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ExplicitFunctors.hpp
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/*
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// Kokkos v. 2.0
// Copyright (2014) Sandia Corporation
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#ifndef KOKKOS_EXPLICITFUNCTORS_HPP
#define KOKKOS_EXPLICITFUNCTORS_HPP
#include <cmath>
#include <Kokkos_Core.hpp>
#include <FEMesh.hpp>
namespace Explicit {
template<typename Scalar , class Device >
struct Fields {
static const int NumStates = 2 ;
static const int SpatialDim = 3 ;
static const int ElemNodeCount = 8 ;
// Indices for full 3x3 tensor:
static const int K_F_XX = 0 ;
static const int K_F_YY = 1 ;
static const int K_F_ZZ = 2 ;
static const int K_F_XY = 3 ;
static const int K_F_YZ = 4 ;
static const int K_F_ZX = 5 ;
static const int K_F_YX = 6 ;
static const int K_F_ZY = 7 ;
static const int K_F_XZ = 8 ;
// Indexes into a 3 by 3 symmetric tensor stored as a length 6 vector
static const int K_S_XX = 0 ;
static const int K_S_YY = 1 ;
static const int K_S_ZZ = 2 ;
static const int K_S_XY = 3 ;
static const int K_S_YZ = 4 ;
static const int K_S_ZX = 5 ;
static const int K_S_YX = 3 ;
static const int K_S_ZY = 4 ;
static const int K_S_XZ = 5 ;
// Indexes into a 3 by 3 skew symmetric tensor stored as a length 3 vector
static const int K_V_XY = 0 ;
static const int K_V_YZ = 1 ;
static const int K_V_ZX = 2 ;
typedef Device execution_space ;
typedef typename execution_space::size_type size_type ;
typedef HybridFEM::FEMesh<double,ElemNodeCount,execution_space> FEMesh ;
typedef typename FEMesh::node_coords_type node_coords_type ;
typedef typename FEMesh::elem_node_ids_type elem_node_ids_type ;
typedef typename FEMesh::node_elem_ids_type node_elem_ids_type ;
typedef typename Kokkos::ParallelDataMap parallel_data_map ;
typedef Kokkos::View< double[][ SpatialDim ][ NumStates ] , execution_space > geom_state_array_type ;
typedef Kokkos::View< Scalar[][ SpatialDim ] , execution_space > geom_array_type ;
typedef Kokkos::View< Scalar[] , execution_space > array_type ;
typedef Kokkos::View< Scalar , execution_space > scalar_type ;
typedef Kokkos::View< Scalar[][ 6 ] , execution_space > elem_sym_tensor_type ;
typedef Kokkos::View< Scalar[][ 9 ] , execution_space > elem_tensor_type ;
typedef Kokkos::View< Scalar[][ 9 ][ NumStates ] , execution_space > elem_tensor_state_type ;
typedef Kokkos::View< Scalar[][ SpatialDim ][ ElemNodeCount ] , execution_space > elem_node_geom_type ;
// Parameters:
const int num_nodes ;
const int num_nodes_owned ;
const int num_elements ;
const Scalar lin_bulk_visc;
const Scalar quad_bulk_visc;
const Scalar two_mu;
const Scalar bulk_modulus;
const Scalar density;
// Mesh:
const elem_node_ids_type elem_node_connectivity ;
const node_elem_ids_type node_elem_connectivity ;
const node_coords_type model_coords ;
// Compute:
const scalar_type dt ;
const scalar_type prev_dt ;
const geom_state_array_type displacement ;
const geom_state_array_type velocity ;
const geom_array_type acceleration ;
const geom_array_type internal_force ;
const array_type nodal_mass ;
const array_type elem_mass ;
const array_type internal_energy ;
const elem_sym_tensor_type stress_new ;
const elem_tensor_state_type rotation ;
const elem_node_geom_type element_force ;
const elem_tensor_type vel_grad ;
const elem_sym_tensor_type stretch ;
const elem_sym_tensor_type rot_stretch ;
Fields(
const FEMesh & mesh,
Scalar arg_lin_bulk_visc,
Scalar arg_quad_bulk_visc,
Scalar youngs_modulus,
Scalar poissons_ratio,
Scalar arg_density )
: num_nodes( mesh.parallel_data_map.count_owned +
mesh.parallel_data_map.count_receive )
, num_nodes_owned( mesh.parallel_data_map.count_owned )
, num_elements( mesh.elem_node_ids.dimension_0() )
, lin_bulk_visc( arg_lin_bulk_visc )
, quad_bulk_visc( arg_quad_bulk_visc )
, two_mu(youngs_modulus/(1.0+poissons_ratio))
, bulk_modulus(youngs_modulus/(3*(1.0-2.0*poissons_ratio)))
, density(arg_density)
// mesh
, elem_node_connectivity( mesh.elem_node_ids ) // ( num_elements , ElemNodeCount )
, node_elem_connectivity( mesh.node_elem_ids ) // ( num_nodes , ... )
, model_coords( mesh.node_coords ) // ( num_nodes , 3 )
// compute with input/output
, dt( "dt" )
, prev_dt( "prev_dt" )
, displacement( "displacement" , num_nodes )
, velocity( "velocity" , num_nodes )
, acceleration( "acceleration" , num_nodes_owned )
, internal_force( "internal_force" , num_nodes_owned )
