Intrepid2
Intrepid2_HCURL_TRI_In_FEMDef.hpp
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49#ifndef __INTREPID2_HCURL_TRI_IN_FEM_DEF_HPP__
50#define __INTREPID2_HCURL_TRI_IN_FEM_DEF_HPP__
51
54
55namespace Intrepid2 {
56
57 // -------------------------------------------------------------------------------------
58
59 namespace Impl {
60
61 template<EOperator opType>
62 template<typename OutputViewType,
63 typename inputViewType,
64 typename workViewType,
65 typename vinvViewType>
66 KOKKOS_INLINE_FUNCTION
67 void
68 Basis_HCURL_TRI_In_FEM::Serial<opType>::
69 getValues( OutputViewType output,
70 const inputViewType input,
71 workViewType work,
72 const vinvViewType coeffs ) {
73
74 constexpr ordinal_type spaceDim = 2;
75 const ordinal_type
76 cardPn = coeffs.extent(0)/spaceDim,
77 card = coeffs.extent(1),
78 npts = input.extent(0);
79
80 // compute order
81 ordinal_type order = 0;
82 for (ordinal_type p=0;p<=Parameters::MaxOrder;++p) {
83 if (card == CardinalityHCurlTri(p)) {
84 order = p;
85 break;
86 }
87 }
88
89 typedef typename Kokkos::DynRankView<typename workViewType::value_type, typename workViewType::memory_space> viewType;
90 auto vcprop = Kokkos::common_view_alloc_prop(work);
91 auto ptr = work.data();
92
93 switch (opType) {
94 case OPERATOR_VALUE: {
95 const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts);
96 workViewType dummyView;
97
98 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
99 Serial<opType>::getValues(phis, input, dummyView, order);
100
101 for (ordinal_type i=0;i<card;++i)
102 for (ordinal_type j=0;j<npts;++j)
103 for (ordinal_type d=0;d<spaceDim;++d) {
104 output.access(i,j,d) = 0.0;
105 for (ordinal_type k=0;k<cardPn;++k)
106 output.access(i,j,d) += coeffs(k+d*cardPn,i) * phis(k,j);
107 }
108 break;
109 }
110 case OPERATOR_CURL: {
111 const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim);
112 ptr += card*npts*spaceDim*get_dimension_scalar(work);
113 const viewType workView(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim+1);
114
115 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
116 Serial<OPERATOR_GRAD>::getValues(phis, input, workView, order);
117
118 for (ordinal_type i=0;i<card;++i)
119 for (ordinal_type j=0;j<npts;++j) {
120 output.access(i,j) = 0.0;
121 for (ordinal_type k=0; k<cardPn; ++k)
122 output.access(i,j) += - coeffs(k,i)*phis(k,j,1) // - dy of x component
123 + coeffs(k+cardPn,i)*phis(k,j,0); // dx of y component
124 }
125 break;
126 }
127 default: {
128 INTREPID2_TEST_FOR_ABORT( true,
129 ">>> ERROR (Basis_HCURL_TRI_In_FEM): Operator type not implemented");
130 }
131 }
132 }
133
134 template<typename DT, ordinal_type numPtsPerEval,
135 typename outputValueValueType, class ...outputValueProperties,
136 typename inputPointValueType, class ...inputPointProperties,
137 typename vinvValueType, class ...vinvProperties>
138 void
139 Basis_HCURL_TRI_In_FEM::
140 getValues( Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValues,
141 const Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPoints,
142 const Kokkos::DynRankView<vinvValueType, vinvProperties...> coeffs,
143 const EOperator operatorType) {
144 typedef Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValueViewType;
145 typedef Kokkos::DynRankView<inputPointValueType, inputPointProperties...> inputPointViewType;
146 typedef Kokkos::DynRankView<vinvValueType, vinvProperties...> vinvViewType;
147 typedef typename ExecSpace<typename inputPointViewType::execution_space,typename DT::execution_space>::ExecSpaceType ExecSpaceType;
148
149 // loopSize corresponds to cardinality
150 const auto loopSizeTmp1 = (inputPoints.extent(0)/numPtsPerEval);
151 const auto loopSizeTmp2 = (inputPoints.extent(0)%numPtsPerEval != 0);
152 const auto loopSize = loopSizeTmp1 + loopSizeTmp2;
153 Kokkos::RangePolicy<ExecSpaceType,Kokkos::Schedule<Kokkos::Static> > policy(0, loopSize);
154
155 typedef typename inputPointViewType::value_type inputPointType;
156
157 const ordinal_type cardinality = outputValues.extent(0);
158 const ordinal_type spaceDim = 2;
159
160 auto vcprop = Kokkos::common_view_alloc_prop(inputPoints);
