Intrepid2
Intrepid2_HDIV_TET_In_FEMDef.hpp
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49#ifndef __INTREPID2_HDIV_TET_IN_FEM_DEF_HPP__
50#define __INTREPID2_HDIV_TET_IN_FEM_DEF_HPP__
51
54
55namespace Intrepid2 {
56
57// -------------------------------------------------------------------------------------
58
59namespace Impl {
60
61template<EOperator opType>
62template<typename OutputViewType,
63typename inputViewType,
64typename workViewType,
65typename vinvViewType>
66KOKKOS_INLINE_FUNCTION
67void
68Basis_HDIV_TET_In_FEM::Serial<opType>::
69getValues( OutputViewType output,
70 const inputViewType input,
71 workViewType work,
72 const vinvViewType coeffs ) {
73
74 constexpr ordinal_type spaceDim = 3;
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 == CardinalityHDivTet(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_TET_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.access(k,j);
107 }
108 break;
109 }
110 case OPERATOR_DIV: {
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_TET_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 for (ordinal_type d=0; d<spaceDim; ++d)
123 output.access(i,j) += coeffs(k+d*cardPn,i)*phis.access(k,j,d);
124 }
125 break;
126 }
127 default: {
128 INTREPID2_TEST_FOR_ABORT( true,
129 ">>> ERROR (Basis_HDIV_TET_In_FEM): Operator type not implemented");
130 }
131 }
132}
133
134template<typename DT, ordinal_type numPtsPerEval,
135typename outputValueValueType, class ...outputValueProperties,
136typename inputPointValueType, class ...inputPointProperties,
137typename vinvValueType, class ...vinvProperties>
138void
139Basis_HDIV_TET_In_FEM::
140getValues( /* */ 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 = 3;
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_HDIV_TET_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_DIV: {
172 workViewType work(Kokkos::view_alloc("Basis_HDIV_TET_In_FEM::getValues::work", vcprop), cardinality*(2*spaceDim+1), inputPoints.extent(0));
173 typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
174 OPERATOR_DIV,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_HDIV_TET_In_FEM): Operator type not implemented" );
181 }
182 }
183}
184}
185
186// -------------------------------------------------------------------------------------
187template<typename DT, typename OT, typename PT>
189Basis_HDIV_TET_In_FEM( const ordinal_type order,
190 const EPointType pointType ) {
191
192 constexpr ordinal_type spaceDim = 3;
193 this->basisCardinality_ = CardinalityHDivTet(order);
194 this->basisDegree_ = order; // small n
195 this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Tetrahedron<4> >() );
196 this->basisType_ = BASIS_FEM_LAGRANGIAN;
197 this->basisCoordinates_ = COORDINATES_CARTESIAN;
198 this->functionSpace_ = FUNCTION_SPACE_HDIV;
199 pointType_ = 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})^3 -- larger space
207 const ordinal_type cardVecPnm1 = spaceDim*cardPnm1; // dim of (P_{n-1})^3 -- smaller space
208 const ordinal_type dim_PkH = cardPnm1 - cardPnm2;
209
210 // 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.
211 // 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.)
212 INTREPID2_TEST_FOR_EXCEPTION( order > Parameters::MaxOrder, std::invalid_argument, "polynomial order exceeds the max supported by this class");
213
214 // Basis-dependent initializations
215 constexpr ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
216 constexpr ordinal_type maxCard = CardinalityHDivTet(Parameters::MaxOrder);
217 ordinal_type tags[maxCard][tagSize];
218
219 // points are computed in the host and will be copied
220 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
221 dofCoords("Hdiv::Tet::In::dofCoords", card, spaceDim);
222
223 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
224 dofCoeffs("Hdiv::Tet::In::dofCoeffs", card, spaceDim);
225
226 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
227 coeffs("Hdiv::Tet::In::coeffs", cardVecPn, card);
228
229 // first, need to project the basis for RT space onto the
230 // orthogonal basis of degree n
231 // get coefficients of PkHx
232
233 const ordinal_type lwork = card*card;
234 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
235 V1("Hdiv::Tet::In::V1", cardVecPn, card);
236
237 // basis for the space is
238 // { (phi_i,0,0) }_{i=0}^{cardPnm1-1} ,
239 // { (0,phi_i,0) }_{i=0}^{cardPnm1-1} ,
240 // { (0,0,phi_i) }_{i=0}^{cardPnm1-1} ,
241 // { (x,y) . phi_i}_{i=cardPnm2}^{cardPnm1-1}
242 // columns of V1 are expansion of this basis in terms of the orthogonal basis
243 // for P_{n}^3
244
245 // these two loops get the first two sets of basis functions
246 for (ordinal_type i=0;i<cardPnm1;i++) {
247 for (ordinal_type k=0; k<3;k++) {
248 V1(k*cardPn+i,k*cardPnm1+i) = 1.0;
249 }
250 }
251
252 // now I need to integrate { (x,y,z) phi } against the big basis
253 // first, get a cubature rule.
