Intrepid2
Intrepid2_HDIV_TRI_In_FEMDef.hpp
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42 
49 #ifndef __INTREPID2_HDIV_TRI_IN_FEM_DEF_HPP__
50 #define __INTREPID2_HDIV_TRI_IN_FEM_DEF_HPP__
51 
54 
55 namespace Intrepid2 {
56 
57 // -------------------------------------------------------------------------------------
58 namespace Impl {
59 
60 template<EOperator opType>
61 template<typename OutputViewType,
62 typename inputViewType,
63 typename workViewType,
64 typename vinvViewType>
65 KOKKOS_INLINE_FUNCTION
66 void
67 Basis_HDIV_TRI_In_FEM::Serial<opType>::
68 getValues( /* */ 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 
133 template<typename DT, ordinal_type numPtsPerEval,
134 typename outputValueValueType, class ...outputValueProperties,
135 typename inputPointValueType, class ...inputPointProperties,
136 typename vinvValueType, class ...vinvProperties>
137 void
138 Basis_HDIV_TRI_In_FEM::
139 getValues( /* */ 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 // -------------------------------------------------------------------------------------
186 template<typename DT, typename OT, typename PT>
188 Basis_HDIV_TRI_In_FEM( const ordinal_type order,
189  const EPointType pointType ) {
190  INTREPID2_TEST_FOR_EXCEPTION(order > Parameters::MaxOrder, std::invalid_argument, "Unsupported polynomial order");
191 
192  constexpr ordinal_type spaceDim = 2;
193  this->basisCardinality_ = CardinalityHDivTri(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_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})^2 -- larger space
207  const ordinal_type cardVecPnm1 = spaceDim*cardPnm1; // dim of (P_{n-1})^2 -- smaller space
208 
209 
210  // Basis-dependent initializations
211  constexpr ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
212  constexpr ordinal_type maxCard = CardinalityHDivTri(Parameters::MaxOrder);
213  ordinal_type tags[maxCard][tagSize];
214 
215  // points are computed in the host and will be copied
216  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
217  dofCoords("Hdiv::Tri::In::dofCoords", card, spaceDim);
218 
219  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
220  dofCoeffs("Hdiv::Tri::In::dofCoeffs", card, spaceDim);
221 
222  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
223  coeffs("Hdiv::Tri::In::coeffs", cardVecPn, card);
224 
225  // first, need to project the basis for RT space onto the
226  // orthogonal basis of degree n
227  // get coefficients of PkHx
228 
229  const ordinal_type lwork = card*card;
230  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
231  V1("Hdiv::Tri::In::V1", cardVecPn, card);
232 
233  // basis for the space is
234  // { (phi_i,0) }_{i=0}^{cardPnm1-1} ,
235  // { (0,phi_i) }_{i=0}^{cardPnm1-1} ,
236  // { (x,y) . phi_i}_{i=cardPnm2}^{cardPnm1-1}
237  // columns of V1 are expansion of this basis in terms of the basis
238  // for P_{n}^2
239 
240  // these two loops get the first two sets of basis functions
241  for (ordinal_type i=0;i<cardPnm1;i++) {
242  V1(i,i) = 1.0;
243  V1(cardPn+i,cardPnm1+i) = 1.0;
244  }
245 
246  // now I need to integrate { (x,y) phi } against the big basis
247  // first, get a cubature rule.
