Intrepid2
Intrepid2_OrientationToolsDefCoeffMatrix_HDIV.hpp
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43 
59 #ifndef __INTREPID2_ORIENTATIONTOOLS_DEF_COEFF_MATRIX_HDIV_HPP__
60 #define __INTREPID2_ORIENTATIONTOOLS_DEF_COEFF_MATRIX_HDIV_HPP__
61 
62 // disable clang warnings
63 #if defined (__clang__) && !defined (__INTEL_COMPILER)
64 #pragma clang system_header
65 #endif
66 
67 namespace Intrepid2 {
68 
69 namespace Impl {
70 
71 namespace Debug {
72 
73 #ifdef HAVE_INTREPID2_DEBUG
74 template<typename subcellBasisType,
75 typename cellBasisType>
76 inline
77 void
78 check_getCoeffMatrix_HDIV(const subcellBasisType& subcellBasis,
79  const cellBasisType& cellBasis,
80  const ordinal_type subcellId,
81  const ordinal_type subcellOrt) {
82  const shards::CellTopology cellTopo = cellBasis.getBaseCellTopology();
83  const shards::CellTopology subcellTopo = subcellBasis.getBaseCellTopology();
84 
85  const ordinal_type cellDim = cellTopo.getDimension();
86  const ordinal_type subcellDim = subcellTopo.getDimension();
87 
88  INTREPID2_TEST_FOR_EXCEPTION( subcellDim >= cellDim,
89  std::logic_error,
90  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): " \
91  "cellDim must be greater than subcellDim.");
92 
93  const auto subcellBaseKey = subcellTopo.getBaseKey();
94  const auto cellBaseKey = cellTopo.getBaseKey();
95 
96  INTREPID2_TEST_FOR_EXCEPTION( subcellBaseKey != shards::Line<>::key &&
97  subcellBaseKey != shards::Quadrilateral<>::key &&
98  subcellBaseKey != shards::Triangle<>::key,
99  std::logic_error,
100  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): " \
101  "subcellBasis must have line, quad, or triangle topology.");
102 
103  INTREPID2_TEST_FOR_EXCEPTION( cellBaseKey != shards::Quadrilateral<>::key &&
104  cellBaseKey != shards::Triangle<>::key &&
105  cellBaseKey != shards::Hexahedron<>::key &&
106  cellBaseKey != shards::Wedge<>::key &&
107  cellBaseKey != shards::Tetrahedron<>::key,
108  std::logic_error,
109  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): " \
110  "cellBasis must have quad, triangle, hexhedron or tetrahedron topology.");
111 
112  //
113  // Function space
114  //
115  {
116  const bool isHDIV = cellBasis.getFunctionSpace() == FUNCTION_SPACE_HDIV;
117  INTREPID2_TEST_FOR_EXCEPTION( !isHDIV,
118  std::logic_error,
119  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): "
120  "cellBasis is not HDIV.");
121  {
122  const bool subcellBasisIsHGRAD = subcellBasis.getFunctionSpace() == FUNCTION_SPACE_HGRAD;
123  const bool subcellBasisIsHVOL = subcellBasis.getFunctionSpace() == FUNCTION_SPACE_HVOL;
124  const bool cellIsTri = cellBaseKey == shards::Triangle<>::key;
125  const bool cellIsTet = cellBaseKey == shards::Tetrahedron<>::key;
126  const bool cellIsHex = cellBaseKey == shards::Hexahedron<>::key;
127  const bool cellIsQuad = cellBaseKey == shards::Quadrilateral<>::key;
128 
129  switch (subcellDim) {
130  case 1: {
131  //TODO: Hex, QUAD, TET and TRI element should have the same 1d basis
132  if (cellIsHex || cellIsQuad) {
133  INTREPID2_TEST_FOR_EXCEPTION( !(subcellBasisIsHGRAD||subcellBasisIsHVOL),
134  std::logic_error,
135  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_DIV): "
136  "subcellBasis function space (1d) is not consistent to cellBasis, which should be open line hgrad, order -1.");
137  } else if (cellIsTet || cellIsTri) {
138  INTREPID2_TEST_FOR_EXCEPTION( !subcellBasisIsHVOL,
139  std::logic_error,
140  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_DIV): "
141  "subcellBasis function space (1d) is not consistent to cellBasis, which should be HVOL line, order -1.");
142  }
143  break;
144  }
145  case 2: {
146  if (subcellBaseKey == shards::Quadrilateral<>::key) {
147  // quad face basis is tensor product of open line basis functions
148  INTREPID2_TEST_FOR_EXCEPTION( !(subcellBasisIsHGRAD||subcellBasisIsHVOL),
149  std::logic_error,
150  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): "
151  "subcellBasis function space is not compatible, which should be open line hgrad, order -1.");
152  } else if (subcellBaseKey == shards::Triangle<>::key) {
153  // triangle face basis comes from HVOL basis