, nodal_mass( "nodal_mass" , num_nodes_owned )
, elem_mass( "elem_mass" , num_elements )
, internal_energy( "internal_energy" , num_elements )
, stress_new( "stress_new" , num_elements )
// temporary arrays
, rotation( "rotation" , num_elements )
, element_force( "element_force" , num_elements )
, vel_grad( "vel_grad" , num_elements )
, stretch( "stretch" , num_elements )
, rot_stretch( "rot_stretch" , num_elements )
{ }
};
//----------------------------------------------------------------------------
template< typename Scalar , class DeviceType >
KOKKOS_INLINE_FUNCTION
Scalar dot8( const Scalar * a , const Scalar * b )
{ return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3] +
a[4] * b[4] + a[5] * b[5] + a[6] * b[6] + a[7] * b[7] ; }
template< typename Scalar , class DeviceType >
KOKKOS_INLINE_FUNCTION
void comp_grad( const Scalar * const x ,
const Scalar * const y ,
const Scalar * const z,
Scalar * const grad_x ,
Scalar * const grad_y ,
Scalar * const grad_z )
{
// calc X difference vectors
Scalar R42=(x[3] - x[1]);
Scalar R52=(x[4] - x[1]);
Scalar R54=(x[4] - x[3]);
Scalar R63=(x[5] - x[2]);
Scalar R83=(x[7] - x[2]);
Scalar R86=(x[7] - x[5]);
Scalar R31=(x[2] - x[0]);
Scalar R61=(x[5] - x[0]);
Scalar R74=(x[6] - x[3]);
Scalar R72=(x[6] - x[1]);
Scalar R75=(x[6] - x[4]);
Scalar R81=(x[7] - x[0]);
Scalar t1=(R63 + R54);
Scalar t2=(R61 + R74);
Scalar t3=(R72 + R81);
Scalar t4 =(R86 + R42);
Scalar t5 =(R83 + R52);
Scalar t6 =(R75 + R31);
// Calculate Y gradient from X and Z data
grad_y[0] = (z[1] * t1) - (z[2] * R42) - (z[3] * t5) + (z[4] * t4) + (z[5] * R52) - (z[7] * R54);
grad_y[1] = (z[2] * t2) + (z[3] * R31) - (z[0] * t1) - (z[5] * t6) + (z[6] * R63) - (z[4] * R61);
grad_y[2] = (z[3] * t3) + (z[0] * R42) - (z[1] * t2) - (z[6] * t4) + (z[7] * R74) - (z[5] * R72);
grad_y[3] = (z[0] * t5) - (z[1] * R31) - (z[2] * t3) + (z[7] * t6) + (z[4] * R81) - (z[6] * R83);
grad_y[4] = (z[5] * t3) + (z[6] * R86) - (z[7] * t2) - (z[0] * t4) - (z[3] * R81) + (z[1] * R61);
grad_y[5] = (z[6] * t5) - (z[4] * t3) - (z[7] * R75) + (z[1] * t6) - (z[0] * R52) + (z[2] * R72);
grad_y[6] = (z[7] * t1) - (z[5] * t5) - (z[4] * R86) + (z[2] * t4) - (z[1] * R63) + (z[3] * R83);
grad_y[7] = (z[4] * t2) - (z[6] * t1) + (z[5] * R75) - (z[3] * t6) - (z[2] * R74) + (z[0] * R54);
// calc Z difference vectors
R42=(z[3] - z[1]);
R52=(z[4] - z[1]);
R54=(z[4] - z[3]);
R63=(z[5] - z[2]);
R83=(z[7] - z[2]);
R86=(z[7] - z[5]);
R31=(z[2] - z[0]);
R61=(z[5] - z[0]);
R74=(z[6] - z[3]);
R72=(z[6] - z[1]);
R75=(z[6] - z[4]);
R81=(z[7] - z[0]);
t1=(R63 + R54);
t2=(R61 + R74);
t3=(R72 + R81);
t4 =(R86 + R42);
t5 =(R83 + R52);
t6 =(R75 + R31);
// Calculate X gradient from Y and Z data
grad_x[0] = (y[1] * t1) - (y[2] * R42) - (y[3] * t5) + (y[4] * t4) + (y[5] * R52) - (y[7] * R54);
grad_x[1] = (y[2] * t2) + (y[3] * R31) - (y[0] * t1) - (y[5] * t6) + (y[6] * R63) - (y[4] * R61);
grad_x[2] = (y[3] * t3) + (y[0] * R42) - (y[1] * t2) - (y[6] * t4) + (y[7] * R74) - (y[5] * R72);
grad_x[3] = (y[0] * t5) - (y[1] * R31) - (y[2] * t3) + (y[7] * t6) + (y[4] * R81) - (y[6] * R83);
grad_x[4] = (y[5] * t3) + (y[6] * R86) - (y[7] * t2) - (y[0] * t4) - (y[3] * R81) + (y[1] * R61);
grad_x[5] = (y[6] * t5) - (y[4] * t3) - (y[7] * R75) + (y[1] * t6) - (y[0] * R52) + (y[2] * R72);
grad_x[6] = (y[7] * t1) - (y[5] * t5) - (y[4] * R86) + (y[2] * t4) - (y[1] * R63) + (y[3] * R83);
grad_x[7] = (y[4] * t2) - (y[6] * t1) + (y[5] * R75) - (y[3] * t6) - (y[2] * R74) + (y[0] * R54);
// calc Y difference vectors
R42=(y[3] - y[1]);
R52=(y[4] - y[1]);
R54=(y[4] - y[3]);
R63=(y[5] - y[2]);
R83=(y[7] - y[2]);
R86=(y[7] - y[5]);
R31=(y[2] - y[0]);
R61=(y[5] - y[0]);
R74=(y[6] - y[3]);
R72=(y[6] - y[1]);
R75=(y[6] - y[4]);
R81=(y[7] - y[0]);
t1=(R63 + R54);
t2=(R61 + R74);
t3=(R72 + R81);
t4 =(R86 + R42);
t5 =(R83 + R52);
t6 =(R75 + R31);
// Calculate Z gradient from X and Y data
grad_z[0] = (x[1] * t1) - (x[2] * R42) - (x[3] * t5) + (x[4] * t4) + (x[5] * R52) - (x[7] * R54);
grad_z[1] = (x[2] * t2) + (x[3] * R31) - (x[0] * t1) - (x[5] * t6) + (x[6] * R63) - (x[4] * R61);
grad_z[2] = (x[3] * t3) + (x[0] * R42) - (x[1] * t2) - (x[6] * t4) + (x[7] * R74) - (x[5] * R72);
grad_z[3] = (x[0] * t5) - (x[1] * R31) - (x[2] * t3) + (x[7] * t6) + (x[4] * R81) - (x[6] * R83);
grad_z[4] = (x[5] * t3) + (x[6] * R86) - (x[7] * t2) - (x[0] * t4) - (x[3] * R81) + (x[1] * R61);
