, dof2nk, fe, Trans, I); }
1762  virtual void ProjectCurl(const FiniteElement &fe,
1763  ElementTransformation &Trans,
1764  DenseMatrix &curl) const
1765  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
1766 };
1767 
1768 
1769 class RT_TriangleElement : public VectorFiniteElement
1770 {
1771  static const double nk[6], c;
1772 
1773 #ifndef MFEM_THREAD_SAFE
1774  mutable Vector shape_x, shape_y, shape_l;
1775  mutable Vector dshape_x, dshape_y, dshape_l;
1776  mutable DenseMatrix u;
1777  mutable Vector divu;
1778 #endif
1779  Array<int> dof2nk;
1780  DenseMatrixInverse Ti;
1781 
1782 public:
1783  RT_TriangleElement(const int p);
1784  virtual void CalcVShape(const IntegrationPoint &ip,
1785  DenseMatrix &shape) const;
1786  virtual void CalcVShape(ElementTransformation &Trans,
1787  DenseMatrix &shape) const
1788  { CalcVShape_RT(Trans, shape); }
1789  virtual void CalcDivShape(const IntegrationPoint &ip,
1790  Vector &divshape) const;
1791  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1792  DenseMatrix &I) const
1793  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1794  using FiniteElement::Project;
1795  virtual void Project(VectorCoefficient &vc,
1796  ElementTransformation &Trans, Vector &dofs) const
1797  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1798  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1799  DenseMatrix &I) const
1800  { Project_RT(nk, dof2nk, fe, Trans, I); }
1801  virtual void ProjectGrad(const FiniteElement &fe,
1802  ElementTransformation &Trans,
1803  DenseMatrix &grad) const
1804  { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
1805 };
1806 
1807 
1808 class RT_TetrahedronElement : public VectorFiniteElement
1809 {
1810  static const double nk[12], c;
1811 
1812 #ifndef MFEM_THREAD_SAFE
1813  mutable Vector shape_x, shape_y, shape_z, shape_l;
1814  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
1815  mutable DenseMatrix u;
1816  mutable Vector divu;
1817 #endif
1818  Array<int> dof2nk;
1819  DenseMatrixInverse Ti;
1820 
1821 public:
1822  RT_TetrahedronElement(const int p);
1823  virtual void CalcVShape(const IntegrationPoint &ip,
1824  DenseMatrix &shape) const;
1825  virtual void CalcVShape(ElementTransformation &Trans,
1826  DenseMatrix &shape) const
1827  { CalcVShape_RT(Trans, shape); }
1828  virtual void CalcDivShape(const IntegrationPoint &ip,
1829  Vector &divshape) const;
1830  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1831  DenseMatrix &I) const
1832  { LocalInterpolation_RT(nk, dof2nk, Trans, I); }
1833  using FiniteElement::Project;
1834  virtual void Project(VectorCoefficient &vc,
1835  ElementTransformation &Trans, Vector &dofs) const
1836  { Project_RT(nk, dof2nk, vc, Trans, dofs); }
1837  virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
1838  DenseMatrix &I) const
1839  { Project_RT(nk, dof2nk, fe, Trans, I); }
1840  virtual void ProjectCurl(const FiniteElement &fe,
1841  ElementTransformation &Trans,
1842  DenseMatrix &curl) const
1843  { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
1844 };
1845 
1846 
1847 class ND_HexahedronElement : public VectorFiniteElement
1848 {
1849  static const double tk[18];
1850 
1851  Poly_1D::Basis &cbasis1d, &obasis1d;
1852 #ifndef MFEM_THREAD_SAFE
1853  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy, shape_cz, shape_oz;
1854  mutable Vector dshape_cx, dshape_cy, dshape_cz;
1855 #endif
1856  Array<int> dof_map, dof2tk;
1857 
1858 public:
1859  ND_HexahedronElement(const int p);
1860 
1861  virtual void CalcVShape(const IntegrationPoint &ip,
1862  DenseMatrix &shape) const;
1863 
1864  virtual void CalcVShape(ElementTransformation &Trans,
1865  DenseMatrix &shape) const
1866  { CalcVShape_ND(Trans, shape); }
1867 
1868  virtual void CalcCurlShape(const IntegrationPoint &ip,
1869  DenseMatrix &curl_shape) const;
1870 
1871  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1872  DenseMatrix &I) const
1873  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1874 
1875  using FiniteElement::Project;
1876 
1877  virtual void Project(VectorCoefficient &vc,
1878  ElementTransformation &Trans, Vector &dofs) const
