5#ifndef DUNE_LOCALFUNCTIONS_LAGRANGE_LAGRANGEPRISM_HH
6#define DUNE_LOCALFUNCTIONS_LAGRANGE_LAGRANGEPRISM_HH
15#include <dune/geometry/referenceelements.hh>
17#include <dune/localfunctions/common/localbasis.hh>
18#include <dune/localfunctions/common/localfiniteelementtraits.hh>
19#include <dune/localfunctions/common/localkey.hh>
21namespace Dune {
namespace Impl
32 template<
class D,
class R,
unsigned int k>
33 class LagrangePrismLocalBasis
35 static constexpr std::size_t dim = 3;
37 using Traits = LocalBasisTraits<D,dim,FieldVector<D,dim>,R,1,FieldVector<R,1>,FieldMatrix<R,1,dim> >;
41 static constexpr unsigned int size ()
48 std::vector<typename Traits::RangeType>& out)
const
61 out[0] = (1.0-in[0]-in[1])*(1.0-in[2]);
62 out[1] = in[0]*(1-in[2]);
63 out[2] = in[1]*(1-in[2]);
64 out[3] = in[2]*(1.0-in[0]-in[1]);
73 FieldVector<R,k+1> segmentShapeFunction;
74 segmentShapeFunction[0] = 1 + in[2] * (-3 + 2*in[2]);
75 segmentShapeFunction[1] = in[2] * (4 - 4*in[2]);
76 segmentShapeFunction[2] = in[2] * (-1 + 2*in[2]);
78 FieldVector<R, 6> triangleShapeFunction;
79 triangleShapeFunction[0] = 2 * (1 - in[0] - in[1]) * (0.5 - in[0] - in[1]);
80 triangleShapeFunction[1] = 2 * in[0] * (-0.5 + in[0]);
81 triangleShapeFunction[2] = 2 * in[1] * (-0.5 + in[1]);
82 triangleShapeFunction[3] = 4*in[0] * (1 - in[0] - in[1]);
83 triangleShapeFunction[4] = 4*in[1] * (1 - in[0] - in[1]);
84 triangleShapeFunction[5] = 4*in[0]*in[1];
87 out[0] = triangleShapeFunction[0] * segmentShapeFunction[0];
88 out[1] = triangleShapeFunction[1] * segmentShapeFunction[0];
89 out[2] = triangleShapeFunction[2] * segmentShapeFunction[0];
92 out[3] = triangleShapeFunction[0] * segmentShapeFunction[2];
93 out[4] = triangleShapeFunction[1] * segmentShapeFunction[2];
94 out[5] = triangleShapeFunction[2] * segmentShapeFunction[2];
97 out[6] = triangleShapeFunction[0] * segmentShapeFunction[1];
98 out[7] = triangleShapeFunction[1] * segmentShapeFunction[1];
99 out[8] = triangleShapeFunction[2] * segmentShapeFunction[1];
102 out[9] = triangleShapeFunction[3] * segmentShapeFunction[0];
103 out[10] = triangleShapeFunction[4] * segmentShapeFunction[0];
104 out[11] = triangleShapeFunction[5] * segmentShapeFunction[0];
107 out[12] = triangleShapeFunction[3] * segmentShapeFunction[2];
108 out[13] = triangleShapeFunction[4] * segmentShapeFunction[2];
109 out[14] = triangleShapeFunction[5] * segmentShapeFunction[2];
112 out[15] = triangleShapeFunction[3] * segmentShapeFunction[1];
113 out[16] = triangleShapeFunction[4] * segmentShapeFunction[1];
114 out[17] = triangleShapeFunction[5] * segmentShapeFunction[1];
119 DUNE_THROW(NotImplemented,
"LagrangePrismLocalBasis::evaluateFunction for order " << k);
128 std::vector<typename Traits::JacobianType>& out)
const
135 std::fill(out[0][0].begin(), out[0][0].end(), 0);
141 out[0][0] = {in[2]-1, in[2]-1, in[0]+in[1]-1};