grad_z[5] = (x[6] * t5) - (x[4] * t3) - (x[7] * R75) + (x[1] * t6) - (x[0] * R52) + (x[2] * R72);
grad_z[6] = (x[7] * t1) - (x[5] * t5) - (x[4] * R86) + (x[2] * t4) - (x[1] * R63) + (x[3] * R83);
grad_z[7] = (x[4] * t2) - (x[6] * t1) + (x[5] * R75) - (x[3] * t6) - (x[2] * R74) + (x[0] * R54);
}
//----------------------------------------------------------------------------
template< typename Scalar , class DeviceType >
struct initialize_element
{
typedef DeviceType execution_space ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
typename Fields::elem_node_ids_type elem_node_connectivity ;
typename Fields::node_coords_type model_coords ;
typename Fields::elem_sym_tensor_type stretch ;
typename Fields::elem_tensor_state_type rotation ;
typename Fields::array_type elem_mass ;
const Scalar density ;
initialize_element( const Fields & mesh_fields )
: elem_node_connectivity( mesh_fields.elem_node_connectivity )
, model_coords( mesh_fields.model_coords )
, stretch( mesh_fields.stretch )
, rotation( mesh_fields.rotation )
, elem_mass( mesh_fields.elem_mass )
, density( mesh_fields.density )
{}
KOKKOS_INLINE_FUNCTION
void operator()( int ielem )const
{
const int K_XX = 0 ;
const int K_YY = 1 ;
const int K_ZZ = 2 ;
const Scalar ONE12TH = 1.0 / 12.0 ;
Scalar x[ Fields::ElemNodeCount ];
Scalar y[ Fields::ElemNodeCount ];
Scalar z[ Fields::ElemNodeCount ];
Scalar grad_x[ Fields::ElemNodeCount ];
Scalar grad_y[ Fields::ElemNodeCount ];
Scalar grad_z[ Fields::ElemNodeCount ];
for ( int i = 0 ; i < Fields::ElemNodeCount ; ++i ) {
const int n = elem_node_connectivity( ielem , i );
x[i] = model_coords( n , 0 );
y[i] = model_coords( n , 1 );
z[i] = model_coords( n , 2 );
}
comp_grad<Scalar,execution_space>( x, y, z, grad_x, grad_y, grad_z);
stretch(ielem,K_XX) = 1 ;
stretch(ielem,K_YY) = 1 ;
stretch(ielem,K_ZZ) = 1 ;
rotation(ielem,K_XX,0) = 1 ;
rotation(ielem,K_YY,0) = 1 ;
rotation(ielem,K_ZZ,0) = 1 ;
rotation(ielem,K_XX,1) = 1 ;
rotation(ielem,K_YY,1) = 1 ;
rotation(ielem,K_ZZ,1) = 1 ;
elem_mass(ielem) = ONE12TH * density *
dot8<Scalar,execution_space>( x , grad_x );
}
static void apply( const Fields & mesh_fields )
{
initialize_element op( mesh_fields );
Kokkos::parallel_for( mesh_fields.num_elements , op );
}
};
template<typename Scalar , class DeviceType >
struct initialize_node
{
typedef DeviceType execution_space ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
typename Fields::node_elem_ids_type node_elem_connectivity ;
typename Fields::array_type nodal_mass ;
typename Fields::array_type elem_mass ;
static const int ElemNodeCount = Fields::ElemNodeCount ;
initialize_node( const Fields & mesh_fields )
: node_elem_connectivity( mesh_fields.node_elem_connectivity )
, nodal_mass( mesh_fields.nodal_mass )
, elem_mass( mesh_fields.elem_mass )
{}
KOKKOS_INLINE_FUNCTION
void operator()( int inode )const
{
const int begin = node_elem_connectivity.row_map[inode];
const int end = node_elem_connectivity.row_map[inode+1];
Scalar node_mass = 0;
for(int i = begin; i != end; ++i) {
const int elem_id = node_elem_connectivity.entries( i , 0 );
node_mass += elem_mass(elem_id);
}
nodal_mass(inode) = node_mass / ElemNodeCount ;
}
static void apply( const Fields & mesh_fields )
{
initialize_node op( mesh_fields );
Kokkos::parallel_for( mesh_fields.num_nodes_owned , op );
}
};
//----------------------------------------------------------------------------
template<typename Scalar, class DeviceType >
struct grad
{
typedef DeviceType execution_space ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
static const int ElemNodeCount = Fields::ElemNodeCount ;
static const int K_F_XX = Fields::K_F_XX ;
static const int K_F_YY = Fields::K_F_YY ;
static const int K_F_ZZ = Fields::K_F_ZZ ;
static const int K_F_XY = Fields::K_F_XY ;
static const int K_F_YZ = Fields::K_F_YZ ;
static const int K_F_ZX = Fields::K_F_ZX ;
static const int K_F_YX = Fields::K_F_YX ;
static const int K_F_ZY = Fields::K_F_ZY ;
static const int K_F_XZ = Fields::K_F_XZ ;
// Global arrays used by this functor.
const typename Fields::elem_node_ids_type elem_node_connectivity ;
const typename Fields::node_coords_type model_coords ;
const typename Fields::geom_state_array_type displacement ;
const typename Fields::geom_state_array_type velocity ;
const typename Fields::elem_tensor_type vel_grad ;
const typename Fields::scalar_type dt ;
const int current_state;
const int previous_state;
// Constructor on the Host to populate this device functor.