1879  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1880 
1881  virtual void Project(const FiniteElement &fe,
1882  ElementTransformation &Trans,
1883  DenseMatrix &I) const
1884  { Project_ND(tk, dof2tk, fe, Trans, I); }
1885 
1886  virtual void ProjectGrad(const FiniteElement &fe,
1887  ElementTransformation &Trans,
1888  DenseMatrix &grad) const
1889  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1890 
1891  virtual void ProjectCurl(const FiniteElement &fe,
1892  ElementTransformation &Trans,
1893  DenseMatrix &curl) const
1894  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
1895 };
1896 
1897 
1898 class ND_QuadrilateralElement : public VectorFiniteElement
1899 {
1900  static const double tk[8];
1901 
1902  Poly_1D::Basis &cbasis1d, &obasis1d;
1903 #ifndef MFEM_THREAD_SAFE
1904  mutable Vector shape_cx, shape_ox, shape_cy, shape_oy;
1905  mutable Vector dshape_cx, dshape_cy;
1906 #endif
1907  Array<int> dof_map, dof2tk;
1908 
1909 public:
1910  ND_QuadrilateralElement(const int p);
1911  virtual void CalcVShape(const IntegrationPoint &ip,
1912  DenseMatrix &shape) const;
1913  virtual void CalcVShape(ElementTransformation &Trans,
1914  DenseMatrix &shape) const
1915  { CalcVShape_ND(Trans, shape); }
1916  virtual void CalcCurlShape(const IntegrationPoint &ip,
1917  DenseMatrix &curl_shape) const;
1918  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1919  DenseMatrix &I) const
1920  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1921  using FiniteElement::Project;
1922  virtual void Project(VectorCoefficient &vc,
1923  ElementTransformation &Trans, Vector &dofs) const
1924  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1925  virtual void Project(const FiniteElement &fe,
1926  ElementTransformation &Trans,
1927  DenseMatrix &I) const
1928  { Project_ND(tk, dof2tk, fe, Trans, I); }
1929  virtual void ProjectGrad(const FiniteElement &fe,
1930  ElementTransformation &Trans,
1931  DenseMatrix &grad) const
1932  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1933 };
1934 
1935 
1936 class ND_TetrahedronElement : public VectorFiniteElement
1937 {
1938  static const double tk[18], c;
1939 
1940 #ifndef MFEM_THREAD_SAFE
1941  mutable Vector shape_x, shape_y, shape_z, shape_l;
1942  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l;
1943  mutable DenseMatrix u;
1944 #endif
1945  Array<int> dof2tk;
1946  DenseMatrixInverse Ti;
1947 
1948 public:
1949  ND_TetrahedronElement(const int p);
1950  virtual void CalcVShape(const IntegrationPoint &ip,
1951  DenseMatrix &shape) const;
1952  virtual void CalcVShape(ElementTransformation &Trans,
1953  DenseMatrix &shape) const
1954  { CalcVShape_ND(Trans, shape); }
1955  virtual void CalcCurlShape(const IntegrationPoint &ip,
1956  DenseMatrix &curl_shape) const;
1957  virtual void GetLocalInterpolation(ElementTransformation &Trans,
1958  DenseMatrix &I) const
1959  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
1960  using FiniteElement::Project;
1961  virtual void Project(VectorCoefficient &vc,
1962  ElementTransformation &Trans, Vector &dofs) const
1963  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
1964  virtual void Project(const FiniteElement &fe,
1965  ElementTransformation &Trans,
1966  DenseMatrix &I) const
1967  { Project_ND(tk, dof2tk, fe, Trans, I); }
1968  virtual void ProjectGrad(const FiniteElement &fe,
1969  ElementTransformation &Trans,
1970  DenseMatrix &grad) const
1971  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
1972 
1973  virtual void ProjectCurl(const FiniteElement &fe,
1974  ElementTransformation &Trans,
1975  DenseMatrix &curl) const
1976  { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
1977 };
1978 
1979 class ND_TriangleElement : public VectorFiniteElement
1980 {
1981  static const double tk[8], c;
1982 
1983 #ifndef MFEM_THREAD_SAFE
1984  mutable Vector shape_x, shape_y, shape_l;
1985  mutable Vector dshape_x, dshape_y, dshape_l;
1986  mutable DenseMatrix u;
1987  mutable Vector curlu;
1988 #endif
1989  Array<int> dof2tk;
1990  DenseMatrixInverse Ti;
1991 
1992 public:
1993  ND_TriangleElement(const int p);
1994  virtual void CalcVShape(const IntegrationPoint &ip,
