Intrepid2_LegendreBasis_HVOL_PYR.hpp

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// @HEADER
// *****************************************************************************
//                           Intrepid2 Package
//
// Copyright 2007 NTESS and the Intrepid2 contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#ifndef Intrepid2_LegendreBasis_HVOL_PYR_h
#define Intrepid2_LegendreBasis_HVOL_PYR_h

#include <Kokkos_DynRankView.hpp>

#include <Intrepid2_config.h>

#include "Intrepid2_Basis.hpp"
#include "Intrepid2_Polynomials.hpp"
#include "Intrepid2_PyramidCoords.hpp"
#include "Intrepid2_Utils.hpp"

#include "Teuchos_RCP.hpp"

namespace Intrepid2
{
  template<class DeviceType, class OutputScalar, class PointScalar,
           class OutputFieldType, class InputPointsType>
  struct Hierarchical_HVOL_PYR_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 OutputScratchView2D = 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_;
    
    static const int numVertices   = 5;
    static const int numMixedEdges = 4;
    static const int numTriEdges   = 4;
    static const int numEdges      = 8;
    // the following ordering of the edges matches that used by ESEAS
    // (it *looks* like this is what ESEAS uses; the basis comparison tests will clarify whether I've read their code correctly)
    // see also PyramidEdgeNodeMap in Shards_BasicTopologies.hpp
    const int edge_start_[numEdges] = {0,1,2,3,0,1,2,3}; // edge i is from edge_start_[i] to edge_end_[i]
    const int edge_end_[numEdges]   = {1,2,3,0,4,4,4,4}; // edge i is from edge_start_[i] to edge_end_[i]
    
    // quadrilateral face comes first
    static const int numQuadFaces = 1;
    static const int numTriFaces  = 4;
    
    // face ordering matches ESEAS.  (See BlendProjectPyraTF in ESEAS.)
    const int tri_face_vertex_0[numTriFaces] = {0,1,3,0}; // faces are abc where 0 ≤ a < b < c ≤ 3
    const int tri_face_vertex_1[numTriFaces] = {1,2,2,3};
    const int tri_face_vertex_2[numTriFaces] = {4,4,4,4};
    
    Hierarchical_HVOL_PYR_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);
      const auto & p = polyOrder;
      const auto p_plus_one_cubed = (p+1) * (p+1) * (p+1);
      INTREPID2_TEST_FOR_EXCEPTION(numPoints_ != inputPoints.extent_int(0), std::invalid_argument, "point counts need to match!");
      INTREPID2_TEST_FOR_EXCEPTION(numFields_ != p_plus_one_cubed, std::invalid_argument, "output field size does not match basis cardinality");
    }
    
    KOKKOS_INLINE_FUNCTION
    void operator()( const TeamMember & teamMember ) const
    {
      auto pointOrdinal = teamMember.league_rank();
      OutputScratchView scratch1D_1, scratch1D_2, scratch1D_3;
      OutputScratchView scratch1D_4, scratch1D_5, scratch1D_6;
      OutputScratchView scratch1D_7, scratch1D_8, scratch1D_9;
      OutputScratchView2D scratch2D_1, scratch2D_2, scratch2D_3;
      const int numAlphaValues = (polyOrder_-1 > 1) ? (polyOrder_-1) : 1; // make numAlphaValues at least 1 so we can avoid zero-extent allocations…
      if (fad_size_output_ > 0) {
        scratch1D_1 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_2 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_3 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_4 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_5 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_6 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_7 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_8 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch1D_9 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1, fad_size_output_);
        scratch2D_1 = OutputScratchView2D(teamMember.team_shmem(), numAlphaValues, polyOrder_ + 1, fad_size_output_);
        scratch2D_2 = OutputScratchView2D(teamMember.team_shmem(), numAlphaValues, polyOrder_ + 1, fad_size_output_);
        scratch2D_3 = OutputScratchView2D(teamMember.team_shmem(), numAlphaValues, polyOrder_ + 1, fad_size_output_);
      }
      else {
        scratch1D_1 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_2 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_3 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_4 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_5 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_6 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_7 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_8 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch1D_9 = OutputScratchView(teamMember.team_shmem(), polyOrder_ + 1);
        scratch2D_1 = OutputScratchView2D(teamMember.team_shmem(), numAlphaValues, polyOrder_ + 1);
        scratch2D_2 = OutputScratchView2D(teamMember.team_shmem(), numAlphaValues, polyOrder_ + 1);
        scratch2D_3 = OutputScratchView2D(teamMember.team_shmem(), numAlphaValues, polyOrder_ + 1);
      }
      
      const auto & x = inputPoints_(pointOrdinal,0);
      const auto & y = inputPoints_(pointOrdinal,1);
      const auto & z = inputPoints_(pointOrdinal,2);
      