// All array view copies are shallow.
grad( const Fields & fields,
const int arg_current_state,
const int arg_previous_state)
: elem_node_connectivity( fields.elem_node_connectivity)
, model_coords( fields.model_coords)
, displacement( fields.displacement)
, velocity( fields.velocity)
, vel_grad( fields.vel_grad)
, dt( fields.dt)
, current_state(arg_current_state)
, previous_state(arg_previous_state)
{ }
//--------------------------------------------------------------------------
// Calculate Velocity Gradients
KOKKOS_INLINE_FUNCTION
void v_grad( int ielem,
Scalar * vx, Scalar * vy, Scalar * vz,
Scalar * grad_x, Scalar * grad_y, Scalar * grad_z,
Scalar inv_vol) const
{
const int K_F_XX = Fields::K_F_XX ;
const int K_F_YY = Fields::K_F_YY ;
const int K_F_ZZ = Fields::K_F_ZZ ;
const int K_F_XY = Fields::K_F_XY ;
const int K_F_YZ = Fields::K_F_YZ ;
const int K_F_ZX = Fields::K_F_ZX ;
const int K_F_YX = Fields::K_F_YX ;
const int K_F_ZY = Fields::K_F_ZY ;
const int K_F_XZ = Fields::K_F_XZ ;
vel_grad(ielem, K_F_XX) = inv_vol * dot8<Scalar,execution_space>( vx , grad_x );
vel_grad(ielem, K_F_YX) = inv_vol * dot8<Scalar,execution_space>( vy , grad_x );
vel_grad(ielem, K_F_ZX) = inv_vol * dot8<Scalar,execution_space>( vz , grad_x );
vel_grad(ielem, K_F_XY) = inv_vol * dot8<Scalar,execution_space>( vx , grad_y );
vel_grad(ielem, K_F_YY) = inv_vol * dot8<Scalar,execution_space>( vy , grad_y );
vel_grad(ielem, K_F_ZY) = inv_vol * dot8<Scalar,execution_space>( vz , grad_y );
vel_grad(ielem, K_F_XZ) = inv_vol * dot8<Scalar,execution_space>( vx , grad_z );
vel_grad(ielem, K_F_YZ) = inv_vol * dot8<Scalar,execution_space>( vy , grad_z );
vel_grad(ielem, K_F_ZZ) = inv_vol * dot8<Scalar,execution_space>( vz , grad_z );
}
//--------------------------------------------------------------------------
// Functor operator() which calls the three member functions.
KOKKOS_INLINE_FUNCTION
void operator()( int ielem )const
{
const int X = 0 ;
const int Y = 1 ;
const int Z = 2 ;
const Scalar dt_scale = -0.5 * *dt;
// declare and reuse local data for frequently accessed data to
// reduce global memory reads and writes.
Scalar x[8], y[8], z[8];
Scalar vx[8], vy[8], vz[8];
Scalar grad_x[8], grad_y[8], grad_z[8];
// Read global velocity once and use many times
// via local registers / L1 cache.
// store the velocity information in local memory before using,
// so it can be returned for other functions to use
// Read global coordinates and velocity once and use many times
// via local registers / L1 cache.
// load X coordinate information and move by half time step
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
const int n = elem_node_connectivity( ielem , i );
vx[i] = velocity( n , X , current_state );
vy[i] = velocity( n , Y , current_state );
vz[i] = velocity( n , Z , current_state );
x[i] = model_coords( n , X ) +
displacement( n , X , current_state ) +
dt_scale * vx[i];
y[i] = model_coords( n , Y ) +
displacement( n , Y , current_state ) +
dt_scale * vy[i];
z[i] = model_coords( n , Z ) +
displacement( n , Z , current_state ) +
dt_scale * vz[i];
}
comp_grad<Scalar,execution_space>( x, y, z, grad_x, grad_y, grad_z);
// Calculate hexahedral volume from x model_coords and gradient information
const Scalar inv_vol = 1.0 / dot8<Scalar,execution_space>( x , grad_x );
v_grad(ielem, vx, vy, vz, grad_x, grad_y, grad_z, inv_vol);
}
static void apply( const Fields & fields ,
const int arg_current_state ,
const int arg_previous_state )
{
grad op( fields, arg_current_state , arg_previous_state );
Kokkos::parallel_for( fields.num_elements , op );
}
};
//----------------------------------------------------------------------------
template<typename Scalar, class DeviceType >
struct decomp_rotate
{
typedef DeviceType execution_space ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
static const int ElemNodeCount = Fields::ElemNodeCount ;
static const int K_F_XX = Fields::K_F_XX ;
static const int K_F_YY = Fields::K_F_YY ;
static const int K_F_ZZ = Fields::K_F_ZZ ;
static const int K_F_XY = Fields::K_F_XY ;
static const int K_F_YZ = Fields::K_F_YZ ;
static const int K_F_ZX = Fields::K_F_ZX ;
static const int K_F_YX = Fields::K_F_YX ;
static const int K_F_ZY = Fields::K_F_ZY ;
static const int K_F_XZ = Fields::K_F_XZ ;
static const int K_S_XX = Fields::K_S_XX ;
static const int K_S_YY = Fields::K_S_YY ;
static const int K_S_ZZ = Fields::K_S_ZZ ;
static const int K_S_XY = Fields::K_S_XY ;
static const int K_S_YZ = Fields::K_S_YZ ;
static const int K_S_ZX = Fields::K_S_ZX ;
static const int K_S_YX = Fields::K_S_YX ;
static const int K_S_ZY = Fields::K_S_ZY ;
static const int K_S_XZ = Fields::K_S_XZ ;
static const int K_V_XY = Fields::K_V_XY ;
static const int K_V_YZ = Fields::K_V_YZ ;
static const int K_V_ZX = Fields::K_V_ZX ;
// Global arrays used by this functor.