142 out[1][0] = {1-in[2], 0, -in[0]};
143 out[2][0] = { 0, 1-in[2], -in[1]};
144 out[3][0] = { -in[2], -in[2], 1-in[0]-in[1]};
145 out[4][0] = { in[2], 0, in[0]};
146 out[5][0] = { 0, in[2], in[1]};
154 FieldVector<R, 6> triangleShapeFunction;
155 triangleShapeFunction[0] = 2 * (1 - in[0] - in[1]) * (0.5 - in[0] - in[1]);
156 triangleShapeFunction[1] = 2 * in[0] * (-0.5 + in[0]);
157 triangleShapeFunction[2] = 2 * in[1] * (-0.5 + in[1]);
158 triangleShapeFunction[3] = 4*in[0] * (1 - in[0] - in[1]);
159 triangleShapeFunction[4] = 4*in[1] * (1 - in[0] - in[1]);
160 triangleShapeFunction[5] = 4*in[0]*in[1];
162 std::array<std::array<R,2>,6> triangleShapeFunctionDer;
163 triangleShapeFunctionDer[0] = {-3 + 4*(in[0] + in[1]), -3 + 4*(in[0] + in[1])};
164 triangleShapeFunctionDer[1] = { -1 + 4*in[0], 0};
165 triangleShapeFunctionDer[2] = { 0, -1 + 4*in[1]};
166 triangleShapeFunctionDer[3] = { 4 - 8*in[0] - 4*in[1], -4*in[0]};
167 triangleShapeFunctionDer[4] = { -4*in[1], 4 - 4*in[0] - 8*in[1]};
168 triangleShapeFunctionDer[5] = { 4*in[1], 4*in[0]};
171 FieldVector<R,k+1> segmentShapeFunction;
172 segmentShapeFunction[0] = 1 + in[2] * (-3 + 2*in[2]);
173 segmentShapeFunction[1] = in[2] * ( 4 - 4*in[2]);
174 segmentShapeFunction[2] = in[2] * (-1 + 2*in[2]);
176 FieldVector<R,k+1> segmentShapeFunctionDer;
177 segmentShapeFunctionDer[0] = -3 + 4*in[2];
178 segmentShapeFunctionDer[1] = 4 - 8*in[2];
179 segmentShapeFunctionDer[2] = -1 + 4*in[2];
182 out[0][0][0] = triangleShapeFunctionDer[0][0] * segmentShapeFunction[0];
183 out[0][0][1] = triangleShapeFunctionDer[0][1] * segmentShapeFunction[0];
184 out[0][0][2] = triangleShapeFunction[0] * segmentShapeFunctionDer[0];
186 out[1][0][0] = triangleShapeFunctionDer[1][0] * segmentShapeFunction[0];
187 out[1][0][1] = triangleShapeFunctionDer[1][1] * segmentShapeFunction[0];
188 out[1][0][2] = triangleShapeFunction[1] * segmentShapeFunctionDer[0];
190 out[2][0][0] = triangleShapeFunctionDer[2][0] * segmentShapeFunction[0];
191 out[2][0][1] = triangleShapeFunctionDer[2][1] * segmentShapeFunction[0];
192 out[2][0][2] = triangleShapeFunction[2] * segmentShapeFunctionDer[0];
195 out[3][0][0] = triangleShapeFunctionDer[0][0] * segmentShapeFunction[2];
196 out[3][0][1] = triangleShapeFunctionDer[0][1] * segmentShapeFunction[2];
197 out[3][0][2] = triangleShapeFunction[0] * segmentShapeFunctionDer[2];
199 out[4][0][0] = triangleShapeFunctionDer[1][0] * segmentShapeFunction[2];
200 out[4][0][1] = triangleShapeFunctionDer[1][1] * segmentShapeFunction[2];
201 out[4][0][2] = triangleShapeFunction[1] * segmentShapeFunctionDer[2];
203 out[5][0][0] = triangleShapeFunctionDer[2][0] * segmentShapeFunction[2];
204 out[5][0][1] = triangleShapeFunctionDer[2][1] * segmentShapeFunction[2];
205 out[5][0][2] = triangleShapeFunction[2] * segmentShapeFunctionDer[2];
208 out[6][0][0] = triangleShapeFunctionDer[0][0] * segmentShapeFunction[1];
