16 #ifndef __INTREPID2_HDIV_HEX_IN_FEM_DEF_HPP__
17 #define __INTREPID2_HDIV_HEX_IN_FEM_DEF_HPP__
24 template<EOperator OpType>
25 template<
typename OutputViewType,
26 typename InputViewType,
27 typename WorkViewType,
28 typename VinvViewType>
29 KOKKOS_INLINE_FUNCTION
31 Basis_HDIV_HEX_In_FEM::Serial<OpType>::
32 getValues( OutputViewType output,
33 const InputViewType input,
35 const VinvViewType vinvLine,
36 const VinvViewType vinvBubble) {
37 const ordinal_type cardLine = vinvLine.extent(0);
38 const ordinal_type cardBubble = vinvBubble.extent(0);
40 const ordinal_type npts = input.extent(0);
42 typedef Kokkos::pair<ordinal_type,ordinal_type> range_type;
43 const auto input_x = Kokkos::subview(input, Kokkos::ALL(), range_type(0,1));
44 const auto input_y = Kokkos::subview(input, Kokkos::ALL(), range_type(1,2));
45 const auto input_z = Kokkos::subview(input, Kokkos::ALL(), range_type(2,3));
47 const ordinal_type dim_s = get_dimension_scalar(input);
48 auto ptr0 = work.data();
49 auto ptr1 = work.data()+cardLine*npts*dim_s;
50 auto ptr2 = work.data()+2*cardLine*npts*dim_s;
51 auto ptr3 = work.data()+(2*cardLine+cardBubble)*npts*dim_s;
53 typedef typename Kokkos::DynRankView<typename InputViewType::value_type, typename WorkViewType::memory_space> ViewType;
54 auto vcprop = Kokkos::common_view_alloc_prop(input);
57 case OPERATOR_VALUE: {
58 ViewType workLine(Kokkos::view_wrap(ptr0, vcprop), cardLine, npts);
59 ViewType outputLine(Kokkos::view_wrap(ptr1, vcprop), cardLine, npts);
60 ViewType outputBubble_A(Kokkos::view_wrap(ptr2, vcprop), cardBubble, npts);
61 ViewType outputBubble_B(Kokkos::view_wrap(ptr3, vcprop), cardBubble, npts);
66 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
67 getValues(outputLine, input_x, workLine, vinvLine);
69 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
70 getValues(outputBubble_A, input_y, workLine, vinvBubble);
72 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
73 getValues(outputBubble_B, input_z, workLine, vinvBubble);
77 const auto output_x = outputLine;
78 const auto output_y = outputBubble_A;
79 const auto output_z = outputBubble_B;
81 for (ordinal_type k=0;k<cardBubble;++k)
82 for (ordinal_type j=0;j<cardBubble;++j)
83 for (ordinal_type i=0;i<cardLine;++i,++idx)
84 for (ordinal_type l=0;l<npts;++l) {
85 output.access(idx,l,0) = output_x.access(i,l)*output_y.access(j,l)*output_z.access(k,l);
86 output.access(idx,l,1) = 0.0;
87 output.access(idx,l,2) = 0.0;
91 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
92 getValues(outputBubble_A, input_x, workLine, vinvBubble);
94 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
95 getValues(outputLine, input_y, workLine, vinvLine);
101 const auto output_x = outputBubble_A;
102 const auto output_y = outputLine;
103 const auto output_z = outputBubble_B;
105 for (ordinal_type k=0;k<cardBubble;++k)
106 for (ordinal_type j=0;j<cardLine;++j)
107 for (ordinal_type i=0;i<cardBubble;++i,++idx)
108 for (ordinal_type l=0;l<npts;++l) {
109 output.access(idx,l,0) = 0.0;
110 output.access(idx,l,1) = output_x.access(i,l)*output_y.access(j,l)*output_z.access(k,l);
111 output.access(idx,l,2) = 0.0;
118 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
119 getValues(outputBubble_B, input_y, workLine, vinvBubble);
121 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
122 getValues(outputLine, input_z, workLine, vinvLine);
125 const auto output_x = outputBubble_A;
126 const auto output_y = outputBubble_B;
127 const auto output_z = outputLine;
129 for (ordinal_type k=0;k<cardLine;++k)
