Dune Core Modules (2.4.2)

quadraturerules.hh
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1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3
4#ifndef DUNE_GEOMETRY_QUADRATURERULES_HH
5#define DUNE_GEOMETRY_QUADRATURERULES_HH
6
7#include <algorithm>
8#include <iostream>
9#include <limits>
10#include <mutex>
11#include <utility>
12#include <vector>
13
17#include <dune/common/stdthread.hh>
19
20#include <dune/geometry/quadraturerules/nocopyvector.hh>
21#include <dune/geometry/type.hh>
23
29namespace Dune {
30
36
42 template<typename ct, int dim>
44 public:
46 enum { dimension = dim };
47
49 typedef ct Field;
50
53
55 QuadraturePoint (const Vector& x, ct w) : local(x)
56 {
57 weight_ = w;
58 }
59
61 const Vector& position () const
62 {
63 return local;
64 }
65
67 const ct &weight () const
68 {
69 return weight_;
70 }
71
72 protected:
74 ct weight_;
75 };
76
80 namespace QuadratureType {
81 enum Enum {
82 GaussLegendre = 0,
83
84 GaussJacobi_1_0 = 1,
85 GaussJacobi_2_0 = 2,
86
87 GaussLobatto = 4,
88 size
89 };
90 }
91
95 template<typename ct, int dim>
96 class QuadratureRule : public std::vector<QuadraturePoint<ct,dim> >
97 {
98 public:
104 QuadratureRule() : delivered_order(-1) {}
105
106 protected:
108 QuadratureRule(GeometryType t) : geometry_type(t), delivered_order(-1) {}
109
111 QuadratureRule(GeometryType t, int order) : geometry_type(t), delivered_order(order) {}
112 public:
114 enum { d=dim };
115
117 typedef ct CoordType;
118
120 virtual int order () const { return delivered_order; }
121
123 virtual GeometryType type () const { return geometry_type; }
124 virtual ~QuadratureRule(){}
125
128 typedef typename std::vector<QuadraturePoint<ct,dim> >::const_iterator iterator;
129
130 protected:
131 GeometryType geometry_type;
132 int delivered_order;
133 };
134
135 // Forward declaration of the factory class,
136 // needed internally by the QuadratureRules container class.
137 template<typename ctype, int dim> class QuadratureRuleFactory;
138
142 template<typename ctype, int dim>
144
149 static void initQuadratureRule(QuadratureRule *qr, QuadratureType::Enum qt,
150 const GeometryType &t, int p)
151 {
153 }
154
155 typedef NoCopyVector<std::pair<std::once_flag, QuadratureRule> >
156 QuadratureOrderVector; // indexed by quadrature order
159 static void initQuadratureOrderVector(QuadratureOrderVector *qov,
160 QuadratureType::Enum qt,
161 const GeometryType &t)
162 {
163 if(dim == 0)
164 // we only need one quadrature rule for points, not maxint
165 qov->resize(1);
166 else
168 }
169
170 typedef NoCopyVector<std::pair<std::once_flag, QuadratureOrderVector> >
171 GeometryTypeVector; // indexed by geometry type
174 static void initGeometryTypeVector(GeometryTypeVector *gtv)
175 {
176 gtv->resize(LocalGeometryTypeIndex::size(dim));
177 }
178
180 DUNE_EXPORT const QuadratureRule& _rule(const GeometryType& t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
181 {
182 assert(t.dim()==dim);
183
184 DUNE_ASSERT_CALL_ONCE();
185
186 static NoCopyVector<std::pair< // indexed by quadrature type
187 std::once_flag,
188 GeometryTypeVector
189 > > quadratureCache(QuadratureType::size);
190
191 auto & quadratureTypeLevel = quadratureCache[qt];
192 std::call_once(quadratureTypeLevel.first, initGeometryTypeVector,
193 &quadratureTypeLevel.second);
194
195 auto & geometryTypeLevel =
196 quadratureTypeLevel.second[LocalGeometryTypeIndex::index(t)];
197 std::call_once(geometryTypeLevel.first, initQuadratureOrderVector,
198 &geometryTypeLevel.second, qt, t);
199
200 // we only have one quadrature rule for points
201 auto & quadratureOrderLevel = geometryTypeLevel.second[dim == 0 ? 0 : p];
202 std::call_once(quadratureOrderLevel.first, initQuadratureRule,
