Intrepid2
Intrepid2_HDIV_TRI_In_FEMDef.hpp
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49#ifndef __INTREPID2_HDIV_TRI_IN_FEM_DEF_HPP__
50#define __INTREPID2_HDIV_TRI_IN_FEM_DEF_HPP__
51
54
55namespace Intrepid2 {
56
57// -------------------------------------------------------------------------------------
58namespace Impl {
59
60template<EOperator opType>
61template<typename OutputViewType,
62typename inputViewType,
63typename workViewType,
64typename vinvViewType>
65KOKKOS_INLINE_FUNCTION
66void
67Basis_HDIV_TRI_In_FEM::Serial<opType>::
68getValues( /* */ OutputViewType output,
69 const inputViewType input,
70 /* */ workViewType work,
71 const vinvViewType coeffs ) {
72
73 constexpr ordinal_type spaceDim = 2;
74 const ordinal_type
75 cardPn = coeffs.extent(0)/spaceDim,
76 card = coeffs.extent(1),
77 npts = input.extent(0);
78
79 // compute order
80 ordinal_type order = 0;
81 for (ordinal_type p=0;p<=Parameters::MaxOrder;++p) {
82 if (card == CardinalityHDivTri(p)) {
83 order = p;
84 break;
85 }
86 }
87
88 typedef typename Kokkos::DynRankView<typename workViewType::value_type, typename workViewType::memory_space> viewType;
89 auto vcprop = Kokkos::common_view_alloc_prop(work);
90 auto ptr = work.data();
91
92 switch (opType) {
93 case OPERATOR_VALUE: {
94 const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts);
95 workViewType dummyView;
96
97 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
98 Serial<opType>::getValues(phis, input, dummyView, order);
99
100 for (ordinal_type i=0;i<card;++i)
101 for (ordinal_type j=0;j<npts;++j)
102 for (ordinal_type d=0;d<spaceDim;++d) {
103 output.access(i,j,d) = 0.0;
104 for (ordinal_type k=0;k<cardPn;++k)
105 output.access(i,j,d) += coeffs(k+d*cardPn,i) * phis.access(k,j);
106 }
107 break;
108 }
109 case OPERATOR_DIV: {
110 const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim);
111 ptr += card*npts*spaceDim*get_dimension_scalar(work);
112 const viewType workView(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim+1);
113
114 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
115 Serial<OPERATOR_GRAD>::getValues(phis, input, workView, order);
116
117 for (ordinal_type i=0;i<card;++i)
118 for (ordinal_type j=0;j<npts;++j) {
119 output.access(i,j) = 0.0;
120 for (ordinal_type k=0; k<cardPn; ++k)
121 for (ordinal_type d=0; d<spaceDim; ++d)
122 output.access(i,j) += coeffs(k+d*cardPn,i)*phis.access(k,j,d);
123 }
124 break;
125 }
126 default: {
127 INTREPID2_TEST_FOR_ABORT( true,
128 ">>> ERROR (Basis_HDIV_TRI_In_FEM): Operator type not implemented");
129 }
130 }
131}
132
133template<typename DT, ordinal_type numPtsPerEval,
134typename outputValueValueType, class ...outputValueProperties,
135typename inputPointValueType, class ...inputPointProperties,
136typename vinvValueType, class ...vinvProperties>
137void
138Basis_HDIV_TRI_In_FEM::
139getValues( /* */ Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValues,
140 const Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPoints,
141 const Kokkos::DynRankView<vinvValueType, vinvProperties...> coeffs,
142 const EOperator operatorType) {
143 typedef Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValueViewType;
144 typedef Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPointViewType;
145 typedef Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvViewType;
146 typedef typename ExecSpace<typename inputPointViewType::execution_space,typename DT::execution_space>::ExecSpaceType ExecSpaceType;
147
148 // loopSize corresponds to cardinality
149 const auto loopSizeTmp1 = (inputPoints.extent(0)/numPtsPerEval);