249  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubPoints("Hdiv::Tri::In::cubPoints", myCub.getNumPoints() , spaceDim );
250  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> cubWeights("Hdiv::Tri::In::cubWeights", myCub.getNumPoints() );
251  myCub.getCubature( cubPoints , cubWeights );
252 
253  // tabulate the scalar orthonormal basis at cubature points
254  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtCubPoints("Hdiv::Tri::In::phisAtCubPoints", cardPn , myCub.getNumPoints() );
255  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtCubPoints, cubPoints, order, OPERATOR_VALUE);
256 
257  // now do the integration
258  for (ordinal_type i=0;i<order;i++) {
259  for (ordinal_type j=0;j<cardPn;j++) { // int (x,y) phi_i \cdot (phi_j,phi_{j+cardPn})
260  V1(j,cardVecPnm1+i) = 0.0;
261  for (ordinal_type d=0; d< spaceDim; ++d)
262  for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
263  V1(j+d*cardPn,cardVecPnm1+i) +=
264  cubWeights(k) * cubPoints(k,d)
265  * phisAtCubPoints(cardPnm2+i,k)
266  * phisAtCubPoints(j,k);
267  }
268  }
269  }
270 
271  // next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
272  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
273  V2("Hdiv::Tri::In::V2", card ,cardVecPn);
274 
275  const ordinal_type numEdges = this->basisCellTopology_.getEdgeCount();
276 
277  shards::CellTopology edgeTop(shards::getCellTopologyData<shards::Line<2> >() );
278 
279  const int numPtsPerEdge = PointTools::getLatticeSize( edgeTop ,
280  order+1 ,
281  1 );
282 
283  // first numEdges * degree nodes are normals at each edge
284  // get the points on the line
285  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> linePts("Hdiv::Tri::In::linePts", numPtsPerEdge , 1 );
286 
287  // construct lattice
288  const ordinal_type offset = 1;
289  PointTools::getLattice( linePts,
290  edgeTop,
291  order+1, offset,
292  pointType );
293 
294  // holds the image of the line points
295  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> edgePts("Hdiv::Tri::In::edgePts", numPtsPerEdge , spaceDim );
296  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> phisAtEdgePoints("Hdiv::Tri::In::phisAtEdgePoints", cardPn , numPtsPerEdge );
297  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace> edgeNormal("Hcurl::Tri::In::edgeNormal", spaceDim );
298 
299  // these are normal scaled by the appropriate edge lengths.
300  for (ordinal_type edge=0;edge<numEdges;edge++) { // loop over edges
302  edge ,
303  this->basisCellTopology_ );
304 
306  linePts ,
307  1 ,
308  edge ,
309  this->basisCellTopology_ );
310 
311  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtEdgePoints , edgePts, order, OPERATOR_VALUE);
312 
313  // loop over points (rows of V2)
314  for (ordinal_type j=0;j<numPtsPerEdge;j++) {
315 
316  const ordinal_type i_card = numPtsPerEdge*edge+j;
317 
318  // loop over orthonormal basis functions (columns of V2)
319  for (ordinal_type k=0;k<cardPn;k++) {
320  // loop over space dimension
321  for (ordinal_type l=0; l<spaceDim; l++)
322  V2(i_card,k+l*cardPn) = edgeNormal(l) * phisAtEdgePoints(k,j);
323  }
324 
325 
326  //save dof coordinates and coefficients
327  for(ordinal_type l=0; l<spaceDim; ++l) {
328  dofCoords(i_card,l) = edgePts(j,l);
329  dofCoeffs(i_card,l) = edgeNormal(l);
330  }
331 
332  tags[i_card][0] = 1; // edge dof
333  tags[i_card][1] = edge; // edge id
334  tags[i_card][2] = j; // local dof id
335  tags[i_card][3] = numPtsPerEdge; // total vert dof
336 
337  }
338 
339 
340  }
341 
342  // remaining nodes are divided into two pieces: point value of x
343  // components and point values of y components. These are
344  // evaluated at the interior of a lattice of degree + 1, For then
345  // the degree == 1 space corresponds classicaly to RT0 and so gets
346  // no internal nodes, and degree == 2 corresponds to RT1 and needs
347  // one internal node per vector component.
348  const ordinal_type numPtsPerCell = PointTools::getLatticeSize( this->basisCellTopology_ ,
349  order + 1 ,
350  1 );
351 
352  if (numPtsPerCell > 0) {
353  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
354  internalPoints( "Hdiv::Tri::In::internalPoints", numPtsPerCell , spaceDim );
355  PointTools::getLattice( internalPoints ,
356  this->basisCellTopology_ ,
357  order + 1 ,
358  1 ,
359  pointType );
360 
361  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
362  phisAtInternalPoints("Hdiv::Tri::In::phisAtInternalPoints", cardPn , numPtsPerCell );
363  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>( phisAtInternalPoints , internalPoints , order, OPERATOR_VALUE );
364 
365  // copy values into right positions of V2
366  for (ordinal_type j=0;j<numPtsPerCell;j++) {
367 
368  const ordinal_type i_card = numEdges*order+spaceDim*j;
369 
370  for (ordinal_type k=0;k<cardPn;k++) {
371  for (ordinal_type l=0;l<spaceDim;l++) {
372  V2(i_card+l,l*cardPn+k) = phisAtInternalPoints(k,j);
373  }
374  }
375 
376  //save dof coordinates and coefficients
377  for(ordinal_type d=0; d<spaceDim; ++d) {
378  for(ordinal_type l=0; l<spaceDim; ++l) {
379  dofCoords(i_card+d,l) = internalPoints(j,l);
380  dofCoeffs(i_card+d,l) = (l==d);
381  }
382 
383  tags[i_card+d][0] = spaceDim; // elem dof
384  tags[i_card+d][1] = 0; // elem id
385  tags[i_card+d][2] = spaceDim*j+d; // local dof id
386  tags[i_card+d][3] = spaceDim*numPtsPerCell; // total vert dof
387  }
388  }
389  }
390 
391  // form Vandermonde matrix. Actually, this is the transpose of the VDM,
392  // so we transpose on copy below.
