Intrepid2_HGRAD_TRI_Cn_FEMDef.hpp

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#ifndef __INTREPID2_HGRAD_TRI_CN_FEM_DEF_HPP__
#define __INTREPID2_HGRAD_TRI_CN_FEM_DEF_HPP__

#include "Intrepid2_HGRAD_TRI_Cn_FEM_ORTH.hpp"

namespace Intrepid2 {

// -------------------------------------------------------------------------------------
namespace Impl {

template<EOperator opType>
template<typename OutputViewType,
typename inputViewType,
typename workViewType,
typename vinvViewType>
KOKKOS_INLINE_FUNCTION
void
Basis_HGRAD_TRI_Cn_FEM::Serial<opType>::
getValues(       OutputViewType output,
    const inputViewType  input,
    workViewType   work,
    const vinvViewType   vinv ) {

  constexpr ordinal_type spaceDim = 2;
  const ordinal_type
  card = vinv.extent(0),
  npts = input.extent(0);

  // compute order
  ordinal_type order = 0;
  for (ordinal_type p=0;p<=Parameters::MaxOrder;++p) {
    if (card == Intrepid2::getPnCardinality<spaceDim>(p) ) {
      order = p;
      break;
    }
  }

  typedef typename Kokkos::DynRankView<typename workViewType::value_type, typename workViewType::memory_space> viewType;
  auto vcprop = Kokkos::common_view_alloc_prop(work);
  auto ptr = work.data();

  switch (opType) {
  case OPERATOR_VALUE: {
    const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts);
    viewType dummyView;

    Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
    Serial<opType>::getValues(phis, input, dummyView, order);

    for (ordinal_type i=0;i<card;++i)
      for (ordinal_type j=0;j<npts;++j) {
        output.access(i,j) = 0.0;
        for (ordinal_type k=0;k<card;++k)
          output.access(i,j) += vinv(k,i)*phis.access(k,j);
      }
    break;
  }
  case OPERATOR_GRAD:
  case OPERATOR_D1: {
    const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim);
    ptr += card*npts*spaceDim*get_dimension_scalar(work);
    const viewType workView(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim+1);
    Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
    Serial<opType>::getValues(phis, input, workView, order);

    for (ordinal_type i=0;i<card;++i)
      for (ordinal_type j=0;j<npts;++j)
        for (ordinal_type k=0;k<spaceDim;++k) {
          output.access(i,j,k) = 0.0;
          for (ordinal_type l=0;l<card;++l)
            output.access(i,j,k) += vinv(l,i)*phis.access(l,j,k);
        }
    break;
  }
  case OPERATOR_D2:
  case OPERATOR_D3:
  case OPERATOR_D4:
  case OPERATOR_D5:
  case OPERATOR_D6:
  case OPERATOR_D7:
  case OPERATOR_D8:
  case OPERATOR_D9:
  case OPERATOR_D10: {
    const ordinal_type dkcard = getDkCardinality<opType,spaceDim>(); //(orDn + 1);
    const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts, dkcard);
    viewType dummyView;

    Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
    Serial<opType>::getValues(phis, input, dummyView, order);

    for (ordinal_type i=0;i<card;++i)
      for (ordinal_type j=0;j<npts;++j)
        for (ordinal_type k=0;k<dkcard;++k) {
          output.access(i,j,k) = 0.0;
          for (ordinal_type l=0;l<card;++l)
            output.access(i,j,k) += vinv(l,i)*phis.access(l,j,k);
        }
    break;
  }
  case OPERATOR_CURL: { // only works in 2d. first component is -d/dy, second is d/dx
    const viewType phis(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim);
    ptr += card*npts*spaceDim*get_dimension_scalar(work);
    const viewType workView(Kokkos::view_wrap(ptr, vcprop), card, npts, spaceDim+1);


    Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::
    Serial<OPERATOR_D1>::getValues(phis, input, workView, order);

    for (ordinal_type i=0;i<card;++i)
      for (ordinal_type j=0;j<npts;++j) {
        output.access(i,j,0) = 0.0;
        for (ordinal_type l=0;l<card;++l)
          output.access(i,j,0) += vinv(l,i)*phis.access(l,j,1);
        output.access(i,j,1) = 0.0;
        for (ordinal_type l=0;l<card;++l)
          output.access(i,j,1) -= vinv(l,i)*phis.access(l,j,0);
      }
    break;
  }
  default: {
    INTREPID2_TEST_FOR_ABORT( true,
        ">>> ERROR (Basis_HGRAD_TRI_Cn_FEM): Operator type not implemented");
  }
  }
}

template<typename DT, ordinal_type numPtsPerEval,
typename outputValueValueType, class ...outputValueProperties,
typename inputPointValueType,  class ...inputPointProperties,
typename vinvValueType,        class ...vinvProperties>
void
Basis_HGRAD_TRI_Cn_FEM::
getValues(
    const typename DT::execution_space& space,
          Kokkos::DynRankView<outputValueValueType,outputValueProperties...> outputValues,
    const Kokkos::DynRankView<inputPointValueType, inputPointProperties...>  inputPoints,
    const Kokkos::DynRankView<vinvValueType,       vinvProperties...>        vinv,
    const EOperator operatorType) {
  typedef          Kokkos::DynRankView<outputValueValueType,outputValueProperties...>         outputValueViewType;
  typedef          Kokkos::DynRankView<inputPointValueType, inputPointProperties...>          inputPointViewType;
  typedef          Kokkos::DynRankView<vinvValueType,       vinvProperties...>                vinvViewType;
  typedef typename ExecSpace<typename inputPointViewType::execution_space,typename DT::execution_space>::ExecSpaceType ExecSpaceType;

  // loopSize corresponds to cardinality
  const auto loopSizeTmp1 = (inputPoints.extent(0)/numPtsPerEval);
  const auto loopSizeTmp2 = (inputPoints.extent(0)%numPtsPerEval != 0);
  const auto loopSize = loopSizeTmp1 + loopSizeTmp2;
  Kokkos::RangePolicy<ExecSpaceType,Kokkos::Schedule<Kokkos::Static> > policy(space, 0, loopSize);

  typedef typename inputPointViewType::value_type inputPointType;

  const ordinal_type cardinality = outputValues.extent(0);
  const ordinal_type spaceDim = 2;

  auto vcprop = Kokkos::common_view_alloc_prop(inputPoints);
  typedef typename Kokkos::DynRankView< inputPointType, typename inputPointViewType::memory_space> workViewType;

  switch (operatorType) {
  case OPERATOR_VALUE: {
    workViewType  work(Kokkos::view_alloc(space, "Basis_HGRAD_TRI_Cn_FEM::getValues::work", vcprop), cardinality, inputPoints.extent(0));
    typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
        OPERATOR_VALUE,numPtsPerEval> FunctorType;
    Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinv, work) );
    break;
  }
  case OPERATOR_GRAD:
  case OPERATOR_D1: {
    workViewType  work(Kokkos::view_alloc(space, "Basis_HGRAD_TRI_Cn_FEM::getValues::work", vcprop), cardinality*(2*spaceDim+1), inputPoints.extent(0));
    typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
        OPERATOR_D1,numPtsPerEval> FunctorType;
    Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinv, work) );
    break;
  }
  case OPERATOR_CURL: {
    workViewType  work(Kokkos::view_alloc(space, "Basis_HGRAD_TRI_Cn_FEM::getValues::work", vcprop), cardinality*(2*spaceDim+1), inputPoints.extent(0));
    typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
        OPERATOR_CURL,numPtsPerEval> FunctorType;
    Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinv, work) );
    break;
  }
  case OPERATOR_D2: {
    typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType,
        OPERATOR_D2,numPtsPerEval> FunctorType;
    workViewType  work(Kokkos::view_alloc(space, "Basis_HGRAD_TRI_Cn_FEM::getValues::work", vcprop), cardinality*outputValues.extent(2), inputPoints.extent(0));
    Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinv, work) );
    break;
  }
  /*  case OPERATOR_D3: {
        typedef Functor<outputValueViewType,inputPointViewType,vinvViewType, workViewType
            OPERATOR_D3,numPtsPerEval> FunctorType;
        workViewType  work(Kokkos::view_alloc("Basis_HGRAD_TRI_Cn_FEM::getValues::work", vcprop), cardinality, inputPoints.extent(0), outputValues.extent(2));
        Kokkos::parallel_for( policy, FunctorType(outputValues, inputPoints, vinv, work) );
        break;
      }*/
  default: {
    INTREPID2_TEST_FOR_EXCEPTION( true , std::invalid_argument,
        ">>> ERROR (Basis_HGRAD_TRI_Cn_FEM): Operator type not implemented" );
  }
  }
}
}