255 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubPoints("Hdiv::Tet::In::cubPoints", myCub.getNumPoints() , spaceDim );
256 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubWeights("Hdiv::Tet::In::cubWeights", myCub.getNumPoints() );
257 myCub.getCubature( cubPoints , cubWeights );
258
259 // tabulate the scalar orthonormal basis at cubature points
260 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtCubPoints("Hdiv::Tet::In::phisAtCubPoints", cardPn , myCub.getNumPoints() );
261 Impl::Basis_HGRAD_TET_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtCubPoints, cubPoints, order, OPERATOR_VALUE);
262
263 // now do the integration
264 for (ordinal_type i=0;i<dim_PkH;i++) {
265 for (ordinal_type j=0;j<cardPn;j++) { // int (x,y,z) phi_i \cdot (phi_j,0,0)
266 V1(j,cardVecPnm1+i) = 0.0;
267 for (ordinal_type d=0; d< spaceDim; ++d)
268 for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
269 V1(j+d*cardPn,cardVecPnm1+i) +=
270 cubWeights(k) * cubPoints(k,d)
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)^3 (columns)
278 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
279 V2("Hdiv::Tet::In::V2", card ,cardVecPn);
280
281 const ordinal_type numFaces = this->basisCellTopology_.getFaceCount();
282
283 shards::CellTopology faceTop(shards::getCellTopologyData<shards::Triangle<3> >() );
284
285 const int numPtsPerFace = PointTools::getLatticeSize( faceTop ,
286 order+2 ,
287 1 );
288
289 // get the points on the tetrahedron face
290 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> triPts("Hdiv::Tet::In::triPts", numPtsPerFace , 2 );
291
292 // construct lattice
293 const ordinal_type offset = 1;
295 faceTop,
296 order+2,
297 offset,
298 pointType );
299
300 // holds the image of the tet points
301 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> facePts("Hdiv::Tet::In::facePts", numPtsPerFace , spaceDim );
302 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtFacePoints("Hdiv::Tet::In::phisAtFacePoints", cardPn , numPtsPerFace );
303 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> faceNormal("Hcurl::Tet::In::faceNormal", spaceDim );
304
305 // loop over faces
306 for (ordinal_type face=0;face<numFaces;face++) { // loop over faces
307
308 // these are normal scaled by the appropriate face areas.
310 face ,
311 this->basisCellTopology_ );
312
314 triPts ,
315 2 ,
316 face ,
317 this->basisCellTopology_ );
318
319 // get phi values at face points
320 Impl::Basis_HGRAD_TET_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtFacePoints, facePts, order, OPERATOR_VALUE);
321
322 // loop over points (rows of V2)
323 for (ordinal_type j=0;j<numPtsPerFace;j++) {
324
325 const ordinal_type i_card = numPtsPerFace*face+j;
326
327 // loop over orthonormal basis functions (columns of V2)
328 for (ordinal_type k=0;k<cardPn;k++) {
329 // loop over space dimension
330 for (ordinal_type l=0; l<spaceDim; l++)
331 V2(i_card,k+l*cardPn) = faceNormal(l) * phisAtFacePoints(k,j);
332 }
333
334 //save dof coordinates and coefficients
335 for(ordinal_type l=0; l<spaceDim; ++l) {
336 dofCoords(i_card,l) = facePts(j,l);
337 dofCoeffs(i_card,l) = faceNormal(l);
338 }
339
340 tags[i_card][0] = 2; // face dof
341 tags[i_card][1] = face; // face id
342 tags[i_card][2] = j; // local dof id
343 tags[i_card][3] = numPtsPerFace; // total vert dof
344
345 }
346 }
347
348 // remaining nodes point values of each vector component on interior
349 // points of a lattice of degree+2
350 // This way, RT0 --> degree = 1 and internal lattice has no points
351 // RT1 --> degree = 2, and internal lattice has one point (inside of quartic)
352 const ordinal_type numPtsPerCell = PointTools::getLatticeSize( this->basisCellTopology_ ,
353 order + 2 ,
354 1 );
355
356 if (numPtsPerCell > 0) {
357 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
