Intrepid2
Intrepid2_HDIV_QUAD_In_FEMDef.hpp
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5 // Copyright 2007 NTESS and the Intrepid2 contributors.
6 // SPDX-License-Identifier: BSD-3-Clause
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9 
16 #ifndef __INTREPID2_HDIV_QUAD_IN_FEM_DEF_HPP__
17 #define __INTREPID2_HDIV_QUAD_IN_FEM_DEF_HPP__
18 
19 namespace Intrepid2 {
20 
21  // -------------------------------------------------------------------------------------
22  namespace Impl {
23 
24  template<EOperator OpType>
25  template<typename OutputViewType,
26  typename InputViewType,
27  typename WorkViewType,
28  typename VinvViewType>
29  KOKKOS_INLINE_FUNCTION
30  void
31  Basis_HDIV_QUAD_In_FEM::Serial<OpType>::
32  getValues( OutputViewType output,
33  const InputViewType input,
34  WorkViewType work,
35  const VinvViewType vinvLine,
36  const VinvViewType vinvBubble) {
37  const ordinal_type cardLine = vinvLine.extent(0);
38  const ordinal_type cardBubble = vinvBubble.extent(0);
39 
40  const ordinal_type npts = input.extent(0);
41 
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 
46  const ordinal_type dim_s = get_dimension_scalar(input);
47  auto ptr0 = work.data();
48  auto ptr1 = work.data()+cardLine*npts*dim_s;
49  auto ptr2 = work.data()+2*cardLine*npts*dim_s;
50 
51  typedef typename Kokkos::DynRankView<typename InputViewType::value_type, typename WorkViewType::memory_space> ViewType;
52  auto vcprop = Kokkos::common_view_alloc_prop(input);
53 
54  switch (OpType) {
55  case OPERATOR_VALUE: {
56  ViewType workLine(Kokkos::view_wrap(ptr0, vcprop), cardLine, npts);
57  ViewType outputLine(Kokkos::view_wrap(ptr1, vcprop), cardLine, npts);
58  ViewType outputBubble(Kokkos::view_wrap(ptr2, vcprop), cardBubble, npts);
59 
60  // tensor product
61  ordinal_type idx = 0;
62  {
63  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
64  getValues(outputBubble, input_x, workLine, vinvBubble);
65 
66  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
67  getValues(outputLine, input_y, workLine, vinvLine);
68 
69  // x component (lineBasis(y) bubbleBasis(x))
70  const auto output_x = outputBubble;
71  const auto output_y = outputLine;
72 
73  for (ordinal_type j=0;j<cardLine;++j) // y
74  for (ordinal_type i=0;i<cardBubble;++i,++idx) // x
75  for (ordinal_type k=0;k<npts;++k) {
76  output.access(idx,k,0) = 0.0;
77  output.access(idx,k,1) = output_x.access(i,k)*output_y.access(j,k);
78  }
79  }
80  {
81  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
82  getValues(outputBubble, input_y, workLine, vinvBubble);
83 
84  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
85  getValues(outputLine, input_x, workLine, vinvLine);
86 
87  // y component (bubbleBasis(y) lineBasis(x))
88  const auto output_x = outputLine;
89  const auto output_y = outputBubble;
90  for (ordinal_type j=0;j<cardBubble;++j) // y
91  for (ordinal_type i=0;i<cardLine;++i,++idx) // x
92  for (ordinal_type k=0;k<npts;++k) {
93  output.access(idx,k,0) = output_x.access(i,k)*output_y.access(j,k);
94  output.access(idx,k,1) = 0.0;
95  }
96  }
97  break;
98  }
99  case OPERATOR_DIV: {
100  ordinal_type idx = 0;
101  { // x - component
102  ViewType workLine(Kokkos::view_wrap(ptr0, vcprop), cardLine, npts);
103  // x bubble value
