Intrepid2_LegendreBasis_HVOL_TET.hpp

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#ifndef Intrepid2_LegendreBasis_HVOL_TET_h
#define Intrepid2_LegendreBasis_HVOL_TET_h
 
#include <Kokkos_DynRankView.hpp>
 
#include <Intrepid2_config.h>
 
#include "Intrepid2_Basis.hpp"
#include "Intrepid2_LegendreBasis_HVOL_LINE.hpp"
#include "Intrepid2_LegendreBasis_HVOL_TRI.hpp"
#include "Intrepid2_Polynomials.hpp"
#include "Intrepid2_Utils.hpp"
 
namespace Intrepid2
{
  template<class DeviceType, class OutputScalar, class PointScalar,
           class OutputFieldType, class InputPointsType>
  struct Hierarchical_HVOL_TET_Functor
  {
    using ExecutionSpace     = typename DeviceType::execution_space;
    using ScratchSpace       = typename ExecutionSpace::scratch_memory_space;
    using OutputScratchView  = Kokkos::View<OutputScalar*,ScratchSpace,Kokkos::MemoryTraits<Kokkos::Unmanaged>>;
    using PointScratchView   = Kokkos::View<PointScalar*, ScratchSpace,Kokkos::MemoryTraits<Kokkos::Unmanaged>>;
    
    using TeamPolicy = Kokkos::TeamPolicy<ExecutionSpace>;
    using TeamMember = typename TeamPolicy::member_type;
    
    EOperator opType_;
    
    OutputFieldType  output_;      // F,P
    InputPointsType  inputPoints_; // P,D
    
    int polyOrder_;
    int numFields_, numPoints_;
    
    size_t fad_size_output_;
    
    Hierarchical_HVOL_TET_Functor(EOperator opType, OutputFieldType output, InputPointsType inputPoints, int polyOrder)
    : opType_(opType), output_(output), inputPoints_(inputPoints),
      polyOrder_(polyOrder),
      fad_size_output_(getScalarDimensionForView(output))
    {
      numFields_ = output.extent_int(0);
      numPoints_ = output.extent_int(1);
      INTREPID2_TEST_FOR_EXCEPTION(numPoints_ != inputPoints.extent_int(0), std::invalid_argument, "point counts need to match!");
      INTREPID2_TEST_FOR_EXCEPTION(numFields_ != (polyOrder_+1)*(polyOrder_+2)*(polyOrder_+3)/6, std::invalid_argument, "output field size does not match basis cardinality");
    }
    
    KOKKOS_INLINE_FUNCTION
    void operator()( const TeamMember & teamMember ) const
    {
      // values are product of [P_i](lambda_0,lambda_1), [P^{2i+1}_j](lambda_0 + lambda_1, lambda_2), and [P^{2*(i+j+1)}_k](1-lambda_3,lambda_3),
      // times ((grad lambda_1) x (grad lambda_2)) \cdot (grad lambda_3).
      // For the canonical orientation (all we support), the last term evaluates to 1, and
      // lambda_0 = 1 - x - y - z
      // lambda_1 = x
      // lambda_2 = y
      // lambda_3 = z
      // [P_i](lambda_0, lambda_1) = P_i(lambda_1; lambda_0 + lambda_1) = P_i(x; 1 - y - z) -- a shifted, scaled Legendre function
      // [P^{2i+1}_j](lambda_0 + lambda_1, lambda_2) = P^{2i+1}_j(lambda_2; lambda_0 + lambda_1 + lambda_2) = P^{2i+1}_j(y; 1 - z) -- a shifted, scaled Jacobi function
      // [P^{2*(i+j+1)}_k](1-lambda_3,lambda_3) = P^{2*(i+j+1)}_k(lambda_3; 1) = P^{2*(i+j+1)}_k(z; 1) -- another shifted, scaled Jacobi function
      auto pointOrdinal = teamMember.league_rank();
      OutputScratchView P, P_2p1, P_2ipjp1;
      if (fad_size_output_ > 0) {
        P        = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        P_2p1    = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        P_2ipjp1 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
      }
      else {
        P        = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        P_2p1    = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        P_2ipjp1 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
      }
      
      const auto & x = inputPoints_(pointOrdinal,0);
      const auto & y = inputPoints_(pointOrdinal,1);
      const auto & z = inputPoints_(pointOrdinal,2);
      