150 const auto loopSizeTmp2 = (inputPoints.extent(0)%numPtsPerEval != 0);
151 const auto loopSize = loopSizeTmp1 + loopSizeTmp2;
152 Kokkos::RangePolicy<ExecSpaceType,Kokkos::Schedule<Kokkos::Static> > policy(0, loopSize);
153
154 typedef typename inputPointViewType::value_type inputPointType;
155
156 const ordinal_type cardinality = outputValues.extent(0);
157 const ordinal_type spaceDim = 2;
158
159 auto vcprop = Kokkos::common_view_alloc_prop(inputPoints);
160 typedef typename Kokkos::DynRankView< inputPointType, typename inputPointViewType::memory_space> workViewType;
161
162 switch (operatorType) {
163 case OPERATOR_VALUE: {
164 workViewType work(Kokkos::view_alloc("Basis_HDIV_TRI_In_FEM::getValues::work", vcprop), cardinality, inputPoints.extent(0));
165 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
166 OPERATOR_VALUE,numPtsPerEval> FunctorType;
167 Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, coeffs, work) );
168 break;
169 }
170 case OPERATOR_DIV: {
171 workViewType work(Kokkos::view_alloc("Basis_HDIV_TRI_In_FEM::getValues::work", vcprop), cardinality*(2*spaceDim+1), inputPoints.extent(0));
172 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
173 OPERATOR_DIV,numPtsPerEval> FunctorType;
174 Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, coeffs, work) );
175 break;
176 }
177 default: {
178 INTREPID2_TEST_FOR_EXCEPTION( true , std::invalid_argument,
179 ">>> ERROR (Basis_HDIV_TRI_In_FEM): Operator type not implemented" );
180 }
181 }
182}
183}
184
185// -------------------------------------------------------------------------------------
186template<typename DT, typename OT, typename PT>
188Basis_HDIV_TRI_In_FEM( const ordinal_type order,
189 const EPointType pointType ) {
190 // Note: the only reason why equispaced can't support higher order than Parameters::MaxOrder appears to be the fact that the tags below get stored into a fixed-length array.
191 // TODO: relax the maximum order requirement by setting up tags in a different container, perhaps directly into an OrdinalTypeArray1DHost (tagView, below). (As of this writing (1/25/22), looks like other nodal bases do this in a similar way -- those should be fixed at the same time; maybe search for Parameters::MaxOrder.)
192 INTREPID2_TEST_FOR_EXCEPTION( order > Parameters::MaxOrder, std::invalid_argument, "polynomial order exceeds the max supported by this class");
193
194 constexpr ordinal_type spaceDim = 2;
195 this->basisCardinality_ = CardinalityHDivTri(order);
196 this->basisDegree_ = order; // small n
197 this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
198 this->basisType_ = BASIS_FEM_LAGRANGIAN;
199 this->basisCoordinates_ = COORDINATES_CARTESIAN;
200 this->functionSpace_ = FUNCTION_SPACE_HDIV;
201 pointType_ = (pointType == POINTTYPE_DEFAULT) ? POINTTYPE_EQUISPACED : pointType;
202
203 const ordinal_type card = this->basisCardinality_;
204
205 const ordinal_type cardPn = Intrepid2::getPnCardinality<spaceDim>(order); // dim of (P_{n}) -- smaller space
206 const ordinal_type cardPnm1 = Intrepid2::getPnCardinality<spaceDim>(order-1); // dim of (P_{n-1}) -- smaller space
207 const ordinal_type cardPnm2 = Intrepid2::getPnCardinality<spaceDim>(order-2); // dim of (P_{n-2}) -- smaller space
208 const ordinal_type cardVecPn = spaceDim*cardPn; // dim of (P_{n})^2 -- larger space
209 const ordinal_type cardVecPnm1 = spaceDim*cardPnm1; // dim of (P_{n-1})^2 -- smaller space
210
211
212 // Basis-dependent initializations
213 constexpr ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
214 constexpr ordinal_type maxCard = CardinalityHDivTri(Parameters::MaxOrder);