203 &quadratureOrderLevel.second, qt, t, p);
204
205 return quadratureOrderLevel.second;
206 }
208 DUNE_EXPORT static QuadratureRules& instance()
209 {
210 static QuadratureRules instance;
211 return instance;
212 }
214 QuadratureRules () {}
215 public:
217 static unsigned
219 QuadratureType::Enum qt=QuadratureType::GaussLegendre)
220 {
222 }
223
225 static const QuadratureRule& rule(const GeometryType& t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
226 {
227 return instance()._rule(t,p,qt);
228 }
230 static const QuadratureRule& rule(const GeometryType::BasicType t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
231 {
232 GeometryType gt(t,dim);
233 return instance()._rule(gt,p,qt);
234 }
235 };
236
237} // end namespace Dune
238
239#include "quadraturerules/pointquadrature.hh"
240
241namespace Dune {
242
244 template<typename ct, bool fundamental = std::numeric_limits<ct>::is_specialized>
246 template<typename ct>
247 struct GaussQuadratureInitHelper<ct, true> {
248 static void init(int p,
249 std::vector< FieldVector<ct, 1> > & _points,
250 std::vector< ct > & _weight,
251 int & delivered_order);
252 };
253 template<typename ct>
254 struct GaussQuadratureInitHelper<ct, false> {
255 static void init(int p,
256 std::vector< FieldVector<ct, 1> > & _points,
257 std::vector< ct > & _weight,
258 int & delivered_order);
259 };
260
262 template<typename ct>
264 public QuadratureRule<ct,1>
265 {
266 public:
267 // compile time parameters
268 enum { dim=1 };
269 enum { highest_order=61 };
270
272 private:
273 friend class QuadratureRuleFactory<ct,dim>;
276 {
278 std::vector< FieldVector<ct, dim> > _points;
279 std::vector< ct > _weight;
280
282 (p, _points, _weight, this->delivered_order);
283
284 assert(_points.size() == _weight.size());
285 for (size_t i = 0; i < _points.size(); i++)
286 this->push_back(QuadraturePoint<ct,dim>(_points[i], _weight[i]));
287 }
288 };
289
292
293} // namespace Dune
294
295#define DUNE_INCLUDING_IMPLEMENTATION
296#include "quadraturerules/gauss_imp.hh"
297
298namespace Dune {
299
301 template<typename ct,
302 bool fundamental = std::numeric_limits<ct>::is_specialized>
304 template<typename ct>
305 struct Jacobi1QuadratureInitHelper<ct, true> {
306 static void init(int p,
307 std::vector< FieldVector<ct, 1> > & _points,
308 std::vector< ct > & _weight,
309 int & delivered_order);
310 };
311 template<typename ct>
312 struct Jacobi1QuadratureInitHelper<ct, false> {
313 static void init(int p,
314 std::vector< FieldVector<ct, 1> > & _points,
315 std::vector< ct > & _weight,
316 int & delivered_order);
317 };
318
322 template<typename ct>
324 public QuadratureRule<ct,1>
325 {
326 public:
328 enum { dim=1 };
329
331 enum { highest_order=61 };
332
334 private:
335 friend class QuadratureRuleFactory<ct,dim>;
337 : QuadratureRule<ct,1>(GeometryType(GeometryType::cube, 1))
338 {
340 std::vector< FieldVector<ct, dim> > _points;
341 std::vector< ct > _weight;
342
343 int delivered_order;
344
346 (p, _points, _weight, delivered_order);
347 this->delivered_order = delivered_order;
348 assert(_points.size() == _weight.size());
349 for (size_t i = 0; i < _points.size(); i++)
350 this->push_back(QuadraturePoint<ct,dim>(_points[i], _weight[i]));
351 }
352 };
353
354#ifndef DOXYGEN
357#endif // !DOXYGEN
358
359} // namespace Dune
360
361#define DUNE_INCLUDING_IMPLEMENTATION
362#include "quadraturerules/jacobi_1_0_imp.hh"
363
364namespace Dune {
365
367 template<typename ct,
368 bool fundamental = std::numeric_limits<ct>::is_specialized>
370 template<typename ct>
371 struct Jacobi2QuadratureInitHelper<ct, true> {
372 static void init(int p,
373 std::vector< FieldVector<ct, 1> > & _points,