130 for (ordinal_type j=0;j<cardBubble;++j)
131 for (ordinal_type i=0;i<cardBubble;++i,++idx)
132 for (ordinal_type l=0;l<npts;++l) {
133 output.access(idx,l,0) = 0.0;
134 output.access(idx,l,1) = 0.0;
135 output.access(idx,l,2) = output_x.access(i,l)*output_y.access(j,l)*output_z.access(k,l);
141 ViewType workLine(Kokkos::view_wrap(ptr0, vcprop), cardLine, npts);
143 ViewType outputBubble_A(Kokkos::view_wrap(ptr2, vcprop), cardBubble, npts);
145 ViewType outputBubble_B(Kokkos::view_wrap(ptr3, vcprop), cardBubble, npts);
147 ViewType outputLine(Kokkos::view_wrap(ptr1, vcprop), cardLine, npts, 1);
150 ordinal_type idx = 0;
153 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_Dn>::
154 getValues(outputLine, input_x, workLine, vinvLine, 1);
156 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
157 getValues(outputBubble_A, input_y, workLine, vinvBubble);
159 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
160 getValues(outputBubble_B, input_z, workLine, vinvBubble);
163 const auto output_dx = outputLine;
164 const auto output_y = outputBubble_A;
165 const auto output_z = outputBubble_B;
167 for (ordinal_type k=0;k<cardBubble;++k)
168 for (ordinal_type j=0;j<cardBubble;++j)
169 for (ordinal_type i=0;i<cardLine;++i,++idx)
170 for (ordinal_type l=0;l<npts;++l)
171 output.access(idx,l) = output_dx.access(i,l,0)*output_y.access (j,l) *output_z.access(k,l);
174 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
175 getValues(outputBubble_A, input_x, workLine, vinvBubble);
177 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_Dn>::
178 getValues(outputLine, input_y, workLine, vinvLine, 1);
184 const auto output_x = outputBubble_A;
185 const auto output_dy = outputLine;
186 const auto output_z = outputBubble_B;
188 for (ordinal_type k=0;k<cardBubble;++k)
189 for (ordinal_type j=0;j<cardLine;++j)
190 for (ordinal_type i=0;i<cardBubble;++i,++idx)
191 for (ordinal_type l=0;l<npts;++l)
192 output.access(idx,l) = output_x.access(i,l)*output_dy.access(j,l,0)*output_z.access(k,l);
198 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
199 getValues(outputBubble_B, input_y, workLine, vinvBubble);
201 Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_Dn>::
202 getValues(outputLine, input_z, workLine, vinvLine, 1);
205 const auto output_x = outputBubble_A;
206 const auto output_y = outputBubble_B;
207 const auto output_dz = outputLine;
209 for (ordinal_type k=0;k<cardLine;++k)
210 for (ordinal_type j=0;j<cardBubble;++j)
211 for (ordinal_type i=0;i<cardBubble;++i,++idx)
212 for (ordinal_type l=0;l<npts;++l)
213 output.access(idx,l) = output_x.access(i,l)*output_y.access(j,l)*output_dz.access(k,l,0);
218 INTREPID2_TEST_FOR_ABORT(
true,
219 ">>> ERROR: (Intrepid2::Basis_HDIV_HEX_In_FEM::Serial::getValues) operator is not supported" );
224 template<
typename DT, ordinal_type numPtsPerEval,
225 typename outputValueValueType,
class ...outputValueProperties,
226 typename inputPointValueType,
class ...inputPointProperties,
227 typename vinvValueType,
class ...vinvProperties>
229 Basis_HDIV_HEX_In_FEM::
230 getValues( Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValues,
231 const Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPoints,
232 const Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvLine,
233 const Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvBubble,
234 const EOperator operatorType ) {
235 typedef Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValueViewType;
236 typedef Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPointViewType;
237 typedef Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvViewType;