215 ordinal_type tags[maxCard][tagSize];
216
217 // points are computed in the host and will be copied
218 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
219 dofCoords("Hdiv::Tri::In::dofCoords", card, spaceDim);
220
221 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
222 dofCoeffs("Hdiv::Tri::In::dofCoeffs", card, spaceDim);
223
224 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
225 coeffs("Hdiv::Tri::In::coeffs", cardVecPn, card);
226
227 // first, need to project the basis for RT space onto the
228 // orthogonal basis of degree n
229 // get coefficients of PkHx
230
231 const ordinal_type lwork = card*card;
232 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
233 V1("Hdiv::Tri::In::V1", cardVecPn, card);
234
235 // basis for the space is
236 // { (phi_i,0) }_{i=0}^{cardPnm1-1} ,
237 // { (0,phi_i) }_{i=0}^{cardPnm1-1} ,
238 // { (x,y) . phi_i}_{i=cardPnm2}^{cardPnm1-1}
239 // columns of V1 are expansion of this basis in terms of the basis
240 // for P_{n}^2
241
242 // these two loops get the first two sets of basis functions
243 for (ordinal_type i=0;i<cardPnm1;i++) {
244 V1(i,i) = 1.0;
245 V1(cardPn+i,cardPnm1+i) = 1.0;
246 }
247
248 // now I need to integrate { (x,y) phi } against the big basis
249 // first, get a cubature rule.
251 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubPoints("Hdiv::Tri::In::cubPoints", myCub.getNumPoints() , spaceDim );
252 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubWeights("Hdiv::Tri::In::cubWeights", myCub.getNumPoints() );
253 myCub.getCubature( cubPoints , cubWeights );
254
255 // tabulate the scalar orthonormal basis at cubature points
256 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtCubPoints("Hdiv::Tri::In::phisAtCubPoints", cardPn , myCub.getNumPoints() );
257 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtCubPoints, cubPoints, order, OPERATOR_VALUE);
258
259 // now do the integration
260 for (ordinal_type i=0;i<order;i++) {
261 for (ordinal_type j=0;j<cardPn;j++) { // int (x,y) phi_i \cdot (phi_j,phi_{j+cardPn})
262 V1(j,cardVecPnm1+i) = 0.0;
263 for (ordinal_type d=0; d< spaceDim; ++d)
264 for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
265 V1(j+d*cardPn,cardVecPnm1+i) +=
266 cubWeights(k) * cubPoints(k,d)
267 * phisAtCubPoints(cardPnm2+i,k)
268 * phisAtCubPoints(j,k);
269 }
270 }
271 }
272
273 // next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
274 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
275 V2("Hdiv::Tri::In::V2", card ,cardVecPn);
276
277 const ordinal_type numEdges = this->basisCellTopology_.getEdgeCount();
278
279 shards::CellTopology edgeTop(shards::getCellTopologyData<shards::Line<2> >() );
280
281 const int numPtsPerEdge = PointTools::getLatticeSize( edgeTop ,
282 order+1 ,
283 1 );
284
285 // first numEdges * degree nodes are normals at each edge
286 // get the points on the line
287 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> linePts("Hdiv::Tri::In::linePts", numPtsPerEdge , 1 );
288
289 // construct lattice
290 const ordinal_type offset = 1;
291 PointTools::getLattice( linePts,
292 edgeTop,
293 order+1, offset,
294 pointType_ );
295
296 // holds the image of the line points
297 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> edgePts("Hdiv::Tri::In::edgePts", numPtsPerEdge , spaceDim );
298 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtEdgePoints("Hdiv::Tri::In::phisAtEdgePoints", cardPn , numPtsPerEdge );
299 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> edgeNormal("Hcurl::Tri::In::edgeNormal", spaceDim );
300
301 // these are normal scaled by the appropriate edge lengths.