      // Intrepid2 uses (-1,1)^2 for x,y
      // ESEAS uses (0,1)^2
      // (Can look at what we do on the HGRAD_LINE for reference; there's a similar difference for line topology.)
      
      Kokkos::Array<PointScalar,3> coords;
      transformToESEASPyramid<>(coords[0], coords[1], coords[2], x, y, z); // map x,y coordinates from (-z,z)^2 to (0,z)^2
      
      // pyramid "affine" coordinates and gradients get stored in lambda, lambdaGrad:
      using Kokkos::Array;
      Array<PointScalar,5> lambda;
      Array<Kokkos::Array<PointScalar,3>,5> lambdaGrad;
      
      Array<Array<PointScalar,3>,2> mu; // first index is subscript; second is superscript: 0 --> (\zeta, xi_1), 1 --> (\zeta, xi_2), 2 --> (\zeta)
      Array<Array<Array<PointScalar,3>,3>,2> muGrad;
      
      Array<Array<PointScalar,2>,3> nu;
      Array<Array<Array<PointScalar,3>,2>,3> nuGrad;
      
      affinePyramid(lambda, lambdaGrad, mu, muGrad, nu, nuGrad, coords);
      
      switch (opType_)
      {
        case OPERATOR_VALUE:
        {
          // interior functions
          // rename scratch
          ordinal_type fieldOrdinalOffset = 0;
          auto & Pi = scratch1D_1;
          auto & Pj = scratch1D_2;
          auto & Pk = scratch1D_3;
          // [P_i](mu_01^{\zeta,\xi_1})
          Polynomials::shiftedScaledLegendreValues(Pi, polyOrder_, mu[1][0], mu[0][0] + mu[1][0]);
          // [P_j](mu_01^{\zeta,\xi_2})
          Polynomials::shiftedScaledLegendreValues(Pj, polyOrder_, mu[1][1], mu[0][1] + mu[1][1]);
          // [P_k](mu_01^{\zeta})
          Polynomials::shiftedScaledLegendreValues(Pk, polyOrder_, mu[1][2], mu[0][2] + mu[1][2]);
          // (grad nu_1^{\zeta,\xi_1} x grad nu_1^{\zeta,\xi_2}) \cdot grad mu_1^zeta:
          PointScalar grad_weight =
            (nuGrad[1][0][1] * nuGrad[1][1][2] - nuGrad[1][0][2] * nuGrad[1][1][1]) * muGrad[1][2][0]
          + (nuGrad[1][0][2] * nuGrad[1][1][0] - nuGrad[1][0][0] * nuGrad[1][1][2]) * muGrad[1][2][1]
          + (nuGrad[1][0][0] * nuGrad[1][1][1] - nuGrad[1][0][1] * nuGrad[1][1][0]) * muGrad[1][2][2];
          