161 typedef typename Kokkos::DynRankView< inputPointType, typename inputPointViewType::memory_space> workViewType;
162
163 switch (operatorType) {
164 case OPERATOR_VALUE: {
165 workViewType work(Kokkos::view_alloc("Basis_HCURL_TRI_In_FEM::getValues::work", vcprop), cardinality, inputPoints.extent(0));
166 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
167 OPERATOR_VALUE,numPtsPerEval> FunctorType;
168 Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, coeffs, work) );
169 break;
170 }
171 case OPERATOR_CURL: {
172 workViewType work(Kokkos::view_alloc("Basis_HCURL_TRI_In_FEM::getValues::work", vcprop), cardinality*(2*spaceDim+1), inputPoints.extent(0));
173 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
174 OPERATOR_CURL,numPtsPerEval> FunctorType;
175 Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, coeffs, work) );
176 break;
177 }
178 default: {
179 INTREPID2_TEST_FOR_EXCEPTION( true , std::invalid_argument,
180 ">>> ERROR (Basis_HCURL_TRI_In_FEM): Operator type not implemented" );
181 }
182 }
183 }
184 }
185
186 // -------------------------------------------------------------------------------------
187 template<typename DT, typename OT, typename PT>
189 Basis_HCURL_TRI_In_FEM( const ordinal_type order,
190 const EPointType pointType ) {
191
192 constexpr ordinal_type spaceDim = 2;
193 this->basisCardinality_ = CardinalityHCurlTri(order);
194 this->basisDegree_ = order; // small n
195 this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
196 this->basisType_ = BASIS_FEM_LAGRANGIAN;
197 this->basisCoordinates_ = COORDINATES_CARTESIAN;
198 this->functionSpace_ = FUNCTION_SPACE_HCURL;
199 pointType_ = (pointType == POINTTYPE_DEFAULT) ? POINTTYPE_EQUISPACED : pointType;
200
201 const ordinal_type card = this->basisCardinality_;
202
203 const ordinal_type cardPn = Intrepid2::getPnCardinality<spaceDim>(order); // dim of (P_{n}) -- smaller space
204 const ordinal_type cardPnm1 = Intrepid2::getPnCardinality<spaceDim>(order-1); // dim of (P_{n-1}) -- smaller space
205 const ordinal_type cardPnm2 = Intrepid2::getPnCardinality<spaceDim>(order-2); // dim of (P_{n-2}) -- smaller space
206 const ordinal_type cardVecPn = spaceDim*cardPn; // dim of (P_{n})^2 -- larger space
207 const ordinal_type cardVecPnm1 = spaceDim*cardPnm1; // dim of (P_{n-1})^2 -- smaller space
208
209 // 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.
210 // 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.)
211 INTREPID2_TEST_FOR_EXCEPTION( order > Parameters::MaxOrder, std::invalid_argument, "polynomial order exceeds the max supported by this class");
212
213 // Basis-dependent initializations
214 constexpr ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
215 constexpr ordinal_type maxCard = CardinalityHCurlTri(Parameters::MaxOrder);
216 ordinal_type tags[maxCard][tagSize];
217
218 // points are computed in the host and will be copied
219 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
220 dofCoords("Hcurl::Tri::In::dofCoords", card, spaceDim);
221
222 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
223 coeffs("Hcurl::Tri::In::coeffs", cardVecPn, card);
224
225 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
226 dofCoeffs("Hcurl::Tri::In::dofCoeffs", card, spaceDim);
227
228 // first, need to project the basis for RT space onto the
229 // orthogonal basis of degree n
230 // get coefficients of PkHx
231
232 const ordinal_type lwork = card*card;
233 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
234 V1("Hcurl::Tri::In::V1", cardVecPn, card);
235
236 // basis for the space is
237 // { (phi_i,0) }_{i=0}^{cardPnm1-1} ,
238 // { (0,phi_i) }_{i=0}^{cardPnm1-1} ,
239 // { (x,y) \times phi_i}_{i=cardPnm2}^{cardPnm1-1}
240 // { (x,y) \times phi = (y phi , -x \phi)
241 // columns of V1 are expansion of this basis in terms of the basis
242 // for P_{n}^2
243
244 // these two loops get the first two sets of basis functions
245 for (ordinal_type i=0;i<cardPnm1;i++)
246 for (ordinal_type d=0;d<spaceDim;d++)
247 V1(d*cardPn+i,d*cardPnm1+i) = 1.0;
248
249
250 // now I need to integrate { (x,y) \times phi } against the big basis
251 // first, get a cubature rule.