302 for (ordinal_type edge=0;edge<numEdges;edge++) { // loop over edges
304 edge ,
305 this->basisCellTopology_ );
306
308 linePts ,
309 1 ,
310 edge ,
311 this->basisCellTopology_ );
312
313 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtEdgePoints , edgePts, order, OPERATOR_VALUE);
314
315 // loop over points (rows of V2)
316 for (ordinal_type j=0;j<numPtsPerEdge;j++) {
317
318 const ordinal_type i_card = numPtsPerEdge*edge+j;
319
320 // loop over orthonormal basis functions (columns of V2)
321 for (ordinal_type k=0;k<cardPn;k++) {
322 // loop over space dimension
323 for (ordinal_type l=0; l<spaceDim; l++)
324 V2(i_card,k+l*cardPn) = edgeNormal(l) * phisAtEdgePoints(k,j);
325 }
326
327
328 //save dof coordinates and coefficients
329 for(ordinal_type l=0; l<spaceDim; ++l) {
330 dofCoords(i_card,l) = edgePts(j,l);
331 dofCoeffs(i_card,l) = edgeNormal(l);
332 }
333
334 tags[i_card][0] = 1; // edge dof
335 tags[i_card][1] = edge; // edge id
336 tags[i_card][2] = j; // local dof id
337 tags[i_card][3] = numPtsPerEdge; // total vert dof
338
339 }
340
341
342 }
343
344 // remaining nodes are divided into two pieces: point value of x
345 // components and point values of y components. These are
346 // evaluated at the interior of a lattice of degree + 1, For then
347 // the degree == 1 space corresponds classicaly to RT0 and so gets
348 // no internal nodes, and degree == 2 corresponds to RT1 and needs
349 // one internal node per vector component.
350 const ordinal_type numPtsPerCell = PointTools::getLatticeSize( this->basisCellTopology_ ,
351 order + 1 ,
352 1 );
353
354 if (numPtsPerCell > 0) {
355 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
356 internalPoints( "Hdiv::Tri::In::internalPoints", numPtsPerCell , spaceDim );
357 PointTools::getLattice( internalPoints ,
358 this->basisCellTopology_ ,
359 order + 1 ,
360 1 ,
361 pointType_ );
362
363 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
364 phisAtInternalPoints("Hdiv::Tri::In::phisAtInternalPoints", cardPn , numPtsPerCell );
365 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>( phisAtInternalPoints , internalPoints , order, OPERATOR_VALUE );
366
367 // copy values into right positions of V2
368 for (ordinal_type j=0;j<numPtsPerCell;j++) {
369
370 const ordinal_type i_card = numEdges*order+spaceDim*j;
371
372 for (ordinal_type k=0;k<cardPn;k++) {
373 for (ordinal_type l=0;l<spaceDim;l++) {
374 V2(i_card+l,l*cardPn+k) = phisAtInternalPoints(k,j);
375 }
376 }
377
378 //save dof coordinates and coefficients
379 for(ordinal_type d=0; d<spaceDim; ++d) {
380 for(ordinal_type l=0; l<spaceDim; ++l) {
381 dofCoords(i_card+d,l) = internalPoints(j,l);
382 dofCoeffs(i_card+d,l) = (l==d);
383 }
384
385 tags[i_card+d][0] = spaceDim; // elem dof
386 tags[i_card+d][1] = 0; // elem id
387 tags[i_card+d][2] = spaceDim*j+d; // local dof id
388 tags[i_card+d][3] = spaceDim*numPtsPerCell; // total vert dof
389 }
390 }
391 }
392
393 // form Vandermonde matrix. Actually, this is the transpose of the VDM,
394 // so we transpose on copy below.