1995  DenseMatrix &shape) const;
1996  virtual void CalcVShape(ElementTransformation &Trans,
1997  DenseMatrix &shape) const
1998  { CalcVShape_ND(Trans, shape); }
1999  virtual void CalcCurlShape(const IntegrationPoint &ip,
2000  DenseMatrix &curl_shape) const;
2001  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2002  DenseMatrix &I) const
2003  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2004  using FiniteElement::Project;
2005  virtual void Project(VectorCoefficient &vc,
2006  ElementTransformation &Trans, Vector &dofs) const
2007  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2008  virtual void Project(const FiniteElement &fe,
2009  ElementTransformation &Trans,
2010  DenseMatrix &I) const
2011  { Project_ND(tk, dof2tk, fe, Trans, I); }
2012  virtual void ProjectGrad(const FiniteElement &fe,
2013  ElementTransformation &Trans,
2014  DenseMatrix &grad) const
2015  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2016 };
2017 
2018 
2019 class ND_SegmentElement : public VectorFiniteElement
2020 {
2021  static const double tk[1];
2022 
2023  Poly_1D::Basis &obasis1d;
2024  Array<int> dof2tk;
2025 
2026 public:
2027  ND_SegmentElement(const int p);
2028  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
2029  { obasis1d.Eval(ip.x, shape); }
2030  virtual void CalcVShape(const IntegrationPoint &ip,
2031  DenseMatrix &shape) const;
2032  virtual void CalcVShape(ElementTransformation &Trans,
2033  DenseMatrix &shape) const
2034  { CalcVShape_ND(Trans, shape); }
2035  // virtual void CalcCurlShape(const IntegrationPoint &ip,
2036  // DenseMatrix &curl_shape) const;
2037  virtual void GetLocalInterpolation(ElementTransformation &Trans,
2038  DenseMatrix &I) const
2039  { LocalInterpolation_ND(tk, dof2tk, Trans, I); }
2040  using FiniteElement::Project;
2041  virtual void Project(VectorCoefficient &vc,
2042  ElementTransformation &Trans, Vector &dofs) const
2043  { Project_ND(tk, dof2tk, vc, Trans, dofs); }
2044  virtual void Project(const FiniteElement &fe,
2045  ElementTransformation &Trans,
2046  DenseMatrix &I) const
2047  { Project_ND(tk, dof2tk, fe, Trans, I); }
2048  virtual void ProjectGrad(const FiniteElement &fe,
2049  ElementTransformation &Trans,
2050  DenseMatrix &grad) const
2051  { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
2052 };
2053 
2054 
2055 class NURBSFiniteElement : public FiniteElement
2056 {
2057 protected:
2058  mutable Array <KnotVector*> kv;
2059  mutable int *ijk, patch, elem;
2060  mutable Vector weights;
2061 
2062 public:
2063  NURBSFiniteElement(int D, int G, int Do, int O, int F)
2064  : FiniteElement(D, G, Do, O, F)
2065  {
2066  ijk = NULL;
2067  patch = elem = -1;
2068  kv.SetSize(Dim);
2069  weights.SetSize(Dof);
2070  weights = 1.0;
2071  }
2072 
2073  void Reset () const { patch = elem = -1; }
2074  void SetIJK (int *IJK) const { ijk = IJK; }
2075  int GetPatch () const { return patch; }
2076  void SetPatch (int p) const { patch = p; }
2077  int GetElement () const { return elem; }
2078  void SetElement (int e) const { elem = e; }
2079  Array <KnotVector*> &KnotVectors() const { return kv; }
2080  Vector &Weights () const { return weights; }
2081 };
2082 
2083 class NURBS1DFiniteElement : public NURBSFiniteElement
2084 {
2085 protected:
2086  mutable Vector shape_x;
2087 
2088 public:
2089  NURBS1DFiniteElement(int p)
2090  : NURBSFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
2091  shape_x(p + 1) { }
2092 
2093  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2094  virtual void CalcDShape(const IntegrationPoint &ip,
2095  DenseMatrix &dshape) const;
2096 };
2097 
2098 class NURBS2DFiniteElement : public NURBSFiniteElement
2099 {
2100 protected:
2101  mutable Vector u, shape_x, shape_y, dshape_x, dshape_y;
2102 
2103 public:
2104  NURBS2DFiniteElement(int p)
2105  : NURBSFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
2106  FunctionSpace::Qk), u(Dof),
2107  shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1), dshape_y(p + 1) { }
2108 
2109  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2110  virtual void CalcDShape(const IntegrationPoint &ip,