// -------------------------------------------------------------------------------------
template<typename DT, typename OT, typename PT>
Basis_HGRAD_TRI_Cn_FEM<DT,OT,PT>::
Basis_HGRAD_TRI_Cn_FEM( const ordinal_type order,
    const EPointType   pointType ) {
  constexpr ordinal_type spaceDim = 2;

  this->basisCardinality_  = Intrepid2::getPnCardinality<spaceDim>(order); // bigN
  this->basisDegree_       = order; // small n
  this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
  this->basisType_         = BASIS_FEM_LAGRANGIAN;
  this->basisCoordinates_  = COORDINATES_CARTESIAN;
  this->functionSpace_     = FUNCTION_SPACE_HGRAD;

  pointType_ = (pointType == POINTTYPE_DEFAULT) ? POINTTYPE_EQUISPACED : pointType;
  const ordinal_type card = this->basisCardinality_;

  // points are computed in the host and will be copied
  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
  dofCoords("Hgrad::Tri::Cn::dofCoords", card, spaceDim);

  // construct lattice
  const ordinal_type offset = 0;
  PointTools::getLattice( dofCoords,
      this->basisCellTopology_,
      order, offset,
      pointType_ );

  this->dofCoords_ = Kokkos::create_mirror_view(typename DT::memory_space(), dofCoords);
  Kokkos::deep_copy(this->dofCoords_, dofCoords);

  // form Vandermonde matrix.  Actually, this is the transpose of the VDM,
  // so we transpose on copy below.
  const ordinal_type lwork = card*card;
  Kokkos::DynRankView<scalarType,Kokkos::LayoutLeft,Kokkos::HostSpace>
  vmat("Hgrad::Tri::Cn::vmat", card, card),
  work("Hgrad::Tri::Cn::work", lwork),
  ipiv("Hgrad::Tri::Cn::ipiv", card);

  Impl::Basis_HGRAD_TRI_Cn_FEM_ORTH::getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>(typename Kokkos::HostSpace::execution_space{},
                                                                                                                     vmat,
                                                                                                                     dofCoords,
                                                                                                                     order,
                                                                                                                     OPERATOR_VALUE);

  ordinal_type info = 0;
  Teuchos::LAPACK<ordinal_type,scalarType> lapack;

  lapack.GETRF(card, card,
      vmat.data(), vmat.stride_1(),
      (ordinal_type*)ipiv.data(),
      &info);

  INTREPID2_TEST_FOR_EXCEPTION( info != 0,
      std::runtime_error ,
      ">>> ERROR: (Intrepid2::Basis_HGRAD_TRI_Cn_FEM) lapack.GETRF returns nonzero info." );

  lapack.GETRI(card,
      vmat.data(), vmat.stride_1(),
      (ordinal_type*)ipiv.data(),
      work.data(), lwork,
      &info);

  INTREPID2_TEST_FOR_EXCEPTION( info != 0,
      std::runtime_error ,
      ">>> ERROR: (Intrepid2::Basis_HGRAD_TRI_Cn_FEM) lapack.GETRI returns nonzero info." );