154  INTREPID2_TEST_FOR_EXCEPTION( !subcellBasisIsHVOL,
155  std::logic_error,
156  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): "
157  "subcellBasis function space is not compatible, which should HVOL, order-1.");
158  }
159  break;
160  }
161  }
162  }
163  }
164 }
165 #endif
166 } //Debug Namespace
167 
168 template<typename OutputViewType,
169 typename subcellBasisHostType,
170 typename cellBasisHostType>
171 inline
172 void
174 getCoeffMatrix_HDIV(OutputViewType &output,
175  const subcellBasisHostType& subcellBasis,
176  const cellBasisHostType& cellBasis,
177  const ordinal_type subcellId,
178  const ordinal_type subcellOrt) {
179 
180 #ifdef HAVE_INTREPID2_DEBUG
181  Debug::check_getCoeffMatrix_HDIV(subcellBasis,cellBasis,subcellId,subcellOrt);
182 #endif
183 
184  using value_type = typename OutputViewType::non_const_value_type;
185  using host_device_type = Kokkos::HostSpace::device_type;
186 
187  //
188  // Collocation points
189  //
190  const shards::CellTopology cellTopo = cellBasis.getBaseCellTopology();
191  const shards::CellTopology subcellTopo = subcellBasis.getBaseCellTopology();
192  const ordinal_type cellDim = cellTopo.getDimension();
193  const ordinal_type subcellDim = subcellTopo.getDimension();
194  const auto subcellBaseKey = subcellTopo.getBaseKey();
195  const ordinal_type numCellBasis = cellBasis.getCardinality();
196  const ordinal_type numSubcellBasis = subcellBasis.getCardinality();
197  const ordinal_type ndofSubcell = cellBasis.getDofCount(subcellDim,subcellId);
198 
199  //
200  // Reference points
201  //
202 
203  //use lattice to compute reference subcell points \xi_j
204  auto latticeDegree = (subcellBaseKey == shards::Triangle<>::key) ?
205  cellBasis.getDegree()+2 : cellBasis.getDegree()+1;
206 
207  // Reference points \xi_j on the subcell
208  Kokkos::DynRankView<value_type,host_device_type> refPtsSubcell("refPtsSubcell", ndofSubcell, subcellDim);
209  auto latticeSize=PointTools::getLatticeSize(subcellTopo, latticeDegree, 1);
210  INTREPID2_TEST_FOR_EXCEPTION( latticeSize != ndofSubcell,
211  std::logic_error,
212  ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): " \
213  "Lattice size should be equal to the onber of subcell internal DoFs");
214  PointTools::getLattice(refPtsSubcell, subcellTopo, latticeDegree, 1);//, POINTTYPE_WARPBLEND);
215 
216  // evaluate values on the modified cell
217  auto subcellParam = Intrepid2::RefSubcellParametrization<host_device_type>::get(subcellDim, cellTopo.getKey());
218 
219  // refPtsCell = F_s (\eta_o (refPtsSubcell))
220  Kokkos::DynRankView<value_type,host_device_type> refPtsCell("refPtsCell", ndofSubcell, cellDim);
221  // map points from the subcell manifold into the cell one
222  mapSubcellCoordsToRefCell(refPtsCell,refPtsSubcell, subcellParam, subcellBaseKey, subcellId, subcellOrt);
223 
224  //computing normal to the subcell accounting for orientation
225  Kokkos::DynRankView<value_type,host_device_type> tangentsAndNormal("trJacobianF", cellDim, cellDim );
226  OrientationTools::getRefSideTangentsAndNormal(tangentsAndNormal, subcellParam, subcellBaseKey, subcellId, subcellOrt);
227  auto sideNormal = Kokkos::subview(tangentsAndNormal, cellDim-1, Kokkos::ALL());
228 
229 
230  //
231  // Basis evaluation on the collocation points
232  //
233 
234  // cellBasisValues = \psi_k(F_s (\eta_o (\xi_j)))
235  Kokkos::DynRankView<value_type,host_device_type> cellBasisValues("cellBasisValues", numCellBasis, ndofSubcell, cellDim);
236  cellBasis.getValues(cellBasisValues, refPtsCell, OPERATOR_VALUE);
237 
238  // subcellBasisValues = \phi_i (\xi_j)
239  Kokkos::DynRankView<value_type,host_device_type> subCellValues("subCellValues", numSubcellBasis, ndofSubcell);
240  subcellBasis.getValues(subCellValues, refPtsSubcell, OPERATOR_VALUE);
241 
242  //
243  // Compute Psi_jk = \psi_k(F_s (\eta_o (\xi_j))) \cdot (n_s det(J_\eta))
244  // and Phi_ji = \phi_i (\xi_j), and solve
245  // Psi A^T = Phi
246  //
247 
248  // construct Psi and Phi matrices. LAPACK wants left layout
249  Kokkos::DynRankView<value_type,Kokkos::LayoutLeft,host_device_type>
250  PsiMat("PsiMat", ndofSubcell, ndofSubcell),
251  PhiMat("PhiMat", ndofSubcell, ndofSubcell);