const typename Fields::elem_tensor_state_type rotation ;
const typename Fields::elem_tensor_type vel_grad ;
const typename Fields::elem_sym_tensor_type stretch ;
const typename Fields::elem_sym_tensor_type rot_stretch ;
const typename Fields::scalar_type dt_value ;
const int current_state;
const int previous_state;
decomp_rotate( const Fields & mesh_fields ,
const int arg_current_state,
const int arg_previous_state)
: rotation( mesh_fields.rotation )
, vel_grad( mesh_fields.vel_grad )
, stretch( mesh_fields.stretch )
, rot_stretch( mesh_fields.rot_stretch )
, dt_value( mesh_fields.dt)
, current_state( arg_current_state)
, previous_state(arg_previous_state)
{}
static void apply( const Fields & mesh_fields ,
const int arg_current_state ,
const int arg_previous_state )
{
decomp_rotate op( mesh_fields , arg_current_state , arg_previous_state );
Kokkos::parallel_for( mesh_fields.num_elements , op );
}
KOKKOS_INLINE_FUNCTION
void additive_decomp(int ielem, Scalar * v_gr, Scalar * str_ten) const
{
// In addition to calculating stretching_tensor,
// use this as an opportunity to load global
// variables into a local space
for ( int i = 0 ; i < 9 ; ++i ) {
v_gr[i] = vel_grad( ielem , i );
}
//
// Symmetric part
//
str_ten[K_S_XX] = v_gr[K_F_XX];
str_ten[K_S_YY] = v_gr[K_F_YY];
str_ten[K_S_ZZ] = v_gr[K_F_ZZ];
str_ten[K_S_XY] = 0.5*(v_gr[K_F_XY] + v_gr[K_F_YX]);
str_ten[K_S_YZ] = 0.5*(v_gr[K_F_YZ] + v_gr[K_F_ZY]);
str_ten[K_S_ZX] = 0.5*(v_gr[K_F_ZX] + v_gr[K_F_XZ]);
}
KOKKOS_INLINE_FUNCTION
void polar_decomp(int ielem, Scalar * v_gr, Scalar * str_ten, Scalar * str, Scalar * vort, Scalar * rot_old, Scalar * rot_new)const
{
const Scalar dt = *dt_value;
const Scalar dt_half = 0.5 * dt;
// Skew Symmetric part
vort[K_V_XY] = 0.5*(v_gr[K_F_XY] - v_gr[K_F_YX]);
vort[K_V_YZ] = 0.5*(v_gr[K_F_YZ] - v_gr[K_F_ZY]);
vort[K_V_ZX] = 0.5*(v_gr[K_F_ZX] - v_gr[K_F_XZ]);
// calculate the rates of rotation via gauss elimination.
for ( int i = 0 ; i < 6 ; ++i ) {
str[i] = stretch(ielem, i);
}
Scalar z1 = str_ten[K_S_XY] * str[K_S_ZX] -
str_ten[K_S_ZX] * str[K_S_XY] +
str_ten[K_S_YY] * str[K_S_YZ] -
str_ten[K_S_YZ] * str[K_S_YY] +
str_ten[K_S_YZ] * str[K_S_ZZ] -
str_ten[K_S_ZZ] * str[K_S_YZ];
Scalar z2 = str_ten[K_S_ZX] * str[K_S_XX] -
str_ten[K_S_XX] * str[K_S_ZX] +
str_ten[K_S_YZ] * str[K_S_XY] -
str_ten[K_S_XY] * str[K_S_YZ] +
str_ten[K_S_ZZ] * str[K_S_ZX] -
str_ten[K_S_ZX] * str[K_S_ZZ];
Scalar z3 = str_ten[K_S_XX] * str[K_S_XY] -
str_ten[K_S_XY] * str[K_S_XX] +
str_ten[K_S_XY] * str[K_S_YY] -
str_ten[K_S_YY] * str[K_S_XY] +
str_ten[K_S_ZX] * str[K_S_YZ] -
str_ten[K_S_YZ] * str[K_S_ZX];
// forward elimination
const Scalar a1inv = 1.0 / (str[K_S_YY] + str[K_S_ZZ]);
const Scalar a4BYa1 = -1 * str[K_S_XY] * a1inv;
const Scalar a2inv = 1.0 / (str[K_S_ZZ] + str[K_S_XX] + str[K_S_XY] * a4BYa1);
const Scalar a5 = -str[K_S_YZ] + str[K_S_ZX] * a4BYa1;
z2 -= z1 * a4BYa1;
Scalar a6BYa1 = -1 * str[K_S_ZX] * a1inv;
const Scalar a5BYa2 = a5 * a2inv;
z3 -= z1 * a6BYa1 - z2 * a5BYa2;
// backward substitution -
z3 /= (str[K_S_XX] + str[K_S_YY] + str[K_S_ZX] * a6BYa1 + a5 * a5BYa2);
z2 = (z2 - a5 * z3) * a2inv;
z1 = (z1*a1inv - a6BYa1 * z3 -a4BYa1 * z2);
// calculate rotation rates - recall that spin_rate is an asymmetric tensor,
// so compute spin rate vector as dual of spin rate tensor,
// i.e w_i = e_ijk * spin_rate_jk
z1 += vort[K_V_YZ];
z2 += vort[K_V_ZX];
z3 += vort[K_V_XY];
// update rotation tensor:
// 1) premultiply old rotation tensor to get right-hand side.
for ( int i = 0 ; i < 9 ; ++i ) {
rot_old[i] = rotation(ielem, i, previous_state);
}
Scalar r_XX = rot_old[K_F_XX] + dt_half*( z3 * rot_old[K_F_YX] - z2 * rot_old[K_F_ZX] );
Scalar r_YX = rot_old[K_F_YX] + dt_half*( z1 * rot_old[K_F_ZX] - z3 * rot_old[K_F_XX] );
Scalar r_ZX = rot_old[K_F_ZX] + dt_half*( z2 * rot_old[K_F_XX] - z1 * rot_old[K_F_YX] );
Scalar r_XY = rot_old[K_F_XY] + dt_half*( z3 * rot_old[K_F_YY] - z2 * rot_old[K_F_ZY] );
Scalar r_YY = rot_old[K_F_YY] + dt_half*( z1 * rot_old[K_F_ZY] - z3 * rot_old[K_F_XY] );
Scalar r_ZY = rot_old[K_F_ZY] + dt_half*( z2 * rot_old[K_F_XY] - z1 * rot_old[K_F_YY] );
Scalar r_XZ = rot_old[K_F_XZ] + dt_half*( z3 * rot_old[K_F_YZ] - z2 * rot_old[K_F_ZZ] );
Scalar r_YZ = rot_old[K_F_YZ] + dt_half*( z1 * rot_old[K_F_ZZ] - z3 * rot_old[K_F_XZ] );
Scalar r_ZZ = rot_old[K_F_ZZ] + dt_half*( z2 * rot_old[K_F_XZ] - z1 * rot_old[K_F_YZ] );
// 2) solve for new rotation tensor via gauss elimination.