238 typedef typename ExecSpace<typename inputPointViewType::execution_space,typename DT::execution_space>::ExecSpaceType ExecSpaceType;
241 const auto loopSizeTmp1 = (inputPoints.extent(0)/numPtsPerEval);
242 const auto loopSizeTmp2 = (inputPoints.extent(0)%numPtsPerEval != 0);
243 const auto loopSize = loopSizeTmp1 + loopSizeTmp2;
244 Kokkos::RangePolicy<ExecSpaceType,Kokkos::Schedule<Kokkos::Static> > policy(0, loopSize);
246 typedef typename inputPointViewType::value_type inputPointType;
248 const ordinal_type cardinality = outputValues.extent(0);
250 ordinal_type order = 0;
251 ordinal_type cardBubble;
252 ordinal_type cardLine;
254 cardBubble = Intrepid2::getPnCardinality<1>(order);
255 cardLine = Intrepid2::getPnCardinality<1>(++order);
258 auto vcprop = Kokkos::common_view_alloc_prop(inputPoints);
259 typedef typename Kokkos::DynRankView< inputPointType, typename inputPointViewType::memory_space> workViewType;
261 switch (operatorType) {
262 case OPERATOR_VALUE: {
263 auto workSize = Serial<OPERATOR_VALUE>::getWorkSizePerPoint(order);
264 workViewType work(Kokkos::view_alloc(
"Basis_HDIV_HEX_In_FEM::getValues::work", vcprop), workSize, inputPoints.extent(0));
265 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
266 OPERATOR_VALUE,numPtsPerEval> FunctorType;
267 Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinvLine, vinvBubble, work) );
271 auto workSize = Serial<OPERATOR_DIV>::getWorkSizePerPoint(order);
272 workViewType work(Kokkos::view_alloc(
"Basis_HDIV_HEX_In_FEM::getValues::work", vcprop), workSize, inputPoints.extent(0));
273 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
274 OPERATOR_DIV,numPtsPerEval> FunctorType;
275 Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinvLine, vinvBubble, work) );
279 INTREPID2_TEST_FOR_EXCEPTION(
true , std::invalid_argument,
280 ">>> ERROR (Basis_HDIV_HEX_In_FEM): Operator type not implemented" );
289 template<
typename DT,
typename OT,
typename PT>
292 const EPointType pointType ) {
294 INTREPID2_TEST_FOR_EXCEPTION( !(pointType == POINTTYPE_EQUISPACED ||
295 pointType == POINTTYPE_WARPBLEND), std::invalid_argument,
296 ">>> ERROR (Basis_HDIV_HEX_In_FEM): pointType must be either equispaced or warpblend.");
306 this->vinvLine_ = Kokkos::DynRankView<typename ScalarViewType::value_type,DT>(
"Hcurl::Hex::In::vinvLine", cardLine, cardLine);
307 this->vinvBubble_ = Kokkos::DynRankView<typename ScalarViewType::value_type,DT>(
"Hcurl::Hex::In::vinvBubble", cardBubble, cardBubble);
309 lineBasis.getVandermondeInverse(this->vinvLine_);
310 bubbleBasis.getVandermondeInverse(this->vinvBubble_);
312 const ordinal_type spaceDim = 3;
313 this->basisCardinality_ = 3*cardLine*cardBubble*cardBubble;
314 this->basisDegree_ = order;
315 this->basisCellTopologyKey_ = shards::Hexahedron<8>::key;
316 this->basisType_ = BASIS_FEM_LAGRANGIAN;
317 this->basisCoordinates_ = COORDINATES_CARTESIAN;
318 this->functionSpace_ = FUNCTION_SPACE_HDIV;
319 pointType_ = pointType;
324 const ordinal_type tagSize = 4;
325 const ordinal_type posScDim = 0;
326 const ordinal_type posScOrd = 1;
327 const ordinal_type posDfOrd = 2;
331 ordinal_type tags[3*maxCardLine*maxCardLine*maxCardLine][4];
333 const ordinal_type face_yz[2] = {3, 1};
334 const ordinal_type face_xz[2] = {0, 2};
335 const ordinal_type face_xy[2] = {4, 5};
338 ordinal_type idx = 0;
348 intr_ndofs_per_direction = (cardLine-2)*cardBubble*cardBubble,
349 intr_ndofs = 3*intr_ndofs_per_direction;
352 for (ordinal_type k=0;k<cardBubble;++k) {
353 const auto tag_z = bubbleBasis.