      // write as barycentric coordinates:
      const PointScalar lambda[4] = {1. - x - y - z, x, y, z};
      
      switch (opType_)
      {
        case OPERATOR_VALUE:
        {
          // face functions
          {
            const PointScalar tLegendre = lambda[0] + lambda[1];
            Polynomials::shiftedScaledLegendreValues(P, polyOrder_, lambda[1], tLegendre);
 
            int fieldOrdinalOffset = 0;
            
            const int min_i  = 0;
            const int min_j  = 0;
            const int min_k  = 0;
            const int min_ij = min_i + min_j;
            const int min_ijk = min_ij + min_k;
            for (int totalPolyOrder_ijk=min_ijk; totalPolyOrder_ijk <= polyOrder_; totalPolyOrder_ijk++)
            {
              for (int totalPolyOrder_ij=min_ij; totalPolyOrder_ij <= totalPolyOrder_ijk-min_j; totalPolyOrder_ij++)
              {
                for (int i=min_i; i <= totalPolyOrder_ij-min_j; i++)
                {
                  const int j = totalPolyOrder_ij - i;
                  const int k = totalPolyOrder_ijk - totalPolyOrder_ij;
                  
                  const double alpha1          = i * 2.0 + 1.;
                  const PointScalar tJacobi1   = lambda[0] + lambda[1] + lambda[2];
                  const PointScalar & xJacobi1 = lambda[2];
                  Polynomials::shiftedScaledJacobiValues(P_2p1, alpha1, polyOrder_, xJacobi1, tJacobi1);
                  
                  const double alpha2          = 2. * (i + j + 1.);
                  const PointScalar tJacobi2   = 1.0; // 1 - lambda[3] + lambda[3]
                  const PointScalar & xJacobi2 = lambda[3];
                  Polynomials::shiftedScaledJacobiValues(P_2ipjp1, alpha2, polyOrder_, xJacobi2, tJacobi2);
                  
                  const auto & P_i        = P(i);
                  const auto & P_2p1_j    = P_2p1(j);
                  const auto & P_2ipjp1_k = P_2ipjp1(k);
                  
                  output_(fieldOrdinalOffset,pointOrdinal) = P_i * P_2p1_j * P_2ipjp1_k;
                  fieldOrdinalOffset++;
                }
              }
            }
          }
        } // end OPERATOR_VALUE
          break;
        default:
          // unsupported operator type
          device_assert(false);
      }
    }
    
    // Provide the shared memory capacity.
    // This function takes the team_size as an argument,
    // which allows team_size-dependent allocations.
    size_t team_shmem_size (int team_size) const
    {
      // we will use shared memory to create a fast buffer for basis computations
      size_t shmem_size = 0;
      if (fad_size_output_ > 0)
        shmem_size += 3 * OutputScratchView::shmem_size(polyOrder_ + 1, fad_size_output_);
      else
        shmem_size += 3 * OutputScratchView::shmem_size(polyOrder_ + 1);
      
      return shmem_size;
    }
  };
  
  template<typename DeviceType,
           typename OutputScalar = double,
           typename PointScalar  = double>
  class LegendreBasis_HVOL_TET
  : public Basis<DeviceType,OutputScalar,PointScalar>
  {
  public:
    using BasisBase = Basis<DeviceType,OutputScalar,PointScalar>;
 
    using typename BasisBase::OrdinalTypeArray1DHost;
    using typename BasisBase::OrdinalTypeArray2DHost;
 
    using typename BasisBase::OutputViewType;
    using typename BasisBase::PointViewType;
    using typename BasisBase::ScalarViewType;
 
    using typename BasisBase::ExecutionSpace;
 
  protected:
    int polyOrder_; // the maximum order of the polynomial
    EPointType pointType_;
  public:
    LegendreBasis_HVOL_TET(int polyOrder, const EPointType pointType=POINTTYPE_DEFAULT)
    :
    polyOrder_(polyOrder),
    pointType_(pointType)
    {
      INTREPID2_TEST_FOR_EXCEPTION(pointType!=POINTTYPE_DEFAULT,std::invalid_argument,"PointType not supported");
 
