epsilon_simple.hpp

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#pragma once
 
#include "../../quadrature/quadrature.hpp"
#include "communication/shell/communication.hpp"
#include "dense/vec.hpp"
#include "fe/wedge/integrands.hpp"
#include "fe/wedge/kernel_helpers.hpp"
#include "grid/shell/spherical_shell.hpp"
#include "linalg/operator.hpp"
#include "linalg/vector.hpp"
#include "linalg/vector_q1.hpp"
#include "util/timer.hpp"
 
namespace terra::fe::wedge::operators::shell {
 
template < typename ScalarT, int VecDim = 3 >
class EpsilonSimple
{
  public:
    using SrcVectorType = linalg::VectorQ1Vec< ScalarT, VecDim >;
    using DstVectorType = linalg::VectorQ1Vec< ScalarT, VecDim >;
    using ScalarType    = ScalarT;
 
  private:
    grid::shell::DistributedDomain domain_;
 
    grid::Grid3DDataVec< ScalarT, 3 >    grid_;
    grid::Grid2DDataScalar< ScalarT >    radii_;
    grid::Grid4DDataScalar< ScalarType > k_;
 
    bool treat_boundary_;
    bool diagonal_;
 
    linalg::OperatorApplyMode         operator_apply_mode_;
    linalg::OperatorCommunicationMode operator_communication_mode_;
 
    communication::shell::SubdomainNeighborhoodSendRecvBuffer< ScalarT, VecDim > send_buffers_;
    communication::shell::SubdomainNeighborhoodSendRecvBuffer< ScalarT, VecDim > recv_buffers_;
 
    grid::Grid4DDataVec< ScalarType, VecDim > src_;
    grid::Grid4DDataVec< ScalarType, VecDim > dst_;
 
  public:
    EpsilonSimple(
        const grid::shell::DistributedDomain&    domain,
        const grid::Grid3DDataVec< ScalarT, 3 >& grid,
        const grid::Grid2DDataScalar< ScalarT >& radii,
        const grid::Grid4DDataScalar< ScalarT >& k,
        bool                                     treat_boundary,
        bool                                     diagonal,
        linalg::OperatorApplyMode                operator_apply_mode = linalg::OperatorApplyMode::Replace,
        linalg::OperatorCommunicationMode        operator_communication_mode =
            linalg::OperatorCommunicationMode::CommunicateAdditively )
    : domain_( domain )
    , grid_( grid )
    , radii_( radii )
    , k_( k )
    , treat_boundary_( treat_boundary )
    , diagonal_( diagonal )
    , operator_apply_mode_( operator_apply_mode )
    , operator_communication_mode_( operator_communication_mode )
    // TODO: we can reuse the send and recv buffers and pass in from the outside somehow
    , send_buffers_( domain )
    , recv_buffers_( domain )
    {}
 
    const grid::Grid4DDataScalar< ScalarType >& k_grid_data() { return k_; }
 
    void set_operator_apply_and_communication_modes(
        const linalg::OperatorApplyMode         operator_apply_mode,
        const linalg::OperatorCommunicationMode operator_communication_mode )
    {
        operator_apply_mode_         = operator_apply_mode;
        operator_communication_mode_ = operator_communication_mode;
    }
 
    void apply_impl( const SrcVectorType& src, DstVectorType& dst )
    {
        util::Timer timer_apply( "vector_laplace_apply" );
 
        if ( operator_apply_mode_ == linalg::OperatorApplyMode::Replace )
        {
            assign( dst, 0 );
        }
 
        src_ = src.grid_data();
        dst_ = dst.grid_data();
 
        if ( src_.extent( 0 ) != dst_.extent( 0 ) || src_.extent( 1 ) != dst_.extent( 1 ) ||
             src_.extent( 2 ) != dst_.extent( 2 ) || src_.extent( 3 ) != dst_.extent( 3 ) )
        {
            throw std::runtime_error( "VectorLaplace: src/dst mismatch" );
        }
 
        if ( src_.extent( 1 ) != grid_.extent( 1 ) || src_.extent( 2 ) != grid_.extent( 2 ) )
        {
            throw std::runtime_error( "VectorLaplace: src/dst mismatch" );
        }
 
        util::Timer timer_kernel( "vector_laplace_kernel" );
        Kokkos::parallel_for( "matvec", grid::shell::local_domain_md_range_policy_cells( domain_ ), *this );
        Kokkos::fence();
        timer_kernel.stop();
 
        if ( operator_communication_mode_ == linalg::OperatorCommunicationMode::CommunicateAdditively )
        {
            util::Timer timer_comm( "vector_laplace_comm" );
 
            communication::shell::pack_send_and_recv_local_subdomain_boundaries(
                domain_, dst_, send_buffers_, recv_buffers_ );
            communication::shell::unpack_and_reduce_local_subdomain_boundaries( domain_, dst_, recv_buffers_ );
        }
    }
 