395 Kokkos::DynRankView<scalarType,Kokkos::LayoutLeft,Kokkos::HostSpace>
396 vmat("Hdiv::Tri::In::vmat", card, card),
397 work("Hdiv::Tri::In::work", lwork),
398 ipiv("Hdiv::Tri::In::ipiv", card);
399
400 //vmat' = V2*V1;
401 for(ordinal_type i=0; i< card; ++i) {
402 for(ordinal_type j=0; j< card; ++j) {
403 scalarType s=0;
404 for(ordinal_type k=0; k< cardVecPn; ++k)
405 s += V2(i,k)*V1(k,j);
406 vmat(i,j) = s;
407 }
408 }
409
410 ordinal_type info = 0;
411 Teuchos::LAPACK<ordinal_type,scalarType> lapack;
412
413 lapack.GETRF(card, card,
414 vmat.data(), vmat.stride_1(),
415 (ordinal_type*)ipiv.data(),
416 &info);
417
418 INTREPID2_TEST_FOR_EXCEPTION( info != 0,
419 std::runtime_error ,
420 ">>> ERROR: (Intrepid2::Basis_HDIV_TRI_In_FEM) lapack.GETRF returns nonzero info." );
421
422 lapack.GETRI(card,
423 vmat.data(), vmat.stride_1(),
424 (ordinal_type*)ipiv.data(),
425 work.data(), lwork,
426 &info);
427
428 INTREPID2_TEST_FOR_EXCEPTION( info != 0,
429 std::runtime_error ,
430 ">>> ERROR: (Intrepid2::Basis_HDIV_TRI_In_FEM) lapack.GETRI returns nonzero info." );
431
432 for (ordinal_type i=0;i<cardVecPn;++i)
433 for (ordinal_type j=0;j<card;++j){
434 scalarType s=0;
435 for(ordinal_type k=0; k< card; ++k)
436 s += V1(i,k)*vmat(k,j);
437 coeffs(i,j) = s;
438 }
439
440 this->coeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), coeffs);
441 Kokkos::deep_copy(this->coeffs_ , coeffs);
442
443 this->dofCoords_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoords);
444 Kokkos::deep_copy(this->dofCoords_, dofCoords);
445
446 this->dofCoeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoeffs);
447 Kokkos::deep_copy(this->dofCoeffs_, dofCoeffs);
448
449
450 // set tags
451 {
452 // Basis-dependent initializations
453 const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
454 const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
455 const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
456
457 OrdinalTypeArray1DHost tagView(&tags[0][0], card*tagSize);
458
459 // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
460 // tags are constructed on host
461 this->setOrdinalTagData(this->tagToOrdinal_,
462 this->ordinalToTag_,
463 tagView,
464 this->basisCardinality_,
465 tagSize,
466 posScDim,
467 posScOrd,
468 posDfOrd);
469 }
470}
471} // namespace Intrepid2
472#endif
Header file for the Intrepid2::CubatureDirectTriDefault class.
Header file for the Intrepid2::Basis_HGRAD_TRI_Cn_FEM_ORTH class.
Basis_HDIV_TRI_In_FEM(const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
Constructor.
static void mapToReferenceSubcell(Kokkos::DynRankView< refSubcellPointValueType, refSubcellPointProperties... > refSubcellPoints, const Kokkos::DynRankView< paramPointValueType, paramPointProperties... > paramPoints, const ordinal_type subcellDim, const ordinal_type subcellOrd, const shards::CellTopology parentCell)
Computes parameterization maps of 1- and 2-subcells of reference cells.
static void getReferenceSideNormal(Kokkos::DynRankView< refSideNormalValueType, refSideNormalProperties... > refSideNormal, const ordinal_type sideOrd, const shards::CellTopology parentCell)
Computes constant normal vectors to sides of 2D or 3D reference cells.
Defines direct integration rules on a triangle.
virtual void getCubature(PointViewType cubPoints, weightViewType cubWeights) const override
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).
virtual ordinal_type getNumPoints() const override
Returns the number of cubature points.
static constexpr ordinal_type MaxOrder
The maximum reconstruction order.
static ordinal_type getLatticeSize(const shards::CellTopology cellType, const ordinal_type order, const ordinal_type offset=0)
Computes the number of points in a lattice of a given order on a simplex (currently disabled for othe...
static void getLattice(Kokkos::DynRankView< pointValueType, pointProperties... > points, const shards::CellTopology cellType, const ordinal_type order, const ordinal_type offset=0, const EPointType pointType=POINTTYPE_EQUISPACED)
Computes a lattice of points of a given order on a reference simplex, quadrilateral or hexahedron (cu...