104  ViewType output_x(Kokkos::view_wrap(ptr2, vcprop), cardBubble, npts);
105  // y line grad
106  ViewType output_y(Kokkos::view_wrap(ptr1, vcprop), cardLine, npts,1);
107 
108  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
109  getValues(output_x, input_x, workLine, vinvBubble);
110 
111  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_Dn>::
112  getValues(output_y, input_y, workLine, vinvLine, 1);
113 
114  // tensor product (extra dimension of ouput x and y are ignored)
115  for (ordinal_type j=0;j<cardLine;++j) // y
116  for (ordinal_type i=0;i<cardBubble;++i,++idx) // x
117  for (ordinal_type k=0;k<npts;++k)
118  output.access(idx,k) = output_x.access(i,k)*output_y.access(j,k,0);
119  }
120  { // y - component
121  ViewType workLine(Kokkos::view_wrap(ptr0, vcprop), cardLine, npts);
122  // x line grad
123  ViewType output_x(Kokkos::view_wrap(ptr1, vcprop), cardLine, npts,1);
124  // y bubble value
125  ViewType output_y(Kokkos::view_wrap(ptr2, vcprop), cardBubble, npts);
126 
127  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_VALUE>::
128  getValues(output_y, input_y, workLine, vinvBubble);
129 
130  Impl::Basis_HGRAD_LINE_Cn_FEM::Serial<OPERATOR_Dn>::
131  getValues(output_x, input_x, workLine, vinvLine, 1);
132 
133  // tensor product (extra dimension of ouput x and y are ignored)
134  for (ordinal_type j=0;j<cardBubble;++j) // y
135  for (ordinal_type i=0;i<cardLine;++i,++idx) // x
136  for (ordinal_type k=0;k<npts;++k)
137  output.access(idx,k) = output_x.access(i,k,0)*output_y.access(j,k);
138  }
139  break;
140  }
141  default: {
142  INTREPID2_TEST_FOR_ABORT( true,
143  ">>> ERROR: (Intrepid2::Basis_HDIV_QUAD_In_FEM::Serial::getValues) operator is not supported" );
144  }
145  }
146  }
147 
148  template<typename DT, ordinal_type numPtsPerEval,
149  typename outputValueValueType, class ...outputValueProperties,
150  typename inputPointValueType, class ...inputPointProperties,
151  typename vinvValueType, class ...vinvProperties>
152  void
153  Basis_HDIV_QUAD_In_FEM::
154  getValues( Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValues,
155  const Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPoints,
156  const Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvLine,
157  const Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvBubble,
158  const EOperator operatorType ) {
159  typedef Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValueViewType;
160  typedef Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPointViewType;
161  typedef Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvViewType;
162  typedef typename ExecSpace<typename inputPointViewType::execution_space,typename DT::execution_space>::ExecSpaceType ExecSpaceType;
163 
164  // loopSize corresponds to cardinality
165  const auto loopSizeTmp1 = (inputPoints.extent(0)/numPtsPerEval);
166  const auto loopSizeTmp2 = (inputPoints.extent(0)%numPtsPerEval != 0);
167  const auto loopSize = loopSizeTmp1 + loopSizeTmp2;
168  Kokkos::RangePolicy<ExecSpaceType,Kokkos::Schedule<Kokkos::Static> > policy(0, loopSize);
169 
170  typedef typename inputPointViewType::value_type inputPointType;
171 
172  const ordinal_type cardinality = outputValues.extent(0);
173  //get basis order based on basis cardinality.