2111  DenseMatrix &dshape) const;
2112 };
2113 
2114 class NURBS3DFiniteElement : public NURBSFiniteElement
2115 {
2116 protected:
2117  mutable Vector u, shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
2118 
2119 public:
2120  NURBS3DFiniteElement(int p)
2121  : NURBSFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
2122  FunctionSpace::Qk), u(Dof),
2123  shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
2124  dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1) { }
2125 
2126  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
2127  virtual void CalcDShape(const IntegrationPoint &ip,
2128  DenseMatrix &dshape) const;
2129 };
2130 
2131 }
2132 
2133 #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:1191
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:8301
mfem::ND_SegmentElement
Definition: fe.hpp:2019
mfem::RT_QuadrilateralElement::RT_QuadrilateralElement
RT_QuadrilateralElement(const int p)
Definition: fe.cpp:9132
mfem::VectorFiniteElement::curlshape_J
DenseMatrix curlshape_J
Definition: fe.hpp:280
mfem::H1Pos_SegmentElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1384
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:1756
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:7171
mfem::L2_TetrahedronElement::L2_TetrahedronElement
L2_TetrahedronElement(const int p, const int _type=0)
Definition: fe.cpp:8924
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:1163
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:1300
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:901
mfem::P2SegmentFiniteElement
Quadratic 1D element with nodes the Gaussian points in [0,1] (trace of RT2)
Definition: fe.hpp:911
mfem::L2Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8721
mfem::NURBS2DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:11040
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:1279
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:1786
mfem::RT_TetrahedronElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1830
mfem::H1_HexahedronElement::H1_HexahedronElement
H1_HexahedronElement(const int p)
Definition: fe.cpp:6851
mfem::L2Pos_TriangleElement
Definition: fe.hpp:1642
mfem::L2Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8460
mfem::RT_TetrahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:9903
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:10354
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:8873
mfem::ND_QuadrilateralElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1929
mfem::RT0TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:756
mfem::H1Pos_SegmentElement::H1Pos_SegmentElement
H1Pos_SegmentElement(const int p)
Definition: fe.cpp:7109
mfem::NURBSFiniteElement::GetPatch
int GetPatch() const
Definition: fe.hpp:2075
mfem::RT_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1840
mfem::FiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:116
mfem::L2_TriangleElement
Definition: fe.hpp:1619
mfem::P0QuadFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:648
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:559
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:1251
mfem::L2Pos_TriangleElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8912
mfem::ND_TetrahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1973
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:7151
mfem::L2_HexahedronElement
Definition: fe.hpp:1585
mfem::VectorFiniteElement::FiniteElement
FiniteElement(D, G, Do, O, F)
mfem::L2Pos_TetrahedronElement::L2Pos_TetrahedronElement
L2Pos_TetrahedronElement(const int p)
Definition: fe.cpp:9075
mfem::NURBSFiniteElement::kv
Array< KnotVector * > kv
Definition: fe.hpp:2058
mfem::VectorFiniteElement::CalcVShape_RT
void CalcVShape_RT(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.cpp:372
mfem::Vector::SetSize
void SetSize(int s)
Resize the vector if the new size is different.
Definition: vector.hpp:263
mfem::RT_QuadrilateralElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9290
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:1111
mfem::L2Pos_SegmentElement
Definition: fe.hpp:1531
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1864
