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 SpT, 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,SpT>::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 SpT, typename OT, typename PT>
188 Basis_HDIV_TRI_In_FEM( const ordinal_type order,
189  const EPointType pointType ) {
190 
191  constexpr ordinal_type spaceDim = 2;
192  this->basisCardinality_ = CardinalityHDivTri(order);
193  this->basisDegree_ = order; // small n
194  this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
195  this->basisType_ = BASIS_FEM_FIAT;
196  this->basisCoordinates_ = COORDINATES_CARTESIAN;
197 
198  const ordinal_type card = this->basisCardinality_;
199 
200  const ordinal_type cardPn = Intrepid2::getPnCardinality<spaceDim>(order); // dim of (P_{n}) -- smaller space
201  const ordinal_type cardPnm1 = Intrepid2::getPnCardinality<spaceDim>(order-1); // dim of (P_{n-1}) -- smaller space
202  const ordinal_type cardPnm2 = Intrepid2::getPnCardinality<spaceDim>(order-2); // dim of (P_{n-2}) -- smaller space
203  const ordinal_type cardVecPn = spaceDim*cardPn; // dim of (P_{n})^2 -- larger space
204  const ordinal_type cardVecPnm1 = spaceDim*cardPnm1; // dim of (P_{n-1})^2 -- smaller space
205 
206 
207  // Basis-dependent initializations
208  constexpr ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
209  constexpr ordinal_type maxCard = CardinalityHDivTri(Parameters::MaxOrder);
210  ordinal_type tags[maxCard][tagSize];
211 
212  // points are computed in the host and will be copied
213  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
214  dofCoords("Hdiv::Tri::In::dofCoords", card, spaceDim);
215 
216  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
217  dofCoeffs("Hdiv::Tri::In::dofCoeffs", card, spaceDim);
218 
219  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
220  coeffs("Hdiv::Tri::In::coeffs", cardVecPn, card);
221 
222  // first, need to project the basis for RT space onto the
223  // orthogonal basis of degree n
224  // get coefficients of PkHx
225 
226  const ordinal_type lwork = card*card;
227  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
228  V1("Hdiv::Tri::In::V1", cardVecPn, card);
229 
230  // basis for the space is
231  // { (phi_i,0) }_{i=0}^{cardPnm1-1} ,
232  // { (0,phi_i) }_{i=0}^{cardPnm1-1} ,
233  // { (x,y) . phi_i}_{i=cardPnm2}^{cardPnm1-1}
234  // columns of V1 are expansion of this basis in terms of the basis
235  // for P_{n}^2
236 
237  // these two loops get the first two sets of basis functions
238  for (ordinal_type i=0;i<cardPnm1;i++) {
239  V1(i,i) = 1.0;
240  V1(cardPn+i,cardPnm1+i) = 1.0;
241  }
242 
243  // now I need to integrate { (x,y) phi } against the big basis
244  // first, get a cubature rule.
246  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> cubPoints("Hdiv::Tri::In::cubPoints", myCub.getNumPoints() , spaceDim );
247  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> cubWeights("Hdiv::Tri::In::cubWeights", myCub.getNumPoints() );
248  myCub.getCubature( cubPoints , cubWeights );
249 
250  // tabulate the scalar orthonormal basis at cubature points
251  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> phisAtCubPoints("Hdiv::Tri::In::phisAtCubPoints", cardPn , myCub.getNumPoints() );
252  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtCubPoints, cubPoints, order, OPERATOR_VALUE);
253 
254  // now do the integration
255  for (ordinal_type i=0;i<order;i++) {
256  for (ordinal_type j=0;j<cardPn;j++) { // int (x,y) phi_i \cdot (phi_j,phi_{j+cardPn})
257  V1(j,cardVecPnm1+i) = 0.0;
258  for (ordinal_type d=0; d< spaceDim; ++d)
259  for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
260  V1(j+d*cardPn,cardVecPnm1+i) +=
261  cubWeights(k) * cubPoints(k,d)
262  * phisAtCubPoints(cardPnm2+i,k)
263  * phisAtCubPoints(j,k);
264  }
265  }
266  }
267 
268  // next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
269  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
270  V2("Hdiv::Tri::In::V2", card ,cardVecPn);
271 
272  const ordinal_type numEdges = this->basisCellTopology_.getEdgeCount();
273 
274  shards::CellTopology edgeTop(shards::getCellTopologyData<shards::Line<2> >() );
275 
276  const int numPtsPerEdge = PointTools::getLatticeSize( edgeTop ,
277  order+1 ,
278  1 );
279 
280  // first numEdges * degree nodes are normals at each edge
281  // get the points on the line
282  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> linePts("Hdiv::Tri::In::linePts", numPtsPerEdge , 1 );
283 
284  // construct lattice
285  const ordinal_type offset = 1;
286  PointTools::getLattice( linePts,
287  edgeTop,
288  order+1, offset,
289  pointType );
290 
291  // holds the image of the line points
292  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> edgePts("Hdiv::Tri::In::edgePts", numPtsPerEdge , spaceDim );
293  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> phisAtEdgePoints("Hdiv::Tri::In::phisAtEdgePoints", cardPn , numPtsPerEdge );
294  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace> edgeNormal("Hcurl::Tri::In::edgeNormal", spaceDim );
295 
296  // these are normal scaled by the appropriate edge lengths.