374 std::vector< ct > & _weight,
375 int & delivered_order);
376 };
377 template<typename ct>
378 struct Jacobi2QuadratureInitHelper<ct, false> {
379 static void init(int p,
380 std::vector< FieldVector<ct, 1> > & _points,
381 std::vector< ct > & _weight,
382 int & delivered_order);
383 };
384
388 template<typename ct>
390 public QuadratureRule<ct,1>
391 {
392 public:
394 enum { dim=1 };
395
397 enum { highest_order=61 };
398
400 private:
401 friend class QuadratureRuleFactory<ct,dim>;
403 : QuadratureRule<ct,1>(GeometryType(GeometryType::cube, 1))
404 {
406 std::vector< FieldVector<ct, dim> > _points;
407 std::vector< ct > _weight;
408
409 int delivered_order;
410
412 (p, _points, _weight, delivered_order);
413
414 this->delivered_order = delivered_order;
415 assert(_points.size() == _weight.size());
416 for (size_t i = 0; i < _points.size(); i++)
417 this->push_back(QuadraturePoint<ct,dim>(_points[i], _weight[i]));
418 }
419 };
420
421#ifndef DOXYGEN
424#endif // !DOXYGEN
425
426} // namespace Dune
427
428#define DUNE_INCLUDING_IMPLEMENTATION
429#include "quadraturerules/jacobi_2_0_imp.hh"
430
431namespace Dune {
432
434 template<typename ct,
435 bool fundamental = std::numeric_limits<ct>::is_specialized>
437 template<typename ct>
438 struct GaussLobattoQuadratureInitHelper<ct, true> {
439 static void init(int p,
440 std::vector< FieldVector<ct, 1> > & _points,
441 std::vector< ct > & _weight,
442 int & delivered_order);
443 };
444 template<typename ct>
445 struct GaussLobattoQuadratureInitHelper<ct, false> {
446 static void init(int p,
447 std::vector< FieldVector<ct, 1> > & _points,
448 std::vector< ct > & _weight,
449 int & delivered_order);
450 };
451
455 template<typename ct>
457 public QuadratureRule<ct,1>
458 {
459 public:
461 enum { dim=1 };
462
464 enum { highest_order=31 };
465
467 private:
468 friend class QuadratureRuleFactory<ct,dim>;
470 : QuadratureRule<ct,1>(GeometryType(GeometryType::cube, 1))
471 {
473 std::vector< FieldVector<ct, dim> > _points;
474 std::vector< ct > _weight;
475
476 int delivered_order;
477
479 (p, _points, _weight, delivered_order);
480
481 this->delivered_order = delivered_order;
482 assert(_points.size() == _weight.size());
483 for (size_t i = 0; i < _points.size(); i++)
484 this->push_back(QuadraturePoint<ct,dim>(_points[i], _weight[i]));
485 }
486 };
487
488#ifndef DOXYGEN
491#endif // !DOXYGEN
492
493} // namespace Dune
494
495#define DUNE_INCLUDING_IMPLEMENTATION
496#include "quadraturerules/gausslobatto_imp.hh"
497
498#include "quadraturerules/tensorproductquadrature.hh"
499
500#include "quadraturerules/simplexquadrature.hh"
501
502namespace Dune {
503
504 /***********************************
505 * quadrature for Prism
506 **********************************/
507
509 template<int dim>
511
513 template<>
515 {
516 public:
517 enum { MAXP=6};
518 enum { highest_order=2 };
519
522 {
523 int m = 0;
524 O[m] = 0;
525
526 // polynom degree 0 ???
527 m = 6;
528 G[m][0][0] = 0.0;
529 G[m][0][1] = 0.0;
530 G[m][0][2] = 0.0;
531
532 G[m][1][0] = 1.0;
533 G[m][1][1] = 0.0;
534 G[m][1][2] = 0.0;
535
536 G[m][2][0] = 0.0;
537 G[m][2][1] = 1.0;
538 G[m][2][2] = 0.0;
539
540 G[m][3][0] = 0.0;
541 G[m][3][1] = 0.0;
542 G[m][3][2] = 1.0;
543
544 G[m][4][0] = 1.0;
545 G[m][4][1] = 0.0;
546 G[m][4][2] = 1.0;
547
548 G[m][5][0] = 0.0;
549 G[m][5][1] = 0.1;
550 G[m][5][2] = 1.0;
551
552 W[m][0] = 0.16666666666666666 / 2.0;
553 W[m][1] = 0.16666666666666666 / 2.0;
554 W[m][2] = 0.16666666666666666 / 2.0;
555 W[m][3] = 0.16666666666666666 / 2.0;
556 W[m][4] = 0.16666666666666666 / 2.0;
557 W[m][5] = 0.16666666666666666 / 2.0;
558
559 O[m] = 0; // verify ????????
560
561
562 // polynom degree 2 ???