253 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubPoints("Hcurl::Tri::In::cubPoints", myCub.getNumPoints() , spaceDim );
254 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubWeights("Hcurl::Tri::In::cubWeights", myCub.getNumPoints() );
255 myCub.getCubature( cubPoints , cubWeights );
256
257 // tabulate the scalar orthonormal basis at cubature points
258 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtCubPoints("Hcurl::Tri::In::phisAtCubPoints", cardPn , myCub.getNumPoints() );
259 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtCubPoints, cubPoints, order, OPERATOR_VALUE);
260
261 // now do the integration
262 for (ordinal_type i=0;i<order;i++) {
263 for (ordinal_type j=0;j<cardPn;j++) { // int (x,y) phi_i \cdot (phi_j,phi_{j+cardPn})
264 for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
265 V1(j,cardVecPnm1+i) -=
266 cubWeights(k) * cubPoints(k,1)
267 * phisAtCubPoints(cardPnm2+i,k)
268 * phisAtCubPoints(j,k);
269 V1(j+cardPn,cardVecPnm1+i) +=
270 cubWeights(k) * cubPoints(k,0)
271 * phisAtCubPoints(cardPnm2+i,k)
272 * phisAtCubPoints(j,k);
273 }
274 }
275 }
276
277 // next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
278 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
279 V2("Hcurl::Tri::In::V2", card ,cardVecPn);
280
281 const ordinal_type numEdges = this->basisCellTopology_.getEdgeCount();
282
283 shards::CellTopology edgeTop(shards::getCellTopologyData<shards::Line<2> >() );
284
285 const int numPtsPerEdge = PointTools::getLatticeSize( edgeTop ,
286 order+1 ,
287 1 );
288
289 // first numEdges * degree nodes are tangents at each edge
290 // get the points on the line
291 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> linePts("Hcurl::Tri::In::linePts", numPtsPerEdge , 1 );
292
293 // construct lattice
294 const ordinal_type offset = 1;
295 PointTools::getLattice( linePts,
296 edgeTop,
297 order+1, offset,
298 pointType_ );
299
300 // holds the image of the line points
301 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> edgePts("Hcurl::Tri::In::edgePts", numPtsPerEdge , spaceDim );
302 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtEdgePoints("Hcurl::Tri::In::phisAtEdgePoints", cardPn , numPtsPerEdge );
303 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> edgeTan("Hcurl::Tri::In::edgeTan", spaceDim );
304
305 // these are tangents scaled by the appropriate edge lengths.
306 for (ordinal_type edge=0;edge<numEdges;edge++) { // loop over edges
308 edge ,
309 this->basisCellTopology_ );
310
312 linePts ,
313 1 ,
314 edge ,
315 this->basisCellTopology_ );
316
317 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtEdgePoints , edgePts, order, OPERATOR_VALUE);
318
319 // loop over points (rows of V2)
320 for (ordinal_type j=0;j<numPtsPerEdge;j++) {
321
322 const ordinal_type i_card = numPtsPerEdge*edge+j;
323
324 // loop over orthonormal basis functions (columns of V2)
325 for (ordinal_type k=0;k<cardPn;k++) {
326 V2(i_card,k) = edgeTan(0) * phisAtEdgePoints(k,j);
327 V2(i_card,k+cardPn) = edgeTan(1) * phisAtEdgePoints(k,j);
328 }
329
330
331 //save dof coordinates
332 for(ordinal_type k=0; k<spaceDim; ++k) {
333 dofCoords(i_card,k) = edgePts(j,k);
334 dofCoeffs(i_card,k) = edgeTan(k);
335 }
336
337 tags[i_card][0] = 1; // edge dof
338 tags[i_card][1] = edge; // edge id
339 tags[i_card][2] = j; // local dof id
340 tags[i_card][3] = numPtsPerEdge; // total edge dof
341
342 }
343
344
345 }
346
347 // remaining nodes are x- and y- components at internal points (this code is same as HDIV).
348 //These are evaluated at the interior of a lattice of degree + 1, For then
349 // the degree == 1 space corresponds classicaly to RT0 and so gets
350 // no internal nodes, and degree == 2 corresponds to RT1 and needs
351 // one internal node per vector component.