getDofTag(k);
354 for (ordinal_type j=0;j<cardBubble;++j) {
355 const auto tag_y = bubbleBasis.
getDofTag(j);
356 for (ordinal_type i=0;i<cardLine;++i,++idx) {
357 const auto tag_x = lineBasis.
getDofTag(i);
359 if (tag_x(0) == 0 && tag_y(0) == 1 && tag_z(0) == 1) {
362 tags[idx][1] = face_yz[tag_x(1)];
363 tags[idx][2] = tag_y(2) + tag_y(3)*tag_z(2);
364 tags[idx][3] = tag_y(3)*tag_z(3);
369 tags[idx][2] = tag_x(2) + tag_x(3)*tag_y(2) + tag_x(3)*tag_y(3)*tag_z(2);
370 tags[idx][3] = intr_ndofs;
377 for (ordinal_type k=0;k<cardBubble;++k) {
378 const auto tag_z = bubbleBasis.
getDofTag(k);
379 for (ordinal_type j=0;j<cardLine;++j) {
380 const auto tag_y = lineBasis.
getDofTag(j);
381 for (ordinal_type i=0;i<cardBubble;++i,++idx) {
382 const auto tag_x = bubbleBasis.
getDofTag(i);
384 if (tag_x(0) == 1 && tag_y(0) == 0 && tag_z(0) == 1) {
387 tags[idx][1] = face_xz[tag_y(1)];
388 tags[idx][2] = tag_x(2) + tag_x(3)*tag_z(2);
389 tags[idx][3] = tag_x(3)*tag_z(3);
394 tags[idx][2] = intr_ndofs_per_direction + tag_x(2) + tag_x(3)*tag_y(2) + tag_x(3)*tag_y(3)*tag_z(2);
395 tags[idx][3] = intr_ndofs;
402 for (ordinal_type k=0;k<cardLine;++k) {
403 const auto tag_z = lineBasis.
getDofTag(k);
404 for (ordinal_type j=0;j<cardBubble;++j) {
405 const auto tag_y = bubbleBasis.
getDofTag(j);
406 for (ordinal_type i=0;i<cardBubble;++i,++idx) {
407 const auto tag_x = bubbleBasis.