209 out[6][0][1] = triangleShapeFunctionDer[0][1] * segmentShapeFunction[1];
210 out[6][0][2] = triangleShapeFunction[0] * segmentShapeFunctionDer[1];
212 out[7][0][0] = triangleShapeFunctionDer[1][0] * segmentShapeFunction[1];
213 out[7][0][1] = triangleShapeFunctionDer[1][1] * segmentShapeFunction[1];
214 out[7][0][2] = triangleShapeFunction[1] * segmentShapeFunctionDer[1];
216 out[8][0][0] = triangleShapeFunctionDer[2][0] * segmentShapeFunction[1];
217 out[8][0][1] = triangleShapeFunctionDer[2][1] * segmentShapeFunction[1];
218 out[8][0][2] = triangleShapeFunction[2] * segmentShapeFunctionDer[1];
221 out[9][0][0] = triangleShapeFunctionDer[3][0] * segmentShapeFunction[0];
222 out[9][0][1] = triangleShapeFunctionDer[3][1] * segmentShapeFunction[0];
223 out[9][0][2] = triangleShapeFunction[3] * segmentShapeFunctionDer[0];
225 out[10][0][0] = triangleShapeFunctionDer[4][0] * segmentShapeFunction[0];
226 out[10][0][1] = triangleShapeFunctionDer[4][1] * segmentShapeFunction[0];
227 out[10][0][2] = triangleShapeFunction[4] * segmentShapeFunctionDer[0];
229 out[11][0][0] = triangleShapeFunctionDer[5][0] * segmentShapeFunction[0];
230 out[11][0][1] = triangleShapeFunctionDer[5][1] * segmentShapeFunction[0];
231 out[11][0][2] = triangleShapeFunction[5] * segmentShapeFunctionDer[0];
234 out[12][0][0] = triangleShapeFunctionDer[3][0] * segmentShapeFunction[2];
235 out[12][0][1] = triangleShapeFunctionDer[3][1] * segmentShapeFunction[2];
236 out[12][0][2] = triangleShapeFunction[3] * segmentShapeFunctionDer[2];
238 out[13][0][0] = triangleShapeFunctionDer[4][0] * segmentShapeFunction[2];
239 out[13][0][1] = triangleShapeFunctionDer[4][1] * segmentShapeFunction[2];
240 out[13][0][2] = triangleShapeFunction[4] * segmentShapeFunctionDer[2];
242 out[14][0][0] = triangleShapeFunctionDer[5][0] * segmentShapeFunction[2];
243 out[14][0][1] = triangleShapeFunctionDer[5][1] * segmentShapeFunction[2];
244 out[14][0][2] = triangleShapeFunction[5] * segmentShapeFunctionDer[2];
247 out[15][0][0] = triangleShapeFunctionDer[3][0] * segmentShapeFunction[1];
248 out[15][0][1] = triangleShapeFunctionDer[3][1] * segmentShapeFunction[1];
249 out[15][0][2] = triangleShapeFunction[3] * segmentShapeFunctionDer[1];
251 out[16][0][0] = triangleShapeFunctionDer[4][0] * segmentShapeFunction[1];
252 out[16][0][1] = triangleShapeFunctionDer[4][1] * segmentShapeFunction[1];
253 out[16][0][2] = triangleShapeFunction[4] * segmentShapeFunctionDer[1];
255 out[17][0][0] = triangleShapeFunctionDer[5][0] * segmentShapeFunction[1];
256 out[17][0][1] = triangleShapeFunctionDer[5][1] * segmentShapeFunction[1];
257 out[17][0][2] = triangleShapeFunction[5] * segmentShapeFunctionDer[1];
262 DUNE_THROW(NotImplemented,
"LagrangePrismLocalBasis::evaluateJacobian for order " << k);
271 void partial(
const std::array<unsigned int,dim>& order,
273 std::vector<typename Traits::RangeType>& out)