393  Kokkos::DynRankView<scalarType,Kokkos::LayoutLeft,Kokkos::HostSpace>
394  vmat("Hdiv::Tri::In::vmat", card, card),
395  work("Hdiv::Tri::In::work", lwork),
396  ipiv("Hdiv::Tri::In::ipiv", card);
397 
398  //vmat' = V2*V1;
399  for(ordinal_type i=0; i< card; ++i) {
400  for(ordinal_type j=0; j< card; ++j) {
401  scalarType s=0;
402  for(ordinal_type k=0; k< cardVecPn; ++k)
403  s += V2(i,k)*V1(k,j);
404  vmat(i,j) = s;
405  }
406  }
407 
408  ordinal_type info = 0;
409  Teuchos::LAPACK<ordinal_type,scalarType> lapack;
410 
411  lapack.GETRF(card, card,
412  vmat.data(), vmat.stride_1(),
413  (ordinal_type*)ipiv.data(),
414  &info);
415 
416  INTREPID2_TEST_FOR_EXCEPTION( info != 0,
417  std::runtime_error ,
418  ">>> ERROR: (Intrepid2::Basis_HDIV_TRI_In_FEM) lapack.GETRF returns nonzero info." );
419 
420  lapack.GETRI(card,
421  vmat.data(), vmat.stride_1(),
422  (ordinal_type*)ipiv.data(),
423  work.data(), lwork,
424  &info);
425 
426  INTREPID2_TEST_FOR_EXCEPTION( info != 0,
427  std::runtime_error ,
428  ">>> ERROR: (Intrepid2::Basis_HDIV_TRI_In_FEM) lapack.GETRI returns nonzero info." );
429 
430  for (ordinal_type i=0;i<cardVecPn;++i)
431  for (ordinal_type j=0;j<card;++j){
432  scalarType s=0;
433  for(ordinal_type k=0; k< card; ++k)
434  s += V1(i,k)*vmat(k,j);
435  coeffs(i,j) = s;
436  }
437 
438  this->coeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), coeffs);
439  Kokkos::deep_copy(this->coeffs_ , coeffs);
440 
441  this->dofCoords_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoords);
442  Kokkos::deep_copy(this->dofCoords_, dofCoords);
443 
444  this->dofCoeffs_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoeffs);
445  Kokkos::deep_copy(this->dofCoeffs_, dofCoeffs);
446 
447 
448  // set tags
449  {
450  // Basis-dependent initializations
451  const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
452  const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
453  const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
454 
455  OrdinalTypeArray1DHost tagView(&tags[0][0], card*tagSize);
456 
457  // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
458  // tags are constructed on host
459  this->setOrdinalTagData(this->tagToOrdinal_,
460  this->ordinalToTag_,
461  tagView,
462  this->basisCardinality_,
463  tagSize,
464  posScDim,
465  posScOrd,
466  posDfOrd);
467  }
468 }
469 } // namespace Intrepid2
470 #endif
Header file for the Intrepid2::Basis_HGRAD_TRI_Cn_FEM_ORTH class.
virtual void getCubature(PointViewType cubPoints, weightViewType cubWeights) const override
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).
Header file for the Intrepid2::CubatureDirectTriDefault class.
Defines direct integration rules on a triangle.
virtual ordinal_type getNumPoints() const override
Returns the number of cubature points.
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.
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.
EPointType
Enumeration of types of point distributions in Intrepid.
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...
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...
Basis_HDIV_TRI_In_FEM(const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
Constructor.