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:6679
mfem::H1Pos_TetrahedronElement::H1Pos_TetrahedronElement
H1Pos_TetrahedronElement(const int p)
Definition: fe.cpp:7893
mfem::NURBS1DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:10988
mfem::L2_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8320
mfem::RT_QuadrilateralElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1715
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:1328
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:1913
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:2073
mfem::RT_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1795
mfem::Quad2DFiniteElement
Class for quadratic FE on triangle.
Definition: fe.hpp:485
mfem::NURBS1DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:11002
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:456
mfem::RT_QuadrilateralElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1710
mfem::RT_TriangleElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9760
mfem::ND_TetrahedronElement
Definition: fe.hpp:1936
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:1759
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:8174
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:1678
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:1362
mfem::L2_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:9040
mfem::ND_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1891
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:9105
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:8244
mfem::H1_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:6763
mfem::P0HexFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:961
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:7281
mfem::FiniteElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.cpp:100
mfem::H1Pos_TetrahedronElement::CalcShape
static void CalcShape(const int p, const double x, const double y, const double z, double *shape)
Definition: fe.cpp:7995
mfem::H1Pos_TetrahedronElement::m_dshape
DenseMatrix m_dshape
Definition: fe.hpp:1492
mfem::ND_TriangleElement
Definition: fe.hpp:1979
mfem::L2_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8982
mfem::RT_HexahedronElement::RT_HexahedronElement
RT_HexahedronElement(const int p)
Definition: fe.cpp:9340
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:2077
mfem::H1Pos_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7253
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:1719
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:1040
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:10885
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:8145
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:8648
mfem::ND_TriangleElement::ND_TriangleElement
ND_TriangleElement(const int p)
Definition: fe.cpp:10805
mfem::L2_TriangleElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1635
mfem::RT_TetrahedronElement::CalcDivShape
virtual void CalcDivShape(const IntegrationPoint &ip, Vector &divshape) const
Definition: fe.cpp:9939
mfem::H1Pos_TetrahedronElement::CalcDShape
static void CalcDShape(const int p, const double x, const double y, const double z, double *dshape_1d, double *dshape)
Definition: fe.cpp:8028
mfem::Poly_1D::CalcBasis
static void CalcBasis(const int p, const double x, double *u)
Definition: fe.hpp:1263
mfem::RT0QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:783
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::H1Pos_TriangleElement::H1Pos_TriangleElement
H1Pos_TriangleElement(const int p)
Definition: fe.cpp:7748
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:1752
mfem::H1Pos_TriangleElement::CalcShape
static void CalcShape(const int p, const double x, const double y, double *shape)
Definition: fe.cpp:7803
mfem::CrouzeixRaviartQuadFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2399
mfem::H1Pos_TriangleElement::dshape_1d
Vector dshape_1d
Definition: fe.hpp:1465
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:451
mfem::L2Pos_QuadrilateralElement
Definition: fe.hpp:1569
mfem::GaussBiLinear2DFiniteElement
Class for bilinear FE on quad with nodes at the 4 Gaussian points.