getDofTag(i);
409 if (tag_x(0) == 1 && tag_y(0) == 1 && tag_z(0) == 0) {
412 tags[idx][1] = face_xy[tag_z(1)];
413 tags[idx][2] = tag_x(2) + tag_x(3)*tag_y(2);
414 tags[idx][3] = tag_x(3)*tag_y(3);
419 tags[idx][2] = 2*intr_ndofs_per_direction + tag_x(2) + tag_x(3)*tag_y(2) + tag_x(3)*tag_y(3)*tag_z(2);
420 tags[idx][3] = intr_ndofs;
426 INTREPID2_TEST_FOR_EXCEPTION( idx != this->basisCardinality_ , std::runtime_error,
427 ">>> ERROR (Basis_HDIV_HEX_In_FEM): " \
428 "counted tag index is not same as cardinality." );
431 OrdinalTypeArray1DHost tagView(&tags[0][0], this->basisCardinality_*4);
435 this->setOrdinalTagData(this->tagToOrdinal_,
438 this->basisCardinality_,
446 Kokkos::DynRankView<typename ScalarViewType::value_type,typename DT::execution_space::array_layout,Kokkos::HostSpace>
447 dofCoordsHost(
"dofCoordsHost", this->basisCardinality_, spaceDim);
450 Kokkos::DynRankView<typename ScalarViewType::value_type,typename DT::execution_space::array_layout,Kokkos::HostSpace>
451 dofCoeffsHost(
"dofCoeffsHost", this->basisCardinality_, spaceDim);
453 Kokkos::DynRankView<typename ScalarViewType::value_type,DT>
454 dofCoordsLine(
"dofCoordsLine", cardLine, 1),
455 dofCoordsBubble(
"dofCoordsBubble", cardBubble, 1);
458 auto dofCoordsLineHost = Kokkos::create_mirror_view(Kokkos::HostSpace(), dofCoordsLine);
459 Kokkos::deep_copy(dofCoordsLineHost, dofCoordsLine);
462 auto dofCoordsBubbleHost = Kokkos::create_mirror_view(Kokkos::HostSpace(), dofCoordsBubble);
463 Kokkos::deep_copy(dofCoordsBubbleHost, dofCoordsBubble);
466 ordinal_type idx = 0;
469 for (ordinal_type k=0;k<cardBubble;++k) {
470 for (ordinal_type j=0;j<cardBubble;++j) {
471 for (ordinal_type i=0;i<cardLine;++i,++idx) {
472 dofCoordsHost(idx,0) = dofCoordsLineHost(i,0);
473 dofCoordsHost(idx,1) = dofCoordsBubbleHost(j,0);
474 dofCoordsHost(idx,2) = dofCoordsBubbleHost(k,0);
475 dofCoeffsHost(idx,0) = 1.0;
481 for (ordinal_type k=0;k<cardBubble;++k) {
482 for (ordinal_type j=0;j<cardLine;++j) {
483 for (ordinal_type i=0;i<cardBubble;++i,++idx) {
484 dofCoordsHost(idx,0) = dofCoordsBubbleHost(i,0);
485 dofCoordsHost(idx,1) = dofCoordsLineHost(j,0);
486 dofCoordsHost(idx,2) = dofCoordsBubbleHost(k,0);
487 dofCoeffsHost(idx,1) = 1.0;
493 for (ordinal_type k=0;k<cardLine;++k) {
494 for (ordinal_type j=0;j<cardBubble;++j) {
495 for (ordinal_type i=0;i<cardBubble;++i,++idx) {
496 dofCoordsHost(idx,0) = dofCoordsBubbleHost(i,0);
497 dofCoordsHost(idx,1) = dofCoordsBubbleHost(j,0);
498 dofCoordsHost(idx,2) = dofCoordsLineHost(k,0);
499 dofCoeffsHost(idx,2) = 1.0;
505 this->dofCoords_ = Kokkos::create_mirror_view(
typename DT::memory_space(), dofCoordsHost);
506 Kokkos::deep_copy(this->dofCoords_, dofCoordsHost);
508 this->dofCoeffs_ = Kokkos::create_mirror_view(
typename DT::memory_space(), dofCoeffsHost);
509 Kokkos::deep_copy(this->dofCoeffs_, dofCoeffsHost);
512 template<
typename DT,
typename OT,
typename PT>
515 ordinal_type& perTeamSpaceSize,
516 ordinal_type& perThreadSpaceSize,
517 const PointViewType inputPoints,
518 const EOperator operatorType)
const {
519 perTeamSpaceSize = 0;
520 perThreadSpaceSize = (2*this->vinvLine_.extent(0)+2*this->vinvBubble_.extent(0))*get_dimension_scalar(inputPoints)*
sizeof(
typename BasisBase::scalarType);
523 template<
typename DT,
typename OT,
typename PT>
524 KOKKOS_INLINE_FUNCTION