252 
253  auto cellTagToOrdinal = cellBasis.getAllDofOrdinal();
254  auto subcellTagToOrdinal = subcellBasis.getAllDofOrdinal();
255 
256  for (ordinal_type i=0;i<ndofSubcell;++i) {
257  const ordinal_type ic = cellTagToOrdinal(subcellDim, subcellId, i);
258  const ordinal_type isc = subcellTagToOrdinal(subcellDim, 0, i);
259  for (ordinal_type j=0;j<ndofSubcell;++j) {
260  PhiMat(j,i) = get_scalar_value(subCellValues(isc,j));
261  for (ordinal_type k=0;k<cellDim;++k)
262  PsiMat(j,i) += get_scalar_value(cellBasisValues(ic,j,k))*sideNormal(k);
263  }
264  }
265 
266  auto RefMat = PsiMat;
267  auto OrtMat = PhiMat;
268 
269  // solve the system
270  {
271  Teuchos::LAPACK<ordinal_type,value_type> lapack;
272  ordinal_type info = 0;
273  Kokkos::DynRankView<ordinal_type,host_device_type> pivVec("pivVec", ndofSubcell);
274 
275  lapack.GESV(ndofSubcell, ndofSubcell,
276  PsiMat.data(),
277  PsiMat.stride_1(),
278  pivVec.data(),
279  PhiMat.data(),
280  PhiMat.stride_1(),
281  &info);
282 
283  if (info) {
284  std::stringstream ss;
285  ss << ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HDIV): "
286  << "LAPACK return with error code: "
287  << info;
288  INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error, ss.str().c_str() );
289  }
290 
291  //After solving the system w/ LAPACK, Phi contains A^T
292 
293  // transpose and clean up numerical noise (for permutation matrices)
294  const double eps = tolerence();
295  for (ordinal_type i=0;i<ndofSubcell;++i) {
296  auto intmatii = std::round(PhiMat(i,i));
297  PhiMat(i,i) = (std::abs(PhiMat(i,i) - intmatii) < eps) ? intmatii : PhiMat(i,i);
298  for (ordinal_type j=i+1;j<ndofSubcell;++j) {
299  auto matij = PhiMat(i,j);
300 
301  auto intmatji = std::round(PhiMat(j,i));
302  PhiMat(i,j) = (std::abs(PhiMat(j,i) - intmatji) < eps) ? intmatji : PhiMat(j,i);
303 
304  auto intmatij = std::round(matij);
305  PhiMat(j,i) = (std::abs(matij - intmatij) < eps) ? intmatij : matij;
306  }
307  }
308 
309  // Print Matrix A
310  /*
311  {
312  std::cout << "|";
313  for (ordinal_type i=0;i<ndofSubcell;++i) {
314  for (ordinal_type j=0;j<ndofSubcell;++j) {
315  std::cout << PhiMat(i,j) << " ";
316  }
317  std::cout << "| ";
318  }
319  std::cout <<std::endl;
320  }
321  */
322 
323  }
324 
325  {
326  // move the data to original device memory
327  const Kokkos::pair<ordinal_type,ordinal_type> range(0, ndofSubcell);
328  auto suboutput = Kokkos::subview(output, range, range);
329  auto tmp = Kokkos::create_mirror_view_and_copy(typename OutputViewType::device_type::memory_space(), PhiMat);
330  Kokkos::deep_copy(suboutput, tmp);
331  }
332 }
333 }
334 
335 }
336 #endif
static KOKKOS_INLINE_FUNCTION void mapSubcellCoordsToRefCell(coordsViewType cellCoords, const subcellCoordsViewType subCellCoords, const ParamViewType subcellParametrization, const unsigned subcellTopoKey, const ordinal_type subCellOrd, const ordinal_type ort)
Maps points defined on the subCell manifold into the parent Cell.
static ConstViewType get(const ordinal_type subcellDim, const unsigned parentCellKey)
Returns a Kokkos view with the coefficients of the parametrization maps for the edges or faces of a r...
static void getCoeffMatrix_HDIV(OutputViewType &output, const subcellBasisHostType &subcellBasis, const cellBasisHostType &cellBasis, const ordinal_type subcellId, const ordinal_type subcellOrt)
Compute orientation matrix for HDIV basis for a given subcell and its reference basis.
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...
KOKKOS_FORCEINLINE_FUNCTION constexpr std::enable_if< !std::is_pod< T >::value, typename ScalarTraits< T >::scalar_type >::type get_scalar_value(const T &obj)
functions returning the scalar value. for pod types, they return the input object itself...
static KOKKOS_INLINE_FUNCTION void getRefSideTangentsAndNormal(TanNormViewType tangentsAndNormal, const ParamViewType subCellParametrization, const unsigned subcellTopoKey, const ordinal_type subCellOrd, const ordinal_type ort)
Computes the (oriented) tangents and normal of the side subCell The normals are only defined for side...
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...