// forward elimination -
Scalar a12 = - dt_half * z3;
Scalar a13 = dt_half * z2;
Scalar b32 = - dt_half * z1;
Scalar a22inv = 1.0 / (1.0 + a12 * a12);
Scalar a13a12 = a13*a12;
Scalar a23 = b32 + a13a12;
r_YX += r_XX * a12;
r_YY += r_XY * a12;
r_YZ += r_XZ * a12;
b32 = (b32 - a13a12) * a22inv;
r_ZX += r_XX * a13 + r_YX * b32;
r_ZY += r_XY * a13 + r_YY * b32;
r_ZZ += r_XZ * a13 + r_YZ * b32;
// backward substitution -
const Scalar a33inv = 1.0 / (1.0 + a13 * a13 + a23 * b32);
rot_new[K_F_ZX] = r_ZX * a33inv;
rot_new[K_F_ZY] = r_ZY * a33inv;
rot_new[K_F_ZZ] = r_ZZ * a33inv;
rot_new[K_F_YX] = ( r_YX - rot_new[K_F_ZX] * a23 ) * a22inv;
rot_new[K_F_YY] = ( r_YY - rot_new[K_F_ZY] * a23 ) * a22inv;
rot_new[K_F_YZ] = ( r_YZ - rot_new[K_F_ZZ] * a23 ) * a22inv;
rot_new[K_F_XX] = r_XX - rot_new[K_F_ZX] * a13 - rot_new[K_F_YX] * a12;
rot_new[K_F_XY] = r_XY - rot_new[K_F_ZY] * a13 - rot_new[K_F_YY] * a12;
rot_new[K_F_XZ] = r_XZ - rot_new[K_F_ZZ] * a13 - rot_new[K_F_YZ] * a12;
for ( int i = 0 ; i < 9 ; ++i ) {
rotation(ielem, i, current_state) = rot_new[i] ;
}
// update stretch tensor in the new configuration -
const Scalar a1 = str_ten[K_S_XY] + vort[K_V_XY];
const Scalar a2 = str_ten[K_S_YZ] + vort[K_V_YZ];
const Scalar a3 = str_ten[K_S_ZX] + vort[K_V_ZX];
const Scalar b1 = str_ten[K_S_ZX] - vort[K_V_ZX];
const Scalar b2 = str_ten[K_S_XY] - vort[K_V_XY];
const Scalar b3 = str_ten[K_S_YZ] - vort[K_V_YZ];
const Scalar s_XX = str[K_S_XX];
const Scalar s_YY = str[K_S_YY];
const Scalar s_ZZ = str[K_S_ZZ];
const Scalar s_XY = str[K_S_XY];
const Scalar s_YZ = str[K_S_YZ];
const Scalar s_ZX = str[K_S_ZX];
str[K_S_XX] += dt * (str_ten[K_S_XX] * s_XX + ( a1 + z3 ) * s_XY + ( b1 - z2 ) * s_ZX);
str[K_S_YY] += dt * (str_ten[K_S_YY] * s_YY + ( a2 + z1 ) * s_YZ + ( b2 - z3 ) * s_XY);
str[K_S_ZZ] += dt * (str_ten[K_S_ZZ] * s_ZZ + ( a3 + z2 ) * s_ZX + ( b3 - z1 ) * s_YZ);
str[K_S_XY] += dt * (str_ten[K_S_XX] * s_XY + ( a1 ) * s_YY + ( b1 ) * s_YZ - z3 * s_XX + z1 * s_ZX);
str[K_S_YZ] += dt * (str_ten[K_S_YY] * s_YZ + ( a2 ) * s_ZZ + ( b2 ) * s_ZX - z1 * s_YY + z2 * s_XY);
str[K_S_ZX] += dt * (str_ten[K_S_ZZ] * s_ZX + ( a3 ) * s_XX + ( b3 ) * s_XY - z2 * s_ZZ + z3 * s_YZ);
}
KOKKOS_INLINE_FUNCTION
void rotate_tensor(int ielem, Scalar * str_ten, Scalar * str, Scalar * rot_new)const {
Scalar t[9];
Scalar rot_str[6]; // Rotated stretch
t[0] = str_ten[K_S_XX]*rot_new[K_F_XX] +
str_ten[K_S_XY]*rot_new[K_F_YX] +
str_ten[K_S_XZ]*rot_new[K_F_ZX];
t[1] = str_ten[K_S_YX]*rot_new[K_F_XX] +
str_ten[K_S_YY]*rot_new[K_F_YX] +
str_ten[K_S_YZ]*rot_new[K_F_ZX];
t[2] = str_ten[K_S_ZX]*rot_new[K_F_XX] +
str_ten[K_S_ZY]*rot_new[K_F_YX] +
str_ten[K_S_ZZ]*rot_new[K_F_ZX];
t[3] = str_ten[K_S_XX]*rot_new[K_F_XY] +
str_ten[K_S_XY]*rot_new[K_F_YY] +
str_ten[K_S_XZ]*rot_new[K_F_ZY];
t[4] = str_ten[K_S_YX]*rot_new[K_F_XY] +
str_ten[K_S_YY]*rot_new[K_F_YY] +
str_ten[K_S_YZ]*rot_new[K_F_ZY];
t[5] = str_ten[K_S_ZX]*rot_new[K_F_XY] +
str_ten[K_S_ZY]*rot_new[K_F_YY] +
str_ten[K_S_ZZ]*rot_new[K_F_ZY];
t[6] = str_ten[K_S_XX]*rot_new[K_F_XZ] +
str_ten[K_S_XY]*rot_new[K_F_YZ] +
str_ten[K_S_XZ]*rot_new[K_F_ZZ];