352 const ordinal_type numPtsPerCell = PointTools::getLatticeSize( this->basisCellTopology_ ,
353 order + 1 ,
354 1 );
355
356 if (numPtsPerCell > 0) {
357 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
358 internalPoints( "Hcurl::Tri::In::internalPoints", numPtsPerCell , spaceDim );
359 PointTools::getLattice( internalPoints ,
360 this->basisCellTopology_ ,
361 order + 1 ,
362 1 ,
363 pointType_ );
364
365 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
366 phisAtInternalPoints("Hcurl::Tri::In::phisAtInternalPoints", cardPn , numPtsPerCell );
367 Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>( phisAtInternalPoints , internalPoints , order, OPERATOR_VALUE );
368
369 // copy values into right positions of V2
370 for (ordinal_type j=0;j<numPtsPerCell;j++) {
371
372 const ordinal_type i_card = numEdges*order+spaceDim*j;
373
374 for (ordinal_type k=0;k<cardPn;k++) {
375 // x component
376 V2(i_card,k) = phisAtInternalPoints(k,j);
377 // y component
378 V2(i_card+1,cardPn+k) = phisAtInternalPoints(k,j);
379 }
380
381 //save dof coordinates
382 for(ordinal_type d=0; d<spaceDim; ++d) {
383 for(ordinal_type dim=0; dim<spaceDim; ++dim) {
384 dofCoords(i_card+d,dim) = internalPoints(j,dim);
385 dofCoeffs(i_card+d,dim) = (d==dim);
386 }
387
388 tags[i_card+d][0] = spaceDim; // elem dof
389 tags[i_card+d][1] = 0; // elem id
390 tags[i_card+d][2] = spaceDim*j+d; // local dof id
391 tags[i_card+d][3] = spaceDim*numPtsPerCell; // total vert dof
392 }
393 }
394 }
395
396 // form Vandermonde matrix. Actually, this is the transpose of the VDM,
397 // so we transpose on copy below.
398 Kokkos::DynRankView<scalarType,Kokkos::LayoutLeft,Kokkos::HostSpace>
399 vmat("Hcurl::Tri::In::vmat", card, card),
400 work("Hcurl::Tri::In::work", lwork),
401 ipiv("Hcurl::Tri::In::ipiv", card);
402
403 //vmat' = V2*V1;
404 for(ordinal_type i=0; i< card; ++i) {
405 for(ordinal_type j=0; j< card; ++j) {
406 scalarType s=0;
407 for(ordinal_type k=0; k< cardVecPn; ++k)
408 s += V2(i,k)*V1(k,j);
409 vmat(i,j) = s;
410 }
411 }
412
413 ordinal_type info = 0;
414 Teuchos::LAPACK<ordinal_type,scalarType> lapack;
415
416 lapack.GETRF(card, card,
417 vmat.data(), vmat.stride_1(),
418 (ordinal_type*)ipiv.data(),
419 &info);
420
421 INTREPID2_TEST_FOR_EXCEPTION( info != 0,
422 std::runtime_error ,
423 ">>> ERROR: (Intrepid2::Basis_HCURL_TRI_In_FEM) lapack.GETRF returns nonzero info." );
424
425 lapack.GETRI(card,
426 vmat.data(), vmat.stride_1(),
427 (ordinal_type*)ipiv.data(),
428 work.data(), lwork,
429 &info);
430
431 INTREPID2_TEST_FOR_EXCEPTION( info != 0,
432 std::runtime_error ,
433 ">>> ERROR: (Intrepid2::Basis_HCURL_TRI_In_FEM) lapack.GETRI returns nonzero info." );
434
435 for (ordinal_type i=0;i<cardVecPn;++i)
436 for (ordinal_type j=0;j<card;++j){
437 scalarType s=0;
438 for(ordinal_type k=0; k< card; ++k)
439 s += V1(i,k)*vmat(k,j);
440 coeffs(i,j) = s;
441 }
442
443 this->coeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), coeffs);
444 Kokkos::deep_copy(this->coeffs_ , coeffs);
445
446 this->dofCoords_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoords);
447 Kokkos::deep_copy(this->dofCoords_, dofCoords);
448
449 this->dofCoeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoeffs);
450 Kokkos::deep_copy(this->dofCoeffs_, dofCoeffs);
451
452
453 // set tags
454 {
455 // Basis-dependent initializations
456 const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
457 const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
458 const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
459
460 OrdinalTypeArray1DHost tagView(&tags[0][0], card*tagSize);
461
462 // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
463 // tags are constructed on host
464 this->setOrdinalTagData(this->tagToOrdinal_,
465 this->ordinalToTag_,
466 tagView,
467 this->basisCardinality_,
468 tagSize,
469 posScDim,
470 posScOrd,
471 posDfOrd);
472 }
473 }
474} // namespace Intrepid2
475#endif
Header file for the Intrepid2::CubatureDirectTriDefault class.
Header file for the Intrepid2::Basis_HGRAD_TRI_Cn_FEM_ORTH class.
Basis_HCURL_TRI_In_FEM(const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
Constructor.
static void getReferenceEdgeTangent(Kokkos::DynRankView< refEdgeTangentValueType, refEdgeTangentProperties... > refEdgeTangent, const ordinal_type edgeOrd, const shards::CellTopology parentCell)
Computes constant tangent vectors to edges of 2D or 3D reference cells.
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.
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...