Definition: fe.hpp:431
mfem::RefinedLinear1DFiniteElement
Class for refined linear FE on interval.
Definition: fe.hpp:987
mfem::L2_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8180
mfem::RefinedLinear2DFiniteElement
Class for refined linear FE on triangle.
Definition: fe.hpp:1007
mfem::RefinedLinear3DFiniteElement
Class for refined linear FE on tetrahedron.
Definition: fe.hpp:1027
mfem::L2_SegmentElement
Definition: fe.hpp:1513
mfem::NURBSFiniteElement::SetPatch
void SetPatch(int p) const
Definition: fe.hpp:2076
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:624
mfem::ND_SegmentElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:2048
mfem::ND_SegmentElement::ND_SegmentElement
ND_SegmentElement(const int p)
Definition: fe.cpp:10964
mfem::H1_TriangleElement::H1_TriangleElement
H1_TriangleElement(const int p)
Definition: fe.cpp:7459
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:7024
mfem::H1Pos_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7274
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:8815
mfem::H1_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7526
mfem::RT_HexahedronElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1762
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:2063
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:1343
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:1060
mfem::ND_TetrahedronElement::ND_TetrahedronElement
ND_TetrahedronElement(const int p)
Definition: fe.cpp:10543
mfem::L2Pos_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8901
mfem::Poly_1D
Definition: fe.hpp:1218
mfem::Quadratic3DFiniteElement
Class for quadratic FE on tetrahedron.
Definition: fe.hpp:679
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:1952
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:1825
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:1957
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:8556
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:1725
mfem::L2Pos_QuadrilateralElement::L2Pos_QuadrilateralElement
L2Pos_QuadrilateralElement(const int p)
Definition: fe.cpp:8396
mfem::P0SegmentFiniteElement::P0SegmentFiniteElement
P0SegmentFiniteElement(int Ord=0)
Definition: fe.cpp:2338
mfem::H1_TetrahedronElement
Definition: fe.hpp:1443
mfem::H1Pos_TriangleElement::CalcDShape
static void CalcDShape(const int p, const double x, const double y, double *dshape_1d, double *dshape)
Definition: fe.cpp:7829
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:11075
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:1961
mfem::RT2TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:863
mfem::Linear3DFiniteElement
Class for linear FE on tetrahedron.
Definition: fe.hpp:654
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:9501
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:727
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:509
mfem::L2_TriangleElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8793
mfem::RT_QuadrilateralElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:9243
mfem::ND_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2001
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:1918
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:9575
mfem::H1_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7689
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:2078
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:8895
mfem::RT_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1837
mfem::RT1TriangleFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:810
mfem::L2_QuadrilateralElement::ProjectCurl
virtual void ProjectCurl(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Definition: fe.hpp:1562
mfem::NURBS3DFiniteElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:11099
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::H1Pos_TriangleElement::m_dshape
DenseMatrix m_dshape
Definition: fe.hpp:1466
mfem::ND_QuadrilateralElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:10489
mfem::L2Pos_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:8421
mfem::ND_HexahedronElement::ND_HexahedronElement
ND_HexahedronElement(const int p)
Definition: fe.cpp:9985
mfem::FiniteElement::Nodes
IntegrationRule Nodes
Definition: fe.hpp:48
mfem::H1Pos_HexahedronElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1422
mfem::ND_SegmentElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:2044
mfem::L2_TetrahedronElement
Definition: fe.hpp:1658
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:8676
mfem::H1Pos_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7131
mfem::H1Pos_HexahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:7452
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:10919
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:1808
mfem::FiniteElement::~FiniteElement
virtual ~FiniteElement()
Definition: fe.hpp:196
mfem::H1_QuadrilateralElement::H1_QuadrilateralElement
H1_QuadrilateralElement(const int p)
Definition: fe.cpp:6707
mfem::RT0TriangleFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:2457
mfem::H1Pos_QuadrilateralElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1403
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:2028
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:1135
mfem::ND_SegmentElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2041
mfem::L2_SegmentElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8191
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:7714
mfem::BiQuad2DFiniteElement
Class for bi-quadratic FE on quadrilateral.