174  ordinal_type order = 0; // = std::sqrt(cardinality/2);
175  ordinal_type cardBubble; // = std::sqrt(cardinality/2);
176  ordinal_type cardLine; // = cardBubble+1;
177  do {
178  cardBubble = Intrepid2::getPnCardinality<1>(order);
179  cardLine = Intrepid2::getPnCardinality<1>(++order);
180  } while((2*cardBubble*cardLine != cardinality) && (order != Parameters::MaxOrder));
181 
182  auto vcprop = Kokkos::common_view_alloc_prop(inputPoints);
183  typedef typename Kokkos::DynRankView< inputPointType, typename inputPointViewType::memory_space> workViewType;
184 
185  switch (operatorType) {
186  case OPERATOR_VALUE: {
187  auto workSize = Serial<OPERATOR_VALUE>::getWorkSizePerPoint(order);
188  workViewType work(Kokkos::view_alloc("Basis_HDIV_QUAD_In_FEM::getValues::work", vcprop), workSize, inputPoints.extent(0));
189  typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
190  OPERATOR_VALUE,numPtsPerEval> FunctorType;
191  Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinvLine, vinvBubble, work) );
192  break;
193  }
194  case OPERATOR_DIV: {
195  auto workSize = Serial<OPERATOR_DIV>::getWorkSizePerPoint(order);
196  workViewType work(Kokkos::view_alloc("Basis_HDIV_QUAD_In_FEM::getValues::work", vcprop), workSize, inputPoints.extent(0));
197  typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
198  OPERATOR_DIV,numPtsPerEval> FunctorType;
199  Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinvLine, vinvBubble, work) );
200  break;
201  }
202  default: {
203  INTREPID2_TEST_FOR_EXCEPTION( true , std::invalid_argument,
204  ">>> ERROR (Basis_HDIV_QUAD_In_FEM): Operator type not implemented" );
205  }
206  }
207  }
208  }
209 
210  // -------------------------------------------------------------------------------------
211  template<typename DT, typename OT, typename PT>
212  Basis_HDIV_QUAD_In_FEM<DT,OT,PT>::
213  Basis_HDIV_QUAD_In_FEM( const ordinal_type order,
214  const EPointType pointType ) {
215 
216  INTREPID2_TEST_FOR_EXCEPTION( !(pointType == POINTTYPE_EQUISPACED ||
217  pointType == POINTTYPE_WARPBLEND), std::invalid_argument,
218  ">>> ERROR (Basis_HDIV_QUAD_In_FEM): pointType must be either equispaced or warpblend.");
219 
220  // this should be in host
221  Basis_HGRAD_LINE_Cn_FEM<DT,OT,PT> lineBasis( order, pointType );
222  Basis_HVOL_LINE_Cn_FEM<DT,OT,PT> bubbleBasis( order - 1, POINTTYPE_GAUSS );
223 
224  const ordinal_type
225  cardLine = lineBasis.getCardinality(),
226  cardBubble = bubbleBasis.getCardinality();
227 
228  this->vinvLine_ = Kokkos::DynRankView<typename ScalarViewType::value_type,DT>("Hdiv::Quad::In::vinvLine", cardLine, cardLine);
229  this->vinvBubble_ = Kokkos::DynRankView<typename ScalarViewType::value_type,DT>("Hdiv::Quad::In::vinvBubble", cardBubble, cardBubble);
230 
231  lineBasis.getVandermondeInverse(this->vinvLine_);
232  bubbleBasis.getVandermondeInverse(this->vinvBubble_);
233 
234  const ordinal_type spaceDim = 2;
235  this->basisCardinality_ = 2*cardLine*cardBubble;
236  this->basisDegree_ = order;
237  this->basisCellTopologyKey_ = shards::Quadrilateral<4>::key;
238  this->basisType_ = BASIS_FEM_LAGRANGIAN;
239  this->basisCoordinates_ = COORDINATES_CARTESIAN;
240  this->functionSpace_ = FUNCTION_SPACE_HDIV;
241  pointType_ = pointType;
242 
243  // initialize tags
244  {
245  // Basis-dependent initializations
246  const ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