t[7] = str_ten[K_S_YX]*rot_new[K_F_XZ] +
str_ten[K_S_YY]*rot_new[K_F_YZ] +
str_ten[K_S_YZ]*rot_new[K_F_ZZ];
t[8] = str_ten[K_S_ZX]*rot_new[K_F_XZ] +
str_ten[K_S_ZY]*rot_new[K_F_YZ] +
str_ten[K_S_ZZ]*rot_new[K_F_ZZ];
rot_str[ K_S_XX ] = rot_new[K_F_XX] * t[0] +
rot_new[K_F_YX] * t[1] +
rot_new[K_F_ZX] * t[2];
rot_str[ K_S_YY ] = rot_new[K_F_XY] * t[3] +
rot_new[K_F_YY] * t[4] +
rot_new[K_F_ZY] * t[5];
rot_str[ K_S_ZZ ] = rot_new[K_F_XZ] * t[6] +
rot_new[K_F_YZ] * t[7] +
rot_new[K_F_ZZ] * t[8];
rot_str[ K_S_XY ] = rot_new[K_F_XX] * t[3] +
rot_new[K_F_YX] * t[4] +
rot_new[K_F_ZX] * t[5];
rot_str[ K_S_YZ ] = rot_new[K_F_XY] * t[6] +
rot_new[K_F_YY] * t[7] +
rot_new[K_F_ZY] * t[8];
rot_str[ K_S_ZX ] = rot_new[K_F_XZ] * t[0] +
rot_new[K_F_YZ] * t[1] +
rot_new[K_F_ZZ] * t[2];
for ( int i = 0 ; i < 6 ; ++i ) {
rot_stretch(ielem, i) = rot_str[i] ;
}
for ( int i = 0 ; i < 6 ; ++i ) {
stretch(ielem, i) = str[i] ;
}
}
KOKKOS_INLINE_FUNCTION
void operator()( int ielem )const {
// Local scratch space to avoid multiple
// accesses to global memory.
Scalar str_ten[6]; // Stretching tensor
Scalar str[6]; // Stretch
Scalar rot_old[9]; // Rotation old
Scalar rot_new[9]; // Rotation new
Scalar vort[3]; // Vorticity
Scalar v_gr[9]; // Velocity gradient
additive_decomp(ielem, v_gr, str_ten);
polar_decomp(ielem, v_gr, str_ten, str, vort, rot_old, rot_new);
rotate_tensor(ielem, str_ten, str, rot_new);
}
};
//----------------------------------------------------------------------------
template<typename Scalar, class DeviceType >
struct internal_force
{
typedef DeviceType execution_space ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
static const int ElemNodeCount = Fields::ElemNodeCount ;
static const int K_F_XX = Fields::K_F_XX ;
static const int K_F_YY = Fields::K_F_YY ;
static const int K_F_ZZ = Fields::K_F_ZZ ;
static const int K_F_XY = Fields::K_F_XY ;
static const int K_F_YZ = Fields::K_F_YZ ;
static const int K_F_ZX = Fields::K_F_ZX ;
static const int K_F_YX = Fields::K_F_YX ;
static const int K_F_ZY = Fields::K_F_ZY ;
static const int K_F_XZ = Fields::K_F_XZ ;
static const int K_S_XX = Fields::K_S_XX ;
static const int K_S_YY = Fields::K_S_YY ;
static const int K_S_ZZ = Fields::K_S_ZZ ;
static const int K_S_XY = Fields::K_S_XY ;
static const int K_S_YZ = Fields::K_S_YZ ;
static const int K_S_ZX = Fields::K_S_ZX ;
static const int K_S_YX = Fields::K_S_YX ;
static const int K_S_ZY = Fields::K_S_ZY ;
static const int K_S_XZ = Fields::K_S_XZ ;
//--------------------------------------------------------------------------
// Reduction:
typedef Scalar value_type;
KOKKOS_INLINE_FUNCTION
static void init(value_type &update) {
update = 1.0e32;
}
KOKKOS_INLINE_FUNCTION
static void join( volatile value_type & update,
const volatile value_type & source )
{
update = update < source ? update : source;
}
// Final serial processing of reduction value:
KOKKOS_INLINE_FUNCTION
void final( value_type & result ) const
{
*prev_dt = *dt ;
*dt = result ;
};
//--------------------------------------------------------------------------
// Global arrays used by this functor.