Definition: fe.hpp:525
mfem::H1Pos_HexahedronElement
Definition: fe.hpp:1407
mfem::TriLinear3DFiniteElement
Class for tri-linear FE on cube.
Definition: fe.hpp:692
mfem::Coefficient
Base class Coefficient that may optionally depend on time.
Definition: coefficient.hpp:31
mfem::H1Pos_TetrahedronElement::m_shape
Vector m_shape
Definition: fe.hpp:1491
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:950
mfem::Nedelec1TetFiniteElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:5113
mfem::H1Pos_TetrahedronElement::dof_map
Array< int > dof_map
Definition: fe.hpp:1494
mfem::L2Pos_TetrahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:9098
mfem::CrouzeixRaviartFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:722
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:636
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:1347
mfem::H1Pos_TetrahedronElement
Definition: fe.hpp:1487
mfem::H1Pos_TetrahedronElement::dshape_1d
Vector dshape_1d
Definition: fe.hpp:1491
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:1722
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:1089
mfem::L2_TetrahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:9007
mfem::ND_HexahedronElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:10201
mfem::RT_TriangleElement
Definition: fe.hpp:1769
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:2032
mfem::H1Pos_HexahedronElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7407
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:420
mfem::H1Pos_TriangleElement::m_shape
Vector m_shape
Definition: fe.hpp:1465
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:1871
mfem::RT2QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:884
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:7178
mfem::ND_QuadrilateralElement
Definition: fe.hpp:1898
mfem::ND_TriangleElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:2005
mfem::NURBSFiniteElement::KnotVectors
Array< KnotVector * > & KnotVectors() const
Definition: fe.hpp:2079
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:8844
mfem::H1Pos_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7428
mfem::L2Pos_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8250
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:1694
mfem::GaussBiQuad2DFiniteElement
Bi-quadratic element on quad with nodes at the 9 Gaussian points.
Definition: fe.hpp:564
mfem::RT1QuadFiniteElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:837
mfem::L2Pos_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8697
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:6979
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:10691
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:10440
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:2012
mfem::NodalFiniteElement::ProjectDiv
virtual void ProjectDiv(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Definition: fe.cpp:288
mfem::H1_TriangleElement
Definition: fe.hpp:1426
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:8261
mfem::RefinedLinear2DFiniteElement::RefinedLinear2DFiniteElement
RefinedLinear2DFiniteElement()
Construct a quadratic FE on triangle.