526 Basis_HDIV_HEX_In_FEM<DT,OT,PT>::getValues(
527 OutputViewType outputValues,
528 const PointViewType inputPoints,
529 const EOperator operatorType,
530 const typename Kokkos::TeamPolicy<typename DT::execution_space>::member_type& team_member,
531 const typename DT::execution_space::scratch_memory_space & scratchStorage,
532 const ordinal_type subcellDim,
533 const ordinal_type subcellOrdinal)
const {
535 INTREPID2_TEST_FOR_ABORT( !((subcellDim == -1) && (subcellOrdinal == -1)),
536 ">>> ERROR: (Intrepid2::Basis_HDIV_HEX_In_FEM::getValues), The capability of selecting subsets of basis functions has not been implemented yet.");
538 const int numPoints = inputPoints.extent(0);
539 using ScalarType =
typename ScalarTraits<typename PointViewType::value_type>::scalar_type;
540 using WorkViewType = Kokkos::DynRankView< ScalarType,typename DT::execution_space::scratch_memory_space,Kokkos::MemoryTraits<Kokkos::Unmanaged> >;
541 ordinal_type sizePerPoint = (2*this->vinvLine_.extent(0)+2*this->vinvBubble_.extent(0))*get_dimension_scalar(inputPoints);
542 WorkViewType workView(scratchStorage, sizePerPoint*team_member.team_size());
543 using range_type = Kokkos::pair<ordinal_type,ordinal_type>;
545 switch(operatorType) {
547 Kokkos::parallel_for (Kokkos::TeamThreadRange (team_member, numPoints), [=] (ordinal_type& pt) {
548 auto output = Kokkos::subview( outputValues, Kokkos::ALL(), range_type (pt,pt+1), Kokkos::ALL() );
549 const auto input = Kokkos::subview( inputPoints, range_type(pt, pt+1), Kokkos::ALL() );
550 WorkViewType work(workView.data() + sizePerPoint*team_member.team_rank(), sizePerPoint);
551 Impl::Basis_HDIV_HEX_In_FEM::Serial<OPERATOR_VALUE>::getValues( output, input, work, this->vinvLine_, this->vinvBubble_ );
555 Kokkos::parallel_for (Kokkos::TeamThreadRange (team_member, numPoints), [=] (ordinal_type& pt) {
556 auto output = Kokkos::subview( outputValues, Kokkos::ALL(), range_type(pt,pt+1), Kokkos::ALL() );
557 const auto input = Kokkos::subview( inputPoints, range_type(pt,pt+1), Kokkos::ALL() );
558 WorkViewType work(workView.data() + sizePerPoint*team_member.team_rank(), sizePerPoint);
559 Impl::Basis_HDIV_HEX_In_FEM::Serial<OPERATOR_DIV>::getValues( output, input, work, this->vinvLine_, this->vinvBubble_ );
563 INTREPID2_TEST_FOR_ABORT(
true,
564 ">>> ERROR (Basis_HDIV_HEX_In_FEM): getValues not implemented for this operator");
const OrdinalTypeArrayStride1DHost getDofTag(const ordinal_type dofOrd) const
DoF ordinal to DoF tag lookup.
virtual void getDofCoords(ScalarViewType dofCoords) const override
Returns spatial locations (coordinates) of degrees of freedom on the reference cell.
ordinal_type getCardinality() const
Returns cardinality of the basis.
Basis_HDIV_HEX_In_FEM(const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
Constructor.
virtual void getDofCoords(ScalarViewType dofCoords) const override
Returns spatial locations (coordinates) of degrees of freedom on the reference cell.
Implementation of the locally H(grad)-compatible FEM basis of variable order on the [-1...
Implementation of the locally HVOL-compatible FEM basis of variable order on the [-1,1] reference line cell, using Lagrange polynomials.
Implementation of the default H(div)-compatible FEM basis on Hexahedron cell.
static constexpr ordinal_type MaxOrder
The maximum reconstruction order.