    KOKKOS_INLINE_FUNCTION void
        operator()( const int local_subdomain_id, const int x_cell, const int y_cell, const int r_cell ) const
    {
        // Gather surface points for each wedge.
        dense::Vec< ScalarT, 3 > wedge_phy_surf[num_wedges_per_hex_cell][num_nodes_per_wedge_surface] = {};
        wedge_surface_physical_coords( wedge_phy_surf, grid_, local_subdomain_id, x_cell, y_cell );
 
        // Gather wedge radii.
        const ScalarT r_1 = radii_( local_subdomain_id, r_cell );
        const ScalarT r_2 = radii_( local_subdomain_id, r_cell + 1 );
 
        // Quadrature points.
        constexpr auto num_quad_points = quadrature::quad_felippa_3x2_num_quad_points;
 
        dense::Vec< ScalarT, 3 > quad_points[num_quad_points];
        ScalarT                  quad_weights[num_quad_points];
 
        quadrature::quad_felippa_3x2_quad_points( quad_points );
        quadrature::quad_felippa_3x2_quad_weights( quad_weights );
 
        dense::Vec< ScalarT, 6 > k[num_wedges_per_hex_cell];
        extract_local_wedge_scalar_coefficients( k, local_subdomain_id, x_cell, y_cell, r_cell, k_ );
 
        // Compute the local element matrix.
        dense::Mat< ScalarT, 18, 18 > A[num_wedges_per_hex_cell] = {};
 
        // FE dimensions: velocity coupling components of epsilon operator
        for ( int dimi = 0; dimi < 3; ++dimi )
        {
            for ( int dimj = 0; dimj < 3; ++dimj )
            {
                if ( diagonal_ and dimi != dimj )
                    continue;
 
                // spatial dimensions: quadrature points and wedge
                for ( int q = 0; q < num_quad_points; q++ )
                {
                    const auto w = quad_weights[q];
 
                    for ( int wedge = 0; wedge < num_wedges_per_hex_cell; wedge++ )
                    {
                        dense::Mat< ScalarT, 3, 3 > J       = jac( wedge_phy_surf[wedge], r_1, r_2, quad_points[q] );
                        const auto                  det     = J.det();
                        const auto                  abs_det = Kokkos::abs( det );
                        const auto                  J_inv_transposed = J.inv_transposed( det );
                        ScalarType                  k_eval           = 0.0;
                        for ( int j = 0; j < num_nodes_per_wedge; j++ )
                        {
                            k_eval += shape( j, quad_points[q] ) * k[wedge]( j );
                        }
                        // FE dimensions: local DoFs/associated shape functions
                        for ( int i = 0; i < num_nodes_per_wedge; i++ )
                        {
                            // basis functions are vectors with VecDim components -> build tensorial gradients
                            dense::Mat< ScalarT, 3, 3 > grad_i =
                                J_inv_transposed * dense::Mat< ScalarT, VecDim, VecDim >::from_single_col_vec(
                                                       grad_shape( i, quad_points[q] ), dimi );
                            dense::Mat< ScalarT, 3, 3 > sym_grad_i = ( grad_i + grad_i.transposed() );
                            //const auto grad_i = J_inv_transposed * grad_shape( i, quad_points[q] );
 
                            for ( int j = 0; j < num_nodes_per_wedge; j++ )
                            {
                                dense::Mat< ScalarT, 3, 3 > grad_j =
                                    J_inv_transposed * dense::Mat< ScalarT, VecDim, VecDim >::from_single_col_vec(
                                                           grad_shape( j, quad_points[q] ), dimj );
 
                                dense::Mat< ScalarT, 3, 3 > sym_grad_j = ( grad_j + grad_j.transposed() );
 