Definition: fe.cpp:3949
mfem::L2_QuadrilateralElement
Definition: fe.hpp:1547
mfem::NodalFiniteElement::NodalLocalInterpolation
void NodalLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I, const NodalFiniteElement &fine_fe) const
Definition: fe.cpp:125
mfem::H1_SegmentElement
Definition: fe.hpp:1309
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:2074
mfem::ND_QuadrilateralElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1922
mfem::ND_HexahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1886
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::H1Pos_TriangleElement::dof_map
Array< int > dof_map
Definition: fe.hpp:1468
mfem::RT_TetrahedronElement::RT_TetrahedronElement
RT_TetrahedronElement(const int p)
Definition: fe.cpp:9802
mfem::Poly_1D::Basis
Definition: fe.hpp:1221
mfem::L2_TriangleElement::L2_TriangleElement
L2_TriangleElement(const int p, const int _type=0)
Definition: fe.cpp:8740
mfem::RT0HexFiniteElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.cpp:5293
mfem::H1Pos_SegmentElement
Definition: fe.hpp:1365
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:2080
mfem::H1_SegmentElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:6660
mfem::H1_TetrahedronElement::H1_TetrahedronElement
H1_TetrahedronElement(const int p)
Definition: fe.cpp:7578
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:966
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:2008
mfem::ND_HexahedronElement
Definition: fe.hpp:1847
mfem::H1Pos_QuadrilateralElement
Definition: fe.hpp:1388
mfem::P0SegmentFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:2344
mfem::L2Pos_HexahedronElement
Definition: fe.hpp:1603
mfem::RT_TriangleElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1798
mfem::RT_TriangleElement::RT_TriangleElement
RT_TriangleElement(const int p)
Definition: fe.cpp:9650
mfem::H1_SegmentElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:6641
mfem::ND_SegmentElement::CalcVShape
virtual void CalcVShape(const IntegrationPoint &ip, DenseMatrix &shape) const
Definition: fe.cpp:10979
mfem::ND_HexahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1877
mfem::ND_HexahedronElement::CalcCurlShape
virtual void CalcCurlShape(const IntegrationPoint &ip, DenseMatrix &curl_shape) const
Definition: fe.cpp:10275
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:8223
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:611
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:1298
mfem::ND_HexahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1881
mfem::H1Pos_QuadrilateralElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:7233
mfem::L2_HexahedronElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:8532
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:9727
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:1925
mfem::RT_TetrahedronElement::Project
virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
Definition: fe.hpp:1834
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:2037
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:8440
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:10733
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:6802
mfem::L2_HexahedronElement::L2_HexahedronElement
L2_HexahedronElement(const int p, const int _type=0)
Definition: fe.cpp:8475
mfem::TriLinear3DFiniteElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.hpp:710
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:1732
mfem::NURBS2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:11021
mfem::RT_TriangleElement::GetLocalInterpolation
virtual void GetLocalInterpolation(ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1791
mfem::ND_TetrahedronElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1968
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:1272
mfem::ND_TetrahedronElement::Project
virtual void Project(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Definition: fe.hpp:1964
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:7000
mfem::RT_TriangleElement::ProjectGrad
virtual void ProjectGrad(const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
Definition: fe.hpp:1801
mfem::H1_QuadrilateralElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:6782
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:8511
mfem::RT_HexahedronElement::CalcVShape
virtual void CalcVShape(ElementTransformation &Trans, DenseMatrix &shape) const
Definition: fe.hpp:1747
mfem::RefinedLinear2DFiniteElement::CalcShape
virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
Definition: fe.cpp:3966
mfem::H1Pos_TriangleElement
Definition: fe.hpp:1461
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:1996
mfem::poly1d
Poly_1D poly1d
Definition: fe.cpp:6614
mfem::CrouzeixRaviartFiniteElement
Crouzeix-Raviart finite element on triangle.
Definition: fe.hpp:715
mfem::L2_QuadrilateralElement::L2_QuadrilateralElement
L2_QuadrilateralElement(const int p, const int _type=0)
Definition: fe.cpp:8268
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::H1_SegmentElement::GetDofMap
const Array< int > & GetDofMap() const
Definition: fe.hpp:1324
mfem::L2Pos_TetrahedronElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:9116
mfem::L2_QuadrilateralElement::ProjectDelta
virtual void ProjectDelta(int vertex, Vector &dofs) const
Definition: fe.cpp:8340
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:672
mfem::H1_TriangleElement::CalcDShape
virtual void CalcDShape(const IntegrationPoint &ip, DenseMatrix &dshape) const
Definition: fe.cpp:7548
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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