const
281 evaluateFunction(in, out);
297 auto direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
317 out[0] = in[0]+in[1]-1;
320 out[3] = 1-in[0]-in[1];
325 DUNE_THROW(RangeError,
"Component out of range.");
327 }
else if (totalOrder == 2) {
329 if (order[0] == 1 && order[2] == 1) {
336 }
else if (order[1] == 1 && order[2] == 1) {
344 for (std::size_t i = 0; i <
size(); ++i)
349 std::fill(out.begin(), out.end(), 0.0);
360 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
365 FieldVector<R,6> triangleShapeFunctionDerX;
366 triangleShapeFunctionDerX[0] = -3 + 4*(in[0] + in[1]);
367 triangleShapeFunctionDerX[1] = -1 + 4* in[0];
368 triangleShapeFunctionDerX[2] = 0;
369 triangleShapeFunctionDerX[3] = 4 - 8* in[0] - 4*in[1];
370 triangleShapeFunctionDerX[4] = -4*in[1];
371 triangleShapeFunctionDerX[5] = 4*in[1];
373 FieldVector<R,k+1> segmentShapeFunction;
374 segmentShapeFunction[0] = 1 + in[2] * (-3 + 2*in[2]);
375 segmentShapeFunction[1] = in[2] * ( 4 - 4*in[2]);
376 segmentShapeFunction[2] = in[2] * (-1 + 2*in[2]);
378 out[0] = triangleShapeFunctionDerX[0] * segmentShapeFunction[0];
379 out[1] = triangleShapeFunctionDerX[1] * segmentShapeFunction[0];
380 out[2] = triangleShapeFunctionDerX[2] * segmentShapeFunction[0];
381 out[3] = triangleShapeFunctionDerX[0] * segmentShapeFunction[2];
382 out[4] = triangleShapeFunctionDerX[1] * segmentShapeFunction[2];
383 out[5] = triangleShapeFunctionDerX[2] * segmentShapeFunction[2];
384 out[6] = triangleShapeFunctionDerX[0] * segmentShapeFunction[1];
385 out[7] = triangleShapeFunctionDerX[1] * segmentShapeFunction[1];
386 out[8] = triangleShapeFunctionDerX[2] * segmentShapeFunction[1];
387 out[9] = triangleShapeFunctionDerX[3] * segmentShapeFunction[0];
388 out[10] = triangleShapeFunctionDerX[4] * segmentShapeFunction[0];
389 out[11] = triangleShapeFunctionDerX[5] * segmentShapeFunction[0];
390 out[12] = triangleShapeFunctionDerX[3] * segmentShapeFunction[2];
391 out[13] = triangleShapeFunctionDerX[4] * segmentShapeFunction[2];
392 out[14] = triangleShapeFunctionDerX[5] * segmentShapeFunction[2];
393 out[15] = triangleShapeFunctionDerX[3] * segmentShapeFunction[1];
394 out[16] = triangleShapeFunctionDerX[4] * segmentShapeFunction[1];
395 out[17] = triangleShapeFunctionDerX[5] * segmentShapeFunction[1];
400 FieldVector<R,6> triangleShapeFunctionDerY;
401 triangleShapeFunctionDerY[0] = -3 + 4*(in[0] + in[1]);
402 triangleShapeFunctionDerY[1] = 0;
403 triangleShapeFunctionDerY[2] = -1 + 4* in[1];
404 triangleShapeFunctionDerY[3] = -4* in[0];
405 triangleShapeFunctionDerY[4] = 4 - 4* in[0] - 8*in[1];
406 triangleShapeFunctionDerY[5] = 4* in[0];
408 FieldVector<R,k+1> segmentShapeFunction;
409 segmentShapeFunction[0] = 1 + in[2] * (-3 + 2*in[2]);
410 segmentShapeFunction[1] = in[2] * ( 4 - 4*in[2]);
411 segmentShapeFunction[2] = in[2] * (-1 + 2*in[2]);