563 m = 6;
564 G[m][0][0] =0.66666666666666666 ;
565 G[m][0][1] =0.16666666666666666 ;
566 G[m][0][2] =0.211324865405187 ;
567
568 G[m][1][0] = 0.16666666666666666;
569 G[m][1][1] =0.66666666666666666 ;
570 G[m][1][2] = 0.211324865405187;
571
572 G[m][2][0] = 0.16666666666666666;
573 G[m][2][1] = 0.16666666666666666;
574 G[m][2][2] = 0.211324865405187;
575
576 G[m][3][0] = 0.66666666666666666;
577 G[m][3][1] = 0.16666666666666666;
578 G[m][3][2] = 0.788675134594813;
579
580 G[m][4][0] = 0.16666666666666666;
581 G[m][4][1] = 0.66666666666666666;
582 G[m][4][2] = 0.788675134594813;
583
584 G[m][5][0] = 0.16666666666666666;
585 G[m][5][1] = 0.16666666666666666;
586 G[m][5][2] = 0.788675134594813;
587
588 W[m][0] = 0.16666666666666666 / 2.0;
589 W[m][1] = 0.16666666666666666 / 2.0;
590 W[m][2] = 0.16666666666666666 / 2.0;
591 W[m][3] = 0.16666666666666666 / 2.0;
592 W[m][4] = 0.16666666666666666 / 2.0;
593 W[m][5] = 0.16666666666666666 / 2.0;
594
595 O[m] = 2; // verify ????????
596
597 }
598
601 {
602 return G[m][i];
603 }
604
606 double weight (int m, int i)
607 {
608 return W[m][i];
609 }
610
612 int order (int m)
613 {
614 return O[m];
615 }
616
617 private:
618 FieldVector<double, 3> G[MAXP+1][MAXP]; //positions
619
620 double W[MAXP+1][MAXP]; // weights associated with points
621 int O[MAXP+1]; // order of the rule
622 };
623
624
628 template<int dim>
630 static PrismQuadraturePoints<3> prqp;
631 };
632
636 template<>
638 static PrismQuadraturePoints<3> prqp;
639 };
640
644 template<typename ct, int dim>
646
650 template<typename ct>
652 {
653 public:
654
656 enum { d = 3 };
657
659 enum { highest_order = 2 };
660
662 private:
663 friend class QuadratureRuleFactory<ct,d>;
664 PrismQuadratureRule(int p) : QuadratureRule<ct,3>(GeometryType(GeometryType::prism, d))
665 {
666 int m=6;
667 this->delivered_order = PrismQuadraturePointsSingleton<3>::prqp.order(m);
668 for(int i=0; i<m; ++i)
669 {
670 FieldVector<ct,3> local;
671 for (int k=0; k<d; k++)
672 local[k] = PrismQuadraturePointsSingleton<3>::prqp.point(m,i)[k];
673 double weight =
675 // put in container
676 this->push_back(QuadraturePoint<ct,d>(local,weight));
677 }
678 }
679 };
680
687 template<typename ctype, int dim>
689 private:
690 friend class QuadratureRules<ctype, dim>;
691 static unsigned maxOrder(const GeometryType &t, QuadratureType::Enum qt)
692 {
693 return TensorProductQuadratureRule<ctype,dim>::maxOrder(t.id(), qt);
694 }
695 static QuadratureRule<ctype, dim> rule(const GeometryType& t, int p, QuadratureType::Enum qt)
696 {
697 return TensorProductQuadratureRule<ctype,dim>(t.id(), p, qt);
698 }
699 };
700
701 template<typename ctype>
703 private:
704 enum { dim = 0 };
705 friend class QuadratureRules<ctype, dim>;
706 static unsigned maxOrder(const GeometryType &t, QuadratureType::Enum qt)
707 {
708 if (t.isVertex())
709 {
710 return std::numeric_limits<int>::max();
711 }
712 DUNE_THROW(Exception, "Unknown GeometryType");
713 }
714 static QuadratureRule<ctype, dim> rule(const GeometryType& t, int p, QuadratureType::Enum qt)
715 {
716 if (t.isVertex())
717 {
718 return PointQuadratureRule<ctype>();
719 }
720 DUNE_THROW(Exception, "Unknown GeometryType");
721 }
722 };
723
724 template<typename ctype>
725 class QuadratureRuleFactory<ctype, 1> {
726 private:
727 enum { dim = 1 };
728 friend class QuadratureRules<ctype, dim>;
729 static unsigned maxOrder(const GeometryType &t, QuadratureType::Enum qt)