297  for (ordinal_type edge=0;edge<numEdges;edge++) { // loop over edges
299  edge ,
300  this->basisCellTopology_ );
301 
302  /* multiply by measure of reference edge so that magnitude of the edgeTan is equal to the edge measure */
303  const scalarType refEdgeMeasure = 2.0;
304  for (ordinal_type j=0;j<spaceDim;j++)
305  edgeNormal(j) *= refEdgeMeasure;
306 
307 
309  linePts ,
310  1 ,
311  edge ,
312  this->basisCellTopology_ );
313 
314  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(phisAtEdgePoints , edgePts, order, OPERATOR_VALUE);
315 
316  // loop over points (rows of V2)
317  for (ordinal_type j=0;j<numPtsPerEdge;j++) {
318 
319  const ordinal_type i_card = numPtsPerEdge*edge+j;
320 
321  // loop over orthonormal basis functions (columns of V2)
322  for (ordinal_type k=0;k<cardPn;k++) {
323  // loop over space dimension
324  for (ordinal_type l=0; l<spaceDim; l++)
325  V2(i_card,k+l*cardPn) = edgeNormal(l) * phisAtEdgePoints(k,j);
326  }
327 
328 
329  //save dof coordinates and coefficients
330  for(ordinal_type l=0; l<spaceDim; ++l) {
331  dofCoords(i_card,l) = edgePts(j,l);
332  dofCoeffs(i_card,l) = edgeNormal(l);
333  }
334 
335  tags[i_card][0] = 1; // edge dof
336  tags[i_card][1] = edge; // edge id
337  tags[i_card][2] = j; // local dof id
338  tags[i_card][3] = numPtsPerEdge; // total vert dof
339 
340  }
341 
342 
343  }
344 
345  // remaining nodes are divided into two pieces: point value of x
346  // components and point values of y components. These are
347  // evaluated at the interior of a lattice of degree + 1, For then
348  // the degree == 1 space corresponds classicaly to RT0 and so gets
349  // no internal nodes, and degree == 2 corresponds to RT1 and needs
350  // one internal node per vector component.
351  const ordinal_type numPtsPerCell = PointTools::getLatticeSize( this->basisCellTopology_ ,
352  order + 1 ,
353  1 );
354 
355  if (numPtsPerCell > 0) {
356  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
357  internalPoints( "Hdiv::Tri::In::internalPoints", numPtsPerCell , spaceDim );
358  PointTools::getLattice( internalPoints ,
359  this->basisCellTopology_ ,
360  order + 1 ,
361  1 ,
362  pointType );
363 
364  Kokkos::DynRankView<scalarType,typename SpT::array_layout,Kokkos::HostSpace>
365  phisAtInternalPoints("Hdiv::Tri::In::phisAtInternalPoints", cardPn , numPtsPerCell );
366  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>( phisAtInternalPoints , internalPoints , order, OPERATOR_VALUE );
367 
368  // copy values into right positions of V2
369  for (ordinal_type j=0;j<numPtsPerCell;j++) {
370 
371  const ordinal_type i_card = numEdges*order+spaceDim*j;
372 
373  for (ordinal_type k=0;k<cardPn;k++) {
374  for (ordinal_type l=0;l<spaceDim;l++) {
375  V2(i_card+l,l*cardPn+k) = phisAtInternalPoints(k,j);
376  }
377  }
378 
379  //save dof coordinates and coefficients
380  for(ordinal_type d=0; d<spaceDim; ++d) {
381  for(ordinal_type l=0; l<spaceDim; ++l) {
382  dofCoords(i_card+d,l) = internalPoints(j,l);
383  dofCoeffs(i_card+d,l) = (l==d);
384  }
385 
386  tags[i_card+d][0] = spaceDim; // elem dof
387  tags[i_card+d][1] = 0; // elem id
388  tags[i_card+d][2] = spaceDim*j+d; // local dof id
389  tags[i_card+d][3] = spaceDim*numPtsPerCell; // total vert dof
390  }
391  }
392  }
393 
394  // form Vandermonde matrix. Actually, this is the transpose of the VDM,
395  // so we transpose on copy below.