413 out[0] = triangleShapeFunctionDerY[0] * segmentShapeFunction[0];
414 out[1] = triangleShapeFunctionDerY[1] * segmentShapeFunction[0];
415 out[2] = triangleShapeFunctionDerY[2] * segmentShapeFunction[0];
416 out[3] = triangleShapeFunctionDerY[0] * segmentShapeFunction[2];
417 out[4] = triangleShapeFunctionDerY[1] * segmentShapeFunction[2];
418 out[5] = triangleShapeFunctionDerY[2] * segmentShapeFunction[2];
419 out[6] = triangleShapeFunctionDerY[0] * segmentShapeFunction[1];
420 out[7] = triangleShapeFunctionDerY[1] * segmentShapeFunction[1];
421 out[8] = triangleShapeFunctionDerY[2] * segmentShapeFunction[1];
422 out[9] = triangleShapeFunctionDerY[3] * segmentShapeFunction[0];
423 out[10] = triangleShapeFunctionDerY[4] * segmentShapeFunction[0];
424 out[11] = triangleShapeFunctionDerY[5] * segmentShapeFunction[0];
425 out[12] = triangleShapeFunctionDerY[3] * segmentShapeFunction[2];
426 out[13] = triangleShapeFunctionDerY[4] * segmentShapeFunction[2];
427 out[14] = triangleShapeFunctionDerY[5] * segmentShapeFunction[2];
428 out[15] = triangleShapeFunctionDerY[3] * segmentShapeFunction[1];
429 out[16] = triangleShapeFunctionDerY[4] * segmentShapeFunction[1];
430 out[17] = triangleShapeFunctionDerY[5] * segmentShapeFunction[1];
435 FieldVector<R, 6> triangleShapeFunction;
436 triangleShapeFunction[0] = 2 * (1 - in[0] - in[1]) * (0.5 - in[0] - in[1]);
437 triangleShapeFunction[1] = 2 * in[0] * (-0.5 + in[0]);
438 triangleShapeFunction[2] = 2 * in[1] * (-0.5 + in[1]);
439 triangleShapeFunction[3] = 4*in[0] * (1 - in[0] - in[1]);
440 triangleShapeFunction[4] = 4*in[1] * (1 - in[0] - in[1]);
441 triangleShapeFunction[5] = 4*in[0]*in[1];
443 FieldVector<R,k+1> segmentShapeFunctionDer;
444 segmentShapeFunctionDer[0] = -3 + 4*in[2];
445 segmentShapeFunctionDer[1] = 4 - 8*in[2];
446 segmentShapeFunctionDer[2] = -1 + 4*in[2];
448 out[0] = triangleShapeFunction[0] * segmentShapeFunctionDer[0];
449 out[1] = triangleShapeFunction[1] * segmentShapeFunctionDer[0];
450 out[2] = triangleShapeFunction[2] * segmentShapeFunctionDer[0];
451 out[3] = triangleShapeFunction[0] * segmentShapeFunctionDer[2];
452 out[4] = triangleShapeFunction[1] * segmentShapeFunctionDer[2];
453 out[5] = triangleShapeFunction[2] * segmentShapeFunctionDer[2];
454 out[6] = triangleShapeFunction[0] * segmentShapeFunctionDer[1];
455 out[7] = triangleShapeFunction[1] * segmentShapeFunctionDer[1];
456 out[8] = triangleShapeFunction[2] * segmentShapeFunctionDer[1];
457 out[9] = triangleShapeFunction[3] * segmentShapeFunctionDer[0];
458 out[10] = triangleShapeFunction[4] * segmentShapeFunctionDer[0];
459 out[11] = triangleShapeFunction[5] * segmentShapeFunctionDer[0];
460 out[12] = triangleShapeFunction[3] * segmentShapeFunctionDer[2];
461 out[13] = triangleShapeFunction[4] * segmentShapeFunctionDer[2];
462 out[14] = triangleShapeFunction[5] * segmentShapeFunctionDer[2];
463 out[15] = triangleShapeFunction[3] * segmentShapeFunctionDer[1];