247  const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
248  const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
249  const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
250 
251  // An array with local DoF tags assigned to the basis functions, in the order of their local enumeration
252  constexpr ordinal_type maxCardLine = Parameters::MaxOrder + 1;
253  constexpr ordinal_type maxCardBubble = Parameters::MaxOrder;
254  ordinal_type tags[2*maxCardLine*maxCardBubble][4];
255 
256  const ordinal_type edge_x[2] = {0,2};
257  const ordinal_type edge_y[2] = {3,1};
258  {
259  ordinal_type idx = 0;
260 
264 
265  // since there are x/y components in the interior
266  // dof sum should be computed before the information
267  // is assigned to tags
268  const ordinal_type
269  intr_ndofs_per_direction = (cardLine-2)*cardBubble,
270  intr_ndofs = 2*intr_ndofs_per_direction;
271 
272  // x component (lineBasis(y) bubbleBasis(x))
273  for (ordinal_type j=0;j<cardLine;++j) { // y
274  const auto tag_y = lineBasis.getDofTag(j);
275  for (ordinal_type i=0;i<cardBubble;++i,++idx) { // x
276  const auto tag_x = bubbleBasis.getDofTag(i);
277 
278  if (tag_x(0) == 1 && tag_y(0) == 0) {
279  // edge: x edge, y vert
280  tags[idx][0] = 1; // edge dof
281  tags[idx][1] = edge_x[tag_y(1)];
282  tags[idx][2] = tag_x(2); // local dof id
283  tags[idx][3] = tag_x(3); // total number of dofs in this vertex
284  } else {
285  // interior
286  tags[idx][0] = 2; // interior dof
287  tags[idx][1] = 0;
288  tags[idx][2] = tag_x(2) + tag_x(3)*tag_y(2); // local dof id
289  tags[idx][3] = intr_ndofs; // total number of dofs in this vertex
290  }
291  }
292  }
293 
294  // y component (bubbleBasis(y) lineBasis(x))
295  for (ordinal_type j=0;j<cardBubble;++j) { // y
296  const auto tag_y = bubbleBasis.getDofTag(j);
297  for (ordinal_type i=0;i<cardLine;++i,++idx) { // x
298  const auto tag_x = lineBasis.getDofTag(i);
299 
300  if (tag_x(0) == 0 && tag_y(0) == 1) {
301  // edge: x vert, y edge
302  tags[idx][0] = 1; // edge dof
303  tags[idx][1] = edge_y[tag_x(1)];
304  tags[idx][2] = tag_y(2); // local dof id
305  tags[idx][3] = tag_y(3); // total number of dofs in this vertex
306  } else {
307  // interior
308  tags[idx][0] = 2; // interior dof
309  tags[idx][1] = 0;
310  tags[idx][2] = intr_ndofs_per_direction + tag_x(2) + tag_x(3)*tag_y(2); // local dof id
311  tags[idx][3] = intr_ndofs; // total number of dofs in this vertex
312  }
313  }
314  }
315  INTREPID2_TEST_FOR_EXCEPTION( idx != this->basisCardinality_ , std::runtime_error,
316  ">>> ERROR (Basis_HDIV_QUAD_In_FEM): " \
317  "counted tag index is not same as cardinality." );
318  }
319 
320  OrdinalTypeArray1DHost tagView(&tags[0][0], this->basisCardinality_*4);
321 
322  // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
323  // tags are constructed on host
324  this->setOrdinalTagData(this->tagToOrdinal_,
325  this->ordinalToTag_,
326  tagView,
327  this->basisCardinality_,
328  tagSize,
329  posScDim,
330  posScOrd,
331  posDfOrd);
332  }
333 
334  // dofCoords on host and create its mirror view to device
335  Kokkos::DynRankView<typename ScalarViewType::value_type,typename DT::execution_space::array_layout,Kokkos::HostSpace>
336  dofCoordsHost("dofCoordsHost", this->basisCardinality_, spaceDim);
337 
338  // dofCoeffs on host and create its mirror view to device