396  Kokkos::DynRankView<scalarType,Kokkos::LayoutLeft,Kokkos::HostSpace>
397  vmat("Hdiv::Tri::In::vmat", card, card),
398  work("Hdiv::Tri::In::work", lwork),
399  ipiv("Hdiv::Tri::In::ipiv", card);
400 
401  //vmat' = V2*V1;
402  for(ordinal_type i=0; i< card; ++i) {
403  for(ordinal_type j=0; j< card; ++j) {
404  scalarType s=0;
405  for(ordinal_type k=0; k< cardVecPn; ++k)
406  s += V2(i,k)*V1(k,j);
407  vmat(i,j) = s;
408  }
409  }
410 
411  ordinal_type info = 0;
412  Teuchos::LAPACK<ordinal_type,scalarType> lapack;
413 
414  lapack.GETRF(card, card,
415  vmat.data(), vmat.stride_1(),
416  (ordinal_type*)ipiv.data(),
417  &info);
418 
419  INTREPID2_TEST_FOR_EXCEPTION( info != 0,
420  std::runtime_error ,
421  ">>> ERROR: (Intrepid2::Basis_HDIV_TRI_In_FEM) lapack.GETRF returns nonzero info." );
422 
423  lapack.GETRI(card,
424  vmat.data(), vmat.stride_1(),
425  (ordinal_type*)ipiv.data(),
426  work.data(), lwork,
427  &info);
428 
429  INTREPID2_TEST_FOR_EXCEPTION( info != 0,
430  std::runtime_error ,
431  ">>> ERROR: (Intrepid2::Basis_HDIV_TRI_In_FEM) lapack.GETRI returns nonzero info." );
432 
433  for (ordinal_type i=0;i<cardVecPn;++i)
434  for (ordinal_type j=0;j<card;++j){
435  scalarType s=0;
436  for(ordinal_type k=0; k< card; ++k)
437  s += V1(i,k)*vmat(k,j);
438  coeffs(i,j) = s;
439  }
440 
441  this->coeffs_ = Kokkos::create_mirror_view(typename SpT::memory_space(), coeffs);
442  Kokkos::deep_copy(this->coeffs_ , coeffs);
443 
444  this->dofCoords_ = Kokkos::create_mirror_view(typename SpT::memory_space(), dofCoords);
445  Kokkos::deep_copy(this->dofCoords_, dofCoords);
446 
447  this->dofCoeffs_ = Kokkos::create_mirror_view(typename SpT::memory_space(), dofCoeffs);
448  Kokkos::deep_copy(this->dofCoeffs_, dofCoeffs);
449 
450 
451  // set tags
452  {
453  // Basis-dependent initializations
454  const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
455  const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
456  const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
457 
458  ordinal_type_array_1d_host tagView(&tags[0][0], card*tagSize);
459 
460  // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
461  // tags are constructed on host
462  this->setOrdinalTagData(this->tagToOrdinal_,
463  this->ordinalToTag_,
464  tagView,
465  this->basisCardinality_,
466  tagSize,
467  posScDim,
468  posScOrd,
469  posDfOrd);
470  }
471 }
472 } // namespace Intrepid2
473 #endif
Basis_HDIV_TRI_In_FEM(const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
Constructor.
Header file for the Intrepid2::Basis_HGRAD_TRI_Cn_FEM_ORTH class.
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.
Header file for the Intrepid2::CubatureDirectTriDefault class.
Defines direct integration rules on a triangle.
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 (currently disabled for other ce...
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.
Kokkos::View< ordinal_type *,typename ExecSpaceType::array_layout, Kokkos::HostSpace > ordinal_type_array_1d_host
View type for 1d host array.
virtual void getCubature(pointViewType cubPoints, weightViewType cubWeights) const
Returns cubature points and weights (return arrays must be pre-sized/pre-allocated).
static constexpr ordinal_type MaxOrder
The maximum reconstruction order.
virtual ordinal_type getNumPoints() const
Returns the number of cubature points.
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...