464 out[16] = triangleShapeFunction[4] * segmentShapeFunctionDer[1];
465 out[17] = triangleShapeFunction[5] * segmentShapeFunctionDer[1];
469 DUNE_THROW(RangeError,
"Component out of range.");
472 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
478 DUNE_THROW(NotImplemented,
"LagrangePrismLocalBasis::partial not implemented for order " << k);
482 static constexpr unsigned int order ()
492 template<
unsigned int k>
493 class LagrangePrismLocalCoefficients
497 LagrangePrismLocalCoefficients ()
502 localKeys_[0] = LocalKey(0,0,0);
508 for (std::size_t i=0; i<
size(); i++)
509 localKeys_[i] = LocalKey(i,3,0);
516 localKeys_[0] = LocalKey(0,3,0);
517 localKeys_[1] = LocalKey(1,3,0);
518 localKeys_[2] = LocalKey(2,3,0);
519 localKeys_[3] = LocalKey(3,3,0);
520 localKeys_[4] = LocalKey(4,3,0);
521 localKeys_[5] = LocalKey(5,3,0);
524 localKeys_[6] = LocalKey(0,2,0);
525 localKeys_[7] = LocalKey(1,2,0);
526 localKeys_[8] = LocalKey(2,2,0);
527 localKeys_[9] = LocalKey(3,2,0);
528 localKeys_[10] = LocalKey(4,2,0);
529 localKeys_[11] = LocalKey(5,2,0);
530 localKeys_[12] = LocalKey(6,2,0);
531 localKeys_[13] = LocalKey(7,2,0);
532 localKeys_[14] = LocalKey(8,2,0);
535 localKeys_[15] = LocalKey(0,1,0);
536 localKeys_[16] = LocalKey(1,1,0);
537 localKeys_[17] = LocalKey(2,1,0);
543 DUNE_THROW(NotImplemented,
"LagrangePrismLocalCoefficients not implemented for order " << k);
548 static constexpr std::size_t
size ()
554 const LocalKey& localKey (std::size_t i)
const
556 return localKeys_[i];
560 std::vector<LocalKey> localKeys_;
567 template<
class LocalBasis>
568 class LagrangePrismLocalInterpolation
579 template<
typename F,
typename C>
580 void interpolate (
const F& f, std::vector<C>& out)
const
582 constexpr auto dim = LocalBasis::Traits::dimDomain;
583 constexpr auto k = LocalBasis::order();
584 using D =
typename LocalBasis::Traits::DomainType;
585 using DF =
typename LocalBasis::Traits::DomainFieldType;
587 out.resize(LocalBasis::size());
600 for (
unsigned int i=0; i<LocalBasis::size(); i++)
610 out[0] = f( D( {0.0, 0.0, 0.0} ) );
611 out[1] = f( D( {1.0, 0.0, 0.0} ) );
612 out[2] = f( D( {0.0, 1.0, 0.0} ) );
613 out[3] = f( D( {0.0, 0.0, 1.0} ) );
614 out[4] = f( D( {1.0, 0.0, 1.0} ) );
615 out[5] = f( D( {0.0, 1.0, 1.0} ) );
616 out[6] = f( D( {0.0, 0.0, 0.5} ) );
617 out[7] = f( D( {1.0, 0.0, 0.5} ) );
618 out[8] = f( D( {0.0, 1.0, 0.5} ) );
619 out[9] = f( D( {0.5, 0.0, 0.0} ) );
620 out[10] = f( D( {0.0, 0.5, 0.0} ) );
621 out[11] = f( D( {0.5, 0.5, 0.0} ) );
622 out[12] = f( D( {0.5, 0.0, 1.0} ) );
623 out[13] = f( D( {0.0, 0.5, 1.0} ) );
624 out[14] = f( D( {0.5, 0.5, 1.0} ) );
625 out[15] = f( D( {0.5, 0.0, 0.5} ) );
626 out[16] = f( D( {0.0, 0.5, 0.5} ) );
627 out[17] = f( D( {0.5, 0.5, 0.5} ) );
632 DUNE_THROW(NotImplemented,
"LagrangePrismLocalInterpolation not implemented for order " << k);