  // create host mirror
  Kokkos::DynRankView<scalarType,typename DT::execution_space::array_layout,Kokkos::HostSpace>
  vinv("Hgrad::Line::Cn::vinv", card, card);

  for (ordinal_type i=0;i<card;++i)
    for (ordinal_type j=0;j<card;++j)
      vinv(i,j) = vmat(j,i);

  this->vinv_ = Kokkos::create_mirror_view(typename DT::memory_space(), vinv);
  Kokkos::deep_copy(this->vinv_ , vinv);

  // initialize tags
  {
    // Basis-dependent initializations
    constexpr ordinal_type tagSize  = 4;        // size of DoF tag, i.e., number of fields in the tag
    const ordinal_type posScDim = 0;        // position in the tag, counting from 0, of the subcell dim
    const ordinal_type posScOrd = 1;        // position in the tag, counting from 0, of the subcell ordinal
    const ordinal_type posDfOrd = 2;        // position in the tag, counting from 0, of DoF ordinal relative to the subcell

    // 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.
    // 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.)
    INTREPID2_TEST_FOR_EXCEPTION( order > Parameters::MaxOrder, std::invalid_argument, "polynomial order exceeds the max supported by this class");
    constexpr ordinal_type maxCard = Intrepid2::getPnCardinality<spaceDim, Parameters::MaxOrder>();
    ordinal_type tags[maxCard][tagSize];

    const ordinal_type
    numEdgeDof = Intrepid2::getPnCardinality<1>(order-2),
    numElemDof = (order > 2 ? Intrepid2::getPnCardinality<2>(order-3) : 0);

    scalarType xi0, xi1, xi2;
    const scalarType eps = threshold();

    ordinal_type edgeId[3] = {}, elemId = 0;
    for (ordinal_type i=0;i<card;++i) {

      // compute barycentric coordinates
      const auto x = dofCoords(i,0);
      const auto y = dofCoords(i,1);
      xi0 = 1.0 - x - y;
      xi1= x;
      xi2= y;

      // vertex
      if ((1.0 - xi0) < eps) { // vert 0
        tags[i][0] = 0; // vertex dof
        tags[i][1] = 0; // vertex id
        tags[i][2] = 0; // local dof id
        tags[i][3] = 1; // total vert dof
      }
      else if ((1.0 - xi1) < eps) { // vert 1
        tags[i][0] = 0; // vertex dof
        tags[i][1] = 1; // vertex id
        tags[i][2] = 0; // local dof id
        tags[i][3] = 1; // total vert dof
      }
      else if ((1.0 - xi2) < eps) { // vert 2
        tags[i][0] = 0; // vertex dof
        tags[i][1] = 2; // vertex id
        tags[i][2] = 0; // local dof id
        tags[i][3] = 1; // total vert dof
      }
      else if (xi2 < eps) { // edge 0
        tags[i][0] = 1; // edge dof
        tags[i][1] = 0; // edge id
        tags[i][2] = edgeId[0]++; // local dof id
        tags[i][3] = numEdgeDof; // total vert dof
      }
      else if (xi0 < eps) { // edge 1
        tags[i][0] = 1; // edge dof
        tags[i][1] = 1; // edge id
        tags[i][2] = edgeId[1]++; // local dof id
        tags[i][3] = numEdgeDof; // total vert dof
      }
      else if (xi1 < eps) { // edge 2
        tags[i][0] = 1; // edge dof
        tags[i][1] = 2; // edge id
        tags[i][2] = edgeId[2]++; // local dof id
        tags[i][3] = numEdgeDof; // total vert dof
      }
      else { // elem
        tags[i][0] = 2; // intr dof
        tags[i][1] = 0; // intr id
        tags[i][2] = elemId++; // local dof id
        tags[i][3] = numElemDof; // total vert dof
      }
    }

    OrdinalTypeArray1DHost tagView(&tags[0][0], card*tagSize);

    // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
    // tags are constructed on host
    this->setOrdinalTagData(this->tagToOrdinal_,
        this->ordinalToTag_,
        tagView,
        this->basisCardinality_,
        tagSize,
        posScDim,
        posScOrd,
        posDfOrd);
  }
}
} // namespace Intrepid2
#endif