                                //const auto grad_j = J_inv_transposed * grad_shape( j, quad_points[q] );
 
                                A[wedge]( i + num_nodes_per_wedge * dimi, j + num_nodes_per_wedge * dimj ) +=
                                    0.5 * w * k_eval * ( ( sym_grad_i ).double_contract( sym_grad_j ) * abs_det );
                            }
                        }
                    }
                }
            }
        }
 
        if ( treat_boundary_ )
        {
            for ( int dimi = 0; dimi < 3; ++dimi )
            {
                for ( int dimj = 0; dimj < 3; ++dimj )
                {
                    for ( int wedge = 0; wedge < num_wedges_per_hex_cell; wedge++ )
                    {
                        dense::Mat< ScalarT, 18, 18 > boundary_mask;
                        boundary_mask.fill( 1.0 );
 
                        if ( r_cell == 0 )
                        {
                            // Inner boundary (CMB).
                            for ( int i = 0; i < 6; i++ )
                            {
                                for ( int j = 0; j < 6; j++ )
                                {
                                    if ( ( dimi == dimj && i != j && ( i < 3 || j < 3 ) ) or
                                         ( dimi != dimj && ( i < 3 || j < 3 ) ) )
                                    {
                                        boundary_mask(
                                            i + num_nodes_per_wedge * dimi, j + num_nodes_per_wedge * dimj ) = 0.0;
                                    }
                                }
                            }
                        }
 
                        if ( r_cell + 1 == radii_.extent( 1 ) - 1 )
                        {
                            // Outer boundary (surface).
                            for ( int i = 0; i < 6; i++ )
                            {
                                for ( int j = 0; j < 6; j++ )
                                {
                                    if ( ( dimi == dimj && i != j && ( i >= 3 || j >= 3 ) ) or
                                         ( dimi != dimj && ( i >= 3 || j >= 3 ) ) )
                                    {
                                        boundary_mask(
                                            i + num_nodes_per_wedge * dimi, j + num_nodes_per_wedge * dimj ) = 0.0;
                                    }
                                }
                            }
                        }
 
                        A[wedge].hadamard_product( boundary_mask );
                    }
                }
            }
        }
 
        if ( diagonal_ )
        {
            A[0] = A[0].diagonal();
            A[1] = A[1].diagonal();
        }
 
        dense::Vec< ScalarT, 18 > src[num_wedges_per_hex_cell];
        for ( int dimj = 0; dimj < 3; dimj++ )
        {
            dense::Vec< ScalarT, 6 > src_d[num_wedges_per_hex_cell];
            extract_local_wedge_vector_coefficients( src_d, local_subdomain_id, x_cell, y_cell, r_cell, dimj, src_ );
 
            for ( int wedge = 0; wedge < num_wedges_per_hex_cell; wedge++ )
            {
                for ( int i = 0; i < num_nodes_per_wedge; i++ )
                {
                    src[wedge]( dimj * num_nodes_per_wedge + i ) = src_d[wedge]( i );
                }
            }
        }
        //extract_local_wedge_vector_coefficients( src, local_subdomain_id, x_cell, y_cell, r_cell, dimj, src_ );
 
        dense::Vec< ScalarT, 18 > dst[num_wedges_per_hex_cell];
 
        dst[0] = A[0] * src[0];
        dst[1] = A[1] * src[1];
 
        //atomically_add_local_wedge_vector_coefficients( dst_, local_subdomain_id, x_cell, y_cell, r_cell, dimi, dst );
        for ( int dimi = 0; dimi < 3; dimi++ )
        {
            dense::Vec< ScalarT, 6 > dst_d[num_wedges_per_hex_cell];
            dst_d[0] = dst[0].template slice< 6 >( dimi * num_nodes_per_wedge );
            dst_d[1] = dst[1].template slice< 6 >( dimi * num_nodes_per_wedge );
 
            atomically_add_local_wedge_vector_coefficients(
                dst_, local_subdomain_id, x_cell, y_cell, r_cell, dimi, dst_d );
        }
    }
};
 
static_assert( linalg::OperatorLike< EpsilonSimple< float > > );
static_assert( linalg::OperatorLike< EpsilonSimple< double > > );
 
} // namespace terra::fe::wedge::operators::shell