730 {
731 if (t.isLine())
732 {
733 switch (qt) {
734 case QuadratureType::GaussLegendre :
735 return GaussQuadratureRule1D<ctype>::highest_order;
736 case QuadratureType::GaussJacobi_1_0 :
737 return Jacobi1QuadratureRule1D<ctype>::highest_order;
738 case QuadratureType::GaussJacobi_2_0 :
739 return Jacobi2QuadratureRule1D<ctype>::highest_order;
740 case QuadratureType::GaussLobatto :
741 return GaussLobattoQuadratureRule1D<ctype>::highest_order;
742 default :
743 DUNE_THROW(Exception, "Unknown QuadratureType");
744 }
745 }
746 DUNE_THROW(Exception, "Unknown GeometryType");
747 }
748 static QuadratureRule<ctype, dim> rule(const GeometryType& t, int p, QuadratureType::Enum qt)
749 {
750 if (t.isLine())
751 {
752 switch (qt) {
753 case QuadratureType::GaussLegendre :
754 return GaussQuadratureRule1D<ctype>(p);
755 case QuadratureType::GaussJacobi_1_0 :
756 return Jacobi1QuadratureRule1D<ctype>(p);
757 case QuadratureType::GaussJacobi_2_0 :
758 return Jacobi2QuadratureRule1D<ctype>(p);
759 case QuadratureType::GaussLobatto :
760 return GaussLobattoQuadratureRule1D<ctype>(p);
761 default :
762 DUNE_THROW(Exception, "Unknown QuadratureType");
763 }
764 }
765 DUNE_THROW(Exception, "Unknown GeometryType");
766 }
767 };
768
769 template<typename ctype>
770 class QuadratureRuleFactory<ctype, 2> {
771 private:
772 enum { dim = 2 };
773 friend class QuadratureRules<ctype, dim>;
774 static unsigned maxOrder(const GeometryType &t, QuadratureType::Enum qt)
775 {
776 unsigned order =
777 TensorProductQuadratureRule<ctype,dim>::maxOrder(t.id(), qt);
778 if (t.isSimplex())
779 order = std::max
780 (order, unsigned(SimplexQuadratureRule<ctype,dim>::highest_order));
781 return order;
782 }
783 static QuadratureRule<ctype, dim> rule(const GeometryType& t, int p, QuadratureType::Enum qt)
784 {
785 if (t.isSimplex()
786 && qt == QuadratureType::GaussLegendre
787 && p <= SimplexQuadratureRule<ctype,dim>::highest_order)
788 {
789 return SimplexQuadratureRule<ctype,dim>(p);
790 }
791 return TensorProductQuadratureRule<ctype,dim>(t.id(), p, qt);
792 }
793 };
794
795 template<typename ctype>
796 class QuadratureRuleFactory<ctype, 3> {
797 private:
798 enum { dim = 3 };
799 friend class QuadratureRules<ctype, dim>;
800 static unsigned maxOrder(const GeometryType &t, QuadratureType::Enum qt)
801 {
802 unsigned order =
803 TensorProductQuadratureRule<ctype,dim>::maxOrder(t.id(), qt);
804 if (t.isSimplex())
805 order = std::max
806 (order, unsigned(SimplexQuadratureRule<ctype,dim>::highest_order));
807 if (t.isPrism())
808 order = std::max
809 (order, unsigned(PrismQuadratureRule<ctype,dim>::highest_order));
810 return order;
811 }
812 static QuadratureRule<ctype, dim> rule(const GeometryType& t, int p, QuadratureType::Enum qt)
813 {
814 if (t.isSimplex()
815 && qt == QuadratureType::GaussLegendre
816 && p <= SimplexQuadratureRule<ctype,dim>::highest_order)
817 {
818 return SimplexQuadratureRule<ctype,dim>(p);
819 }
820 if (t.isPrism()
821 && qt == QuadratureType::GaussLegendre
822 && p <= PrismQuadratureRule<ctype,dim>::highest_order)
823 {
824 return PrismQuadratureRule<ctype,dim>(p);
825 }
826 return TensorProductQuadratureRule<ctype,dim>(t.id(), p, qt);
827 }
828 };
829
830} // end namespace
831
832#endif // DUNE_GEOMETRY_QUADRATURERULES_HH
Jacobi-Gauss quadrature for alpha=2, beta=0.
Definition: quadraturerules.hh:458
Gauss quadrature rule in 1D.