647 template<
class D,
class R,
int k>
654 Impl::LagrangePrismLocalCoefficients<k>,
655 Impl::LagrangePrismLocalInterpolation<Impl::LagrangePrismLocalBasis<D,R,k> > >;
668 return coefficients_;
675 return interpolation_;
679 static constexpr std::size_t
size ()
692 Impl::LagrangePrismLocalBasis<D,R,k> basis_;
693 Impl::LagrangePrismLocalCoefficients<k> coefficients_;
694 Impl::LagrangePrismLocalInterpolation<Impl::LagrangePrismLocalBasis<D,R,k> > interpolation_;
Unique label for each type of entities that can occur in DUNE grids.
Definition: type.hh:114
Lagrange finite element for 3d prisms with arbitrary compile-time polynomial order.
Definition: lagrangeprism.hh:649
static constexpr std::size_t size()
The number of shape functions.
Definition: lagrangeprism.hh:679
const Traits::LocalInterpolationType & localInterpolation() const
Returns object that evaluates degrees of freedom.
Definition: lagrangeprism.hh:673
static constexpr GeometryType type()
The reference element that the local finite element is defined on.
Definition: lagrangeprism.hh:686
const Traits::LocalCoefficientsType & localCoefficients() const
Returns the assignment of the degrees of freedom to the element subentities.
Definition: lagrangeprism.hh:666
const Traits::LocalBasisType & localBasis() const
Returns the local basis, i.e., the set of shape functions.
Definition: lagrangeprism.hh:659
Implements a matrix constructed from a given type representing a field and compile-time given number ...
Implements a vector constructed from a given type representing a field and a compile-time given size.
static void interpolate(const GridFunction &u, DiscreteFunction &v)
perform native interpolation of a discrete function space
Definition: interpolate.hh:54
#define DUNE_THROW(E, m)
Definition: exceptions.hh:218
constexpr GeometryType prism
GeometryType representing a 3D prism.
Definition: type.hh:528
constexpr GeometryType vertex
GeometryType representing a vertex.
Definition: type.hh:492
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:279
Some useful basic math stuff.
Dune namespace.
Definition: alignedallocator.hh:13
constexpr std::integral_constant< std::size_t, sizeof...(II)> size(std::integer_sequence< T, II... >)
Return the size of the sequence.
Definition: integersequence.hh:75
static constexpr T binomial(const T &n, const T &k) noexcept
calculate the binomial coefficient n over k as a constexpr
Definition: math.hh:131
static const ReferenceElement & general(const GeometryType &type)
get general reference elements
Definition: referenceelements.hh:156
D DomainType
domain type
Definition: localbasis.hh:43
traits helper struct
Definition: localfiniteelementtraits.hh:13
LB LocalBasisType
Definition: localfiniteelementtraits.hh:16
LC LocalCoefficientsType
Definition: localfiniteelementtraits.hh:20
LI LocalInterpolationType
Definition: localfiniteelementtraits.hh:24