358 internalPoints( "Hdiv::Tet::In::internalPoints", numPtsPerCell , spaceDim );
359 PointTools::getLattice( internalPoints ,
360 this->basisCellTopology_ ,
361 order + 2 ,
362 1 ,
363 pointType );
364
365 Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
366 phisAtInternalPoints("Hdiv::Tet::In::phisAtInternalPoints", cardPn , numPtsPerCell );
367 Impl::Basis_HGRAD_TET_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 = numFaces*numPtsPerFace+spaceDim*j;
373
374 for (ordinal_type k=0;k<cardPn;k++) {
375 for (ordinal_type l=0;l<spaceDim;l++) {
376 V2(i_card+l,l*cardPn+k) = phisAtInternalPoints(k,j);
377 }
378 }
379
380 //save dof coordinates and coefficients
381 for(ordinal_type d=0; d<spaceDim; ++d) {
382 for(ordinal_type l=0; l<spaceDim; ++l) {
383 dofCoords(i_card+d,l) = internalPoints(j,l);
384 dofCoeffs(i_card+d,l) = (l==d);
385 }
386
387 tags[i_card+d][0] = spaceDim; // elem dof
388 tags[i_card+d][1] = 0; // elem id
389 tags[i_card+d][2] = spaceDim*j+d; // local dof id
390 tags[i_card+d][3] = spaceDim*numPtsPerCell; // total vert dof
391 }
392 }
393 }
394
395 // form Vandermonde matrix. Actually, this is the transpose of the VDM,
396 // so we transpose on copy below.
397 Kokkos::DynRankView<scalarType,Kokkos::LayoutLeft,Kokkos::HostSpace>
398 vmat("Hdiv::Tet::In::vmat", card, card),
399 work("Hdiv::Tet::In::work", lwork),
400 ipiv("Hdiv::Tet::In::ipiv", card);
401
402 //vmat' = V2*V1;
403 for(ordinal_type i=0; i< card; ++i) {
404 for(ordinal_type j=0; j< card; ++j) {
405 scalarType s=0;
406 for(ordinal_type k=0; k< cardVecPn; ++k)
407 s += V2(i,k)*V1(k,j);
408 vmat(i,j) = s;
409 }
410 }
411
412 ordinal_type info = 0;
413 Teuchos::LAPACK<ordinal_type,scalarType> lapack;
414
415 lapack.GETRF(card, card,
416 vmat.data(), vmat.stride_1(),
417 (ordinal_type*)ipiv.data(),
418 &info);
419
420 INTREPID2_TEST_FOR_EXCEPTION( info != 0,
421 std::runtime_error ,
422 ">>> ERROR: (Intrepid2::Basis_HDIV_TET_In_FEM) lapack.GETRF returns nonzero info." );
423
424 lapack.GETRI(card,
425 vmat.data(), vmat.stride_1(),
426 (ordinal_type*)ipiv.data(),
427 work.data(), lwork,
428 &info);
429
430 INTREPID2_TEST_FOR_EXCEPTION( info != 0,
431 std::runtime_error ,
432 ">>> ERROR: (Intrepid2::Basis_HDIV_TET_In_FEM) lapack.GETRI returns nonzero info." );
433
434 for (ordinal_type i=0;i<cardVecPn;++i)
435 for (ordinal_type j=0;j<card;++j){
436 scalarType s=0;
437 for(ordinal_type k=0; k< card; ++k)
438 s += V1(i,k)*vmat(k,j);
439 coeffs(i,j) = s;
440 }
441
442 this->coeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), coeffs);
443 Kokkos::deep_copy(this->coeffs_ , coeffs);
444
445 this->dofCoords_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoords);
446 Kokkos::deep_copy(this->dofCoords_, dofCoords);
447
448 this->dofCoeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoeffs);
449 Kokkos::deep_copy(this->dofCoeffs_, dofCoeffs);
450
451
452 // set tags
453 {
454 // Basis-dependent initializations
455 const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
456 const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
457 const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
458
459 OrdinalTypeArray1DHost tagView(&tags[0][0], card*tagSize);
460
461 // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
462 // tags are constructed on host
463 this->setOrdinalTagData(this->tagToOrdinal_,
464 this->ordinalToTag_,
465 tagView,
466 this->basisCardinality_,
467 tagSize,
468 posScDim,
469 posScOrd,
470 posDfOrd);
471 }
472}
473} // namespace Intrepid2
474#endif
Header file for the Intrepid2::CubatureDirectTetDefault class.
Header file for the Intrepid2::Basis_HGRAD_TET_Cn_FEM_ORTH class.
Basis_HDIV_TET_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 tetrahedron.
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...