      this->basisCardinality_  = ((polyOrder+3) * (polyOrder+2) * (polyOrder+1)) / 6;
      this->basisDegree_       = polyOrder;
      this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Tetrahedron<> >() );
      this->basisType_         = BASIS_FEM_HIERARCHICAL;
      this->basisCoordinates_  = COORDINATES_CARTESIAN;
      this->functionSpace_     = FUNCTION_SPACE_HVOL;
      
      const int degreeLength = 1;
      this->fieldOrdinalPolynomialDegree_ = OrdinalTypeArray2DHost("Integrated Legendre H(vol) triangle polynomial degree lookup", this->basisCardinality_, degreeLength);
      
      int fieldOrdinalOffset = 0;
      // **** volume/interior functions **** //
      const int min_i  = 0;
      const int min_j  = 0;
      const int min_k  = 0;
      const int min_ij = min_i + min_j;
      const int min_ijk = min_ij + min_k;
      for (int totalPolyOrder_ijk=min_ijk; totalPolyOrder_ijk <= polyOrder_; totalPolyOrder_ijk++)
      {
        for (int totalPolyOrder_ij=min_ij; totalPolyOrder_ij <= totalPolyOrder_ijk-min_j; totalPolyOrder_ij++)
        {
          for (int i=min_i; i <= totalPolyOrder_ij-min_j; i++)
          {
            const int j = totalPolyOrder_ij - i;
            const int k = totalPolyOrder_ijk - totalPolyOrder_ij;
            
            this->fieldOrdinalPolynomialDegree_(fieldOrdinalOffset,0) = i+j+k;
            fieldOrdinalOffset++;
          }
        }
      }
      INTREPID2_TEST_FOR_EXCEPTION(fieldOrdinalOffset != this->basisCardinality_, std::invalid_argument, "Internal error: basis enumeration is incorrect");
      
      // initialize tags
      {
        const auto & cardinality = this->basisCardinality_;
        
        // Basis-dependent initializations
        const 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
        
        OrdinalTypeArray1DHost tagView("tag view", cardinality*tagSize);
        const int volumeDim = 3;
 
        for (ordinal_type i=0;i<cardinality;++i) {
          tagView(i*tagSize+0) = volumeDim;   // volume dimension
          tagView(i*tagSize+1) = 0;           // volume id
          tagView(i*tagSize+2) = i;           // local dof id
          tagView(i*tagSize+3) = cardinality; // total number of dofs on this face
        }
        
        // 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);
      }
    }
    
    const char* getName() const override {
      return "Intrepid2_LegendreBasis_HVOL_TET";
    }
    
    virtual bool requireOrientation() const override {
      return (this->getDegree() > 2);
    }
 
    // since the getValues() below only overrides the FEM variant, we specify that
    // we use the base class's getValues(), which implements the FVD variant by throwing an exception.
    // (It's an error to use the FVD variant on this basis.)
    using BasisBase::getValues;
    
    virtual void getValues( OutputViewType outputValues, const PointViewType inputPoints,
                           const EOperator operatorType = OPERATOR_VALUE ) const override
    {
      auto numPoints = inputPoints.extent_int(0);
      
      using FunctorType = Hierarchical_HVOL_TET_Functor<DeviceType, OutputScalar, PointScalar, OutputViewType, PointViewType>;
      
      FunctorType functor(operatorType, outputValues, inputPoints, polyOrder_);
      
      const int outputVectorSize = getVectorSizeForHierarchicalParallelism<OutputScalar>();
      const int pointVectorSize  = getVectorSizeForHierarchicalParallelism<PointScalar>();
      const int vectorSize = std::max(outputVectorSize,pointVectorSize);
      const int teamSize = 1; // because of the way the basis functions are computed, we don't have a second level of parallelism...
 
      auto policy = Kokkos::TeamPolicy<ExecutionSpace>(numPoints,teamSize,vectorSize);
      Kokkos::parallel_for("Hierarchical_HVOL_TET_Functor", policy , functor);
    }

    virtual BasisPtr<typename Kokkos::HostSpace::device_type, OutputScalar, PointScalar>
    getHostBasis() const override {
      using HostDeviceType = typename Kokkos::HostSpace::device_type;
      using HostBasisType  = LegendreBasis_HVOL_TET<HostDeviceType, OutputScalar, PointScalar>;
      return Teuchos::rcp( new HostBasisType(polyOrder_, pointType_) );
    }
  };
} // end namespace Intrepid2
 
#endif /* Intrepid2_LegendreBasis_HVOL_TET_h */