339  Kokkos::DynRankView<typename ScalarViewType::value_type,typename DT::execution_space::array_layout,Kokkos::HostSpace>
340  dofCoeffsHost("dofCoeffsHost", this->basisCardinality_, spaceDim);
341 
342  Kokkos::DynRankView<typename ScalarViewType::value_type,DT>
343  dofCoordsLine("dofCoordsLine", cardLine, 1),
344  dofCoordsBubble("dofCoordsBubble", cardBubble, 1);
345 
346  lineBasis.getDofCoords(dofCoordsLine);
347  auto dofCoordsLineHost = Kokkos::create_mirror_view(Kokkos::HostSpace(), dofCoordsLine);
348  Kokkos::deep_copy(dofCoordsLineHost, dofCoordsLine);
349 
350  bubbleBasis.getDofCoords(dofCoordsBubble);
351  auto dofCoordsBubbleHost = Kokkos::create_mirror_view(Kokkos::HostSpace(), dofCoordsBubble);
352  Kokkos::deep_copy(dofCoordsBubbleHost, dofCoordsBubble);
353 
354  {
355  ordinal_type idx = 0;
356 
357  // x component (lineBasis(y) bubbleBasis(x))
358  for (ordinal_type j=0;j<cardLine;++j) { // y
359  for (ordinal_type i=0;i<cardBubble;++i,++idx) { // x
360  dofCoordsHost(idx,0) = dofCoordsBubbleHost(i,0);
361  dofCoordsHost(idx,1) = dofCoordsLineHost(j,0);
362  dofCoeffsHost(idx,1) = 1.0;
363  }
364  }
365 
366  // y component (bubbleBasis(y) lineBasis(x))
367  for (ordinal_type j=0;j<cardBubble;++j) { // y
368  for (ordinal_type i=0;i<cardLine;++i,++idx) { // x
369  dofCoordsHost(idx,0) = dofCoordsLineHost(i,0);
370  dofCoordsHost(idx,1) = dofCoordsBubbleHost(j,0);
371  dofCoeffsHost(idx,0) = 1.0;
372  }
373  }
374  }
375 
376  this->dofCoords_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoordsHost);
377  Kokkos::deep_copy(this->dofCoords_, dofCoordsHost);
378 
379  this->dofCoeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoeffsHost);
380  Kokkos::deep_copy(this->dofCoeffs_, dofCoeffsHost);
381  }
382 
383  template<typename DT, typename OT, typename PT>
384  void
385  Basis_HDIV_QUAD_In_FEM<DT,OT,PT>::getScratchSpaceSize(
386  ordinal_type& perTeamSpaceSize,
387  ordinal_type& perThreadSpaceSize,
388  const PointViewType inputPoints,
389  const EOperator operatorType) const {
390  perTeamSpaceSize = 0;
391  perThreadSpaceSize = (2*this->vinvLine_.extent(0)+this->vinvBubble_.extent(0))*get_dimension_scalar(inputPoints)*sizeof(typename BasisBase::scalarType);
392  }
393 
394  template<typename DT, typename OT, typename PT>
395  KOKKOS_INLINE_FUNCTION
396  void
397  Basis_HDIV_QUAD_In_FEM<DT,OT,PT>::getValues(
398  OutputViewType outputValues,
399  const PointViewType inputPoints,
400  const EOperator operatorType,
401  const typename Kokkos::TeamPolicy<typename DT::execution_space>::member_type& team_member,
402  const typename DT::execution_space::scratch_memory_space & scratchStorage,
403  const ordinal_type subcellDim,
404  const ordinal_type subcellOrdinal) const {
405 
406  INTREPID2_TEST_FOR_ABORT( !((subcellDim == -1) && (subcellOrdinal == -1)),
407  ">>> ERROR: (Intrepid2::Basis_HDIV_QUAD_In_FEM::getValues), The capability of selecting subsets of basis functions has not been implemented yet.");
408 
409  const int numPoints = inputPoints.extent(0);
410  using ScalarType = typename ScalarTraits<typename PointViewType::value_type>::scalar_type;
411  using WorkViewType = Kokkos::DynRankView< ScalarType,typename DT::execution_space::scratch_memory_space,Kokkos::MemoryTraits<Kokkos::Unmanaged> >;
412  ordinal_type sizePerPoint = (2*this->vinvLine_.extent(0)+this->vinvBubble_.extent(0))*get_dimension_scalar(inputPoints);