          // following the ESEAS ordering: k increments first
          for (int k=0; k<=polyOrder_; k++)
          {
            for (int j=0; j<=polyOrder_; j++)
            {
              for (int i=0; i<=polyOrder_; i++)
              {
                output_(fieldOrdinalOffset,pointOrdinal) = Pk(k) * Pi(i) * Pj(j) * grad_weight;
                fieldOrdinalOffset++;
              }
            }
          }
        } // end OPERATOR_VALUE
          break;
        case OPERATOR_GRAD:
        case OPERATOR_D1:
        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:
          INTREPID2_TEST_FOR_ABORT( true,
                                   ">>> ERROR: (Intrepid2::Hierarchical_HVOL_PYR_Functor) Computing of derivatives is not supported");
        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 use shared memory to create a fast buffer for basis computations
      // for the (integrated) Legendre computations, we just need p+1 values stored.  For interior functions on the pyramid, we have up to 3 scratch arrays with (integrated) Legendre values stored, for each of the 3 directions (i,j,k indices): a total of 9.
      // for the (integrated) Jacobi computations, though, we want (p+1)*(# alpha values)
      // alpha is either 2i or 2(i+j), where i=2,…,p or i+j=3,…,p.  So there are at most (p-1) alpha values needed.
      // We can have up to 3 of the (integrated) Jacobi values needed at once.
      const int numAlphaValues = std::max(polyOrder_-1, 1); // make it at least 1 so we can avoid zero-extent ranks…
      size_t shmem_size = 0;
      if (fad_size_output_ > 0)
      {
        // Legendre:
        shmem_size += 9 * OutputScratchView::shmem_size(polyOrder_ + 1, fad_size_output_);
        // Jacobi:
        shmem_size += 3 * OutputScratchView2D::shmem_size(numAlphaValues, polyOrder_ + 1, fad_size_output_);
      }
      else
      {
        // Legendre:
        shmem_size += 9 * OutputScratchView::shmem_size(polyOrder_ + 1);
        // Jacobi:
        shmem_size += 3 * OutputScratchView2D::shmem_size(numAlphaValues, polyOrder_ + 1);
      }
      
      return shmem_size;
    }
  };
  
  template<typename DeviceType,
           typename OutputScalar = double,
           typename PointScalar  = double>
  class LegendreBasis_HVOL_PYR
  : 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_PYR(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 + 1) * (polyOrder + 1) * (polyOrder + 1);
      this->basisDegree_          = polyOrder;
      this->basisCellTopologyKey_ = shards::Pyramid<>::key;
      this->basisType_            = BASIS_FEM_HIERARCHICAL;
      this->basisCoordinates_     = COORDINATES_CARTESIAN;
      this->functionSpace_        = FUNCTION_SPACE_HVOL;
      
      const int degreeLength = 1;
      this->fieldOrdinalPolynomialDegree_ = OrdinalTypeArray2DHost("Legendre H(vol) pyramid polynomial degree lookup", this->basisCardinality_, degreeLength);
      this->fieldOrdinalH1PolynomialDegree_ = OrdinalTypeArray2DHost("Legendre H(vol) pyramid polynomial H^1 degree lookup", this->basisCardinality_, degreeLength);
      
      int fieldOrdinalOffset = 0;
      
      // **** interior functions **** //
      const int numVolumes = 1; // interior
      for (int volumeOrdinal=0; volumeOrdinal<numVolumes; volumeOrdinal++)
      {
        // following the ESEAS ordering: k increments first
        for (int k=0; k<=polyOrder_; k++)
        {
          for (int j=0; j<=polyOrder_; j++)
          {
            for (int i=0; i<=polyOrder_; i++)
            {
              const int max_ij  = std::max(i,j);
              const int max_ijk = std::max(max_ij,k);
              this->fieldOrdinalPolynomialDegree_  (fieldOrdinalOffset,0) = max_ijk;     // L^2 degree
              this->fieldOrdinalH1PolynomialDegree_(fieldOrdinalOffset,0) = max_ijk + 1; // H^1 degree
              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 ordinal_type volumeDim = 3;

        for (ordinal_type i=0;i<cardinality;++i) {
          tagView(i*tagSize+0) = volumeDim;   // volume dimension
          tagView(i*tagSize+1) = 0;           // volume ordinal
          tagView(i*tagSize+2) = i;           // local dof id
          tagView(i*tagSize+3) = cardinality; // total number of dofs on this volume
        }
        
        // 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_PYR";
    }
    
    virtual bool requireOrientation() const override {
      return false;
    }

    // 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_PYR_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_PYR_Functor", policy, functor);
    }

    BasisPtr<DeviceType,OutputScalar,PointScalar>
    getSubCellRefBasis(const ordinal_type subCellDim, const ordinal_type subCellOrd) const override{
      // no subcell ref basis for HVOL
      INTREPID2_TEST_FOR_EXCEPTION(true,std::invalid_argument,"Input parameters out of bounds");
    }

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

// do ETI with default (double) type
extern template class Intrepid2::LegendreBasis_HVOL_PYR<Kokkos::DefaultExecutionSpace::device_type,double,double>;

#endif /* Intrepid2_LegendreBasis_HVOL_PYR_h */