Definition: quadraturerules.hh:265
Unique label for each type of entities that can occur in DUNE grids.
Definition: type.hh:25
BasicType
Each entity can be tagged by one of these basic types plus its space dimension.
Definition: type.hh:29
@ cube
Cube element in any nonnegative dimension.
Definition: type.hh:31
Jacobi-Gauss quadrature for alpha=1, beta=0.
Definition: quadraturerules.hh:325
Jacobi-Gauss quadrature for alpha=2, beta=0.
Definition: quadraturerules.hh:391
static DUNE_CONSTEXPR std::size_t size(std::size_t dim)
Compute total number of geometry types for the given dimension.
Definition: typeindex.hh:58
static std::size_t index(const GeometryType &gt)
Compute the index for the given geometry type within its dimension.
Definition: typeindex.hh:70
Default exception for dummy implementations.
Definition: exceptions.hh:288
Definition: quadraturerules.hh:515
double weight(int m, int i)
Definition: quadraturerules.hh:606
int order(int m)
Definition: quadraturerules.hh:612
PrismQuadraturePoints()
initialize quadrature points on the interval for all orders
Definition: quadraturerules.hh:521
FieldVector< double, 3 > point(int m, int i)
Definition: quadraturerules.hh:600
Definition: quadraturerules.hh:510
Quadrature rules for prisms.
Definition: quadraturerules.hh:652
Quadrature rules for prisms.
Definition: quadraturerules.hh:645
Exception thrown if a desired QuadratureRule is not available, because the requested order is to high...
Definition: quadraturerules.hh:35
Single evaluation point in a quadrature rule.
Definition: quadraturerules.hh:43
const Vector & position() const
return local coordinates of integration point i
Definition: quadraturerules.hh:61
Dune::FieldVector< ct, dim > Vector
Type used for the position of a quadrature point.
Definition: quadraturerules.hh:52
ct Field
Number type used for coordinates and quadrature weights.
Definition: quadraturerules.hh:49
const ct & weight() const
return weight associated with integration point i
Definition: quadraturerules.hh:67
QuadraturePoint(const Vector &x, ct w)
set up quadrature of given order in d dimensions
Definition: quadraturerules.hh:55
Factory class for creation of quadrature rules, depending on GeometryType, order and QuadratureType.
Definition: quadraturerules.hh:688
Abstract base class for quadrature rules.
Definition: quadraturerules.hh:97
virtual GeometryType type() const
return type of element
Definition: quadraturerules.hh:123
QuadratureRule(GeometryType t, int order)
Constructor for a given geometry type and a given quadrature order.
Definition: quadraturerules.hh:111
ct CoordType
The type used for coordinates.
Definition: quadraturerules.hh:117
QuadratureRule()
Default constructor.
Definition: quadraturerules.hh:104
virtual int order() const
return order
Definition: quadraturerules.hh:120
QuadratureRule(GeometryType t)
Constructor for a given geometry type. Leaves the quadrature order invalid
Definition: quadraturerules.hh:108
std::vector< QuadraturePoint< ct, dim > >::const_iterator iterator
Definition: quadraturerules.hh:128
A container for all quadrature rules of dimension dim
Definition: quadraturerules.hh:143
static unsigned maxOrder(const GeometryType &t, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
maximum quadrature order for given geometry type and quadrature type
Definition: quadraturerules.hh:218
static const QuadratureRule & rule(const GeometryType::BasicType t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:230
static const QuadratureRule & rule(const GeometryType &t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:225
A few common exception classes.
Implements a vector constructed from a given type representing a field and a compile-time given size.
#define DUNE_THROW(E, m)
Definition: exceptions.hh:243
bool gt(const T &first, const T &second, typename EpsilonType< T >::Type epsilon)
test if first greater than second
Definition: float_cmp.cc:132
Dune namespace.
Definition: alignment.hh:10
Standard Dune debug streams.
Definition: quadraturerules.hh:436
Definition: quadraturerules.hh:245
Definition: quadraturerules.hh:303
Definition: quadraturerules.hh:369
Singleton holding the Prism Quadrature points.
Definition: quadraturerules.hh:637
Singleton holding the Prism Quadrature points.
Definition: quadraturerules.hh:629
A unique label for each type of element that can occur in a grid.
Helper classes to provide indices for geometrytypes for use in a vector.
Definition of macros controlling symbol visibility at the ABI level.
#define DUNE_EXPORT
Export a symbol as part of the public ABI.
Definition: visibility.hh:18
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