413  WorkViewType workView(scratchStorage, sizePerPoint*team_member.team_size());
414  using range_type = Kokkos::pair<ordinal_type,ordinal_type>;
415 
416  switch(operatorType) {
417  case OPERATOR_VALUE:
418  Kokkos::parallel_for (Kokkos::TeamThreadRange (team_member, numPoints), [=] (ordinal_type& pt) {
419  auto output = Kokkos::subview( outputValues, Kokkos::ALL(), range_type (pt,pt+1), Kokkos::ALL() );
420  const auto input = Kokkos::subview( inputPoints, range_type(pt, pt+1), Kokkos::ALL() );
421  WorkViewType work(workView.data() + sizePerPoint*team_member.team_rank(), sizePerPoint);
422  Impl::Basis_HDIV_QUAD_In_FEM::Serial<OPERATOR_VALUE>::getValues( output, input, work, this->vinvLine_, this->vinvBubble_ );
423  });
424  break;
425  case OPERATOR_DIV:
426  Kokkos::parallel_for (Kokkos::TeamThreadRange (team_member, numPoints), [=] (ordinal_type& pt) {
427  auto output = Kokkos::subview( outputValues, Kokkos::ALL(), range_type(pt,pt+1), Kokkos::ALL() );
428  const auto input = Kokkos::subview( inputPoints, range_type(pt,pt+1), Kokkos::ALL() );
429  WorkViewType work(workView.data() + sizePerPoint*team_member.team_rank(), sizePerPoint);
430  Impl::Basis_HDIV_QUAD_In_FEM::Serial<OPERATOR_DIV>::getValues( output, input, work, this->vinvLine_, this->vinvBubble_ );
431  });
432  break;
433  default: {
434  INTREPID2_TEST_FOR_ABORT( true,
435  ">>> ERROR (Basis_HDIV_QUAD_In_FEM): getValues not implemented for this operator");
436  }
437  }
438  }
439 
440 } // namespace Intrepid2
441 
442 #endif
Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::getDofTag
const OrdinalTypeArrayStride1DHost getDofTag(const ordinal_type dofOrd) const
DoF ordinal to DoF tag lookup.
Definition: Intrepid2_Basis.hpp:941
Intrepid2::Basis_HDIV_QUAD_In_FEM
Implementation of the default H(div)-compatible FEM basis on Quadrilateral cell.
Definition: Intrepid2_HDIV_QUAD_In_FEM.hpp:135
Intrepid2::Basis_HVOL_LINE_Cn_FEM::getDofCoords
virtual void getDofCoords(ScalarViewType dofCoords) const override
Returns spatial locations (coordinates) of degrees of freedom on the reference cell.
Definition: Intrepid2_HVOL_LINE_Cn_FEM.hpp:205
Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::getCardinality
ordinal_type getCardinality() const
Returns cardinality of the basis.
Definition: Intrepid2_Basis.hpp:805
Intrepid2::Basis_HGRAD_LINE_Cn_FEM::getDofCoords
virtual void getDofCoords(ScalarViewType dofCoords) const override
Returns spatial locations (coordinates) of degrees of freedom on the reference cell.
Definition: Intrepid2_HGRAD_LINE_Cn_FEM.hpp:214
Intrepid2::Basis_HGRAD_LINE_Cn_FEM
Implementation of the locally H(grad)-compatible FEM basis of variable order on the [-1...
Definition: Intrepid2_HGRAD_LINE_Cn_FEM.hpp:143
Intrepid2::Basis_HVOL_LINE_Cn_FEM
Implementation of the locally HVOL-compatible FEM basis of variable order on the [-1,1] reference line cell, using Lagrange polynomials.
Definition: Intrepid2_HVOL_LINE_Cn_FEM.hpp:144
Intrepid2::Basis_HDIV_QUAD_In_FEM::Basis_HDIV_QUAD_In_FEM
Basis_HDIV_QUAD_In_FEM(const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
Constructor.
Definition: Intrepid2_HDIV_QUAD_In_FEMDef.hpp:213
Intrepid2::Parameters::MaxOrder
static constexpr ordinal_type MaxOrder
The maximum reconstruction order.
Definition: Intrepid2_Types.hpp:102
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