const typename Fields::elem_node_ids_type elem_node_connectivity ;
const typename Fields::node_coords_type model_coords ;
const typename Fields::scalar_type dt ;
const typename Fields::scalar_type prev_dt ;
const typename Fields::geom_state_array_type displacement ;
const typename Fields::geom_state_array_type velocity ;
const typename Fields::array_type elem_mass ;
const typename Fields::array_type internal_energy ;
const typename Fields::elem_sym_tensor_type stress_new ;
const typename Fields::elem_node_geom_type element_force ;
const typename Fields::elem_tensor_state_type rotation ;
const typename Fields::elem_sym_tensor_type rot_stretch ;
const Scalar two_mu;
const Scalar bulk_modulus;
const Scalar lin_bulk_visc;
const Scalar quad_bulk_visc;
const Scalar user_dt;
const int current_state;
internal_force( const Fields & mesh_fields,
const Scalar arg_user_dt,
const int arg_current_state )
: elem_node_connectivity( mesh_fields.elem_node_connectivity )
, model_coords( mesh_fields.model_coords )
, dt( mesh_fields.dt )
, prev_dt( mesh_fields.prev_dt )
, displacement( mesh_fields.displacement )
, velocity( mesh_fields.velocity )
, elem_mass( mesh_fields.elem_mass )
, internal_energy( mesh_fields.internal_energy )
, stress_new( mesh_fields.stress_new )
, element_force( mesh_fields.element_force )
, rotation( mesh_fields.rotation )
, rot_stretch( mesh_fields.rot_stretch )
, two_mu( mesh_fields.two_mu )
, bulk_modulus( mesh_fields.bulk_modulus )
, lin_bulk_visc( mesh_fields.lin_bulk_visc )
, quad_bulk_visc( mesh_fields.quad_bulk_visc )
, user_dt( arg_user_dt )
, current_state( arg_current_state )
{}
static void apply( const Fields & mesh_fields ,
const Scalar arg_user_dt,
const int arg_current_state )
{
internal_force op_force( mesh_fields , arg_user_dt , arg_current_state );
Kokkos::parallel_reduce( mesh_fields.num_elements, op_force );
}
//--------------------------------------------------------------------------
KOKKOS_INLINE_FUNCTION
void rotate_tensor_backward(int ielem ,
const Scalar * const s_n ,
Scalar * const rot_stress )const
{
const int rot_state = current_state ; // 1 ;
// t : temporary variables
// s_n : stress_new in local memory space
// r_n : rotation_new in local memory space
Scalar t[9], r_n[9];
r_n[0] = rotation(ielem, 0, rot_state );
r_n[1] = rotation(ielem, 1, rot_state );
r_n[2] = rotation(ielem, 2, rot_state );
r_n[3] = rotation(ielem, 3, rot_state );
r_n[4] = rotation(ielem, 4, rot_state );
r_n[5] = rotation(ielem, 5, rot_state );
r_n[6] = rotation(ielem, 6, rot_state );
r_n[7] = rotation(ielem, 7, rot_state );
r_n[8] = rotation(ielem, 8, rot_state );
t[0] = s_n[K_S_XX]*r_n[K_F_XX]+ s_n[K_S_XY]*r_n[K_F_XY]+ s_n[K_S_XZ]*r_n[K_F_XZ];
t[1] = s_n[K_S_YX]*r_n[K_F_XX]+ s_n[K_S_YY]*r_n[K_F_XY]+ s_n[K_S_YZ]*r_n[K_F_XZ];
t[2] = s_n[K_S_ZX]*r_n[K_F_XX]+ s_n[K_S_ZY]*r_n[K_F_XY]+ s_n[K_S_ZZ]*r_n[K_F_XZ];
t[3] = s_n[K_S_XX]*r_n[K_F_YX]+ s_n[K_S_XY]*r_n[K_F_YY]+ s_n[K_S_XZ]*r_n[K_F_YZ];
t[4] = s_n[K_S_YX]*r_n[K_F_YX]+ s_n[K_S_YY]*r_n[K_F_YY]+ s_n[K_S_YZ]*r_n[K_F_YZ];
t[5] = s_n[K_S_ZX]*r_n[K_F_YX]+ s_n[K_S_ZY]*r_n[K_F_YY]+ s_n[K_S_ZZ]*r_n[K_F_YZ];
t[6] = s_n[K_S_XX]*r_n[K_F_ZX]+ s_n[K_S_XY]*r_n[K_F_ZY]+ s_n[K_S_XZ]*r_n[K_F_ZZ];
t[7] = s_n[K_S_YX]*r_n[K_F_ZX]+ s_n[K_S_YY]*r_n[K_F_ZY]+ s_n[K_S_YZ]*r_n[K_F_ZZ];
t[8] = s_n[K_S_ZX]*r_n[K_F_ZX]+ s_n[K_S_ZY]*r_n[K_F_ZY]+ s_n[K_S_ZZ]*r_n[K_F_ZZ];
rot_stress[ K_S_XX ] = r_n[K_F_XX]*t[0] + r_n[K_F_XY]*t[1] + r_n[K_F_XZ]*t[2];
rot_stress[ K_S_YY ] = r_n[K_F_YX]*t[3] + r_n[K_F_YY]*t[4] + r_n[K_F_YZ]*t[5];
rot_stress[ K_S_ZZ ] = r_n[K_F_ZX]*t[6] + r_n[K_F_ZY]*t[7] + r_n[K_F_ZZ]*t[8];
rot_stress[ K_S_XY ] = r_n[K_F_XX]*t[3] + r_n[K_F_XY]*t[4] + r_n[K_F_XZ]*t[5];
rot_stress[ K_S_YZ ] = r_n[K_F_YX]*t[6] + r_n[K_F_YY]*t[7] + r_n[K_F_YZ]*t[8];
rot_stress[ K_S_ZX ] = r_n[K_F_ZX]*t[0] + r_n[K_F_ZY]*t[1] + r_n[K_F_ZZ]*t[2];
}
//--------------------------------------------------------------------------
KOKKOS_INLINE_FUNCTION
void comp_force(int ielem,
const Scalar * const vx ,
const Scalar * const vy ,
const Scalar * const vz ,
const Scalar * const grad_x ,
const Scalar * const grad_y ,
const Scalar * const grad_z ,
Scalar * total_stress12th ) const
{
Scalar internal_energy_inc = 0 ;
for(int inode = 0; inode < 8; ++inode) {
const Scalar fx =
total_stress12th[K_S_XX] * grad_x[inode] +
total_stress12th[K_S_XY] * grad_y[inode] +
total_stress12th[K_S_XZ] * grad_z[inode] ;
element_force(ielem, 0, inode) = fx ;
const Scalar fy =
total_stress12th[K_S_YX] * grad_x[inode] +
total_stress12th[K_S_YY] * grad_y[inode] +
total_stress12th[K_S_YZ] * grad_z[inode] ;
element_force(ielem, 1, inode) = fy ;
const Scalar fz =
total_stress12th[K_S_ZX] * grad_x[inode] +
total_stress12th[K_S_ZY] * grad_y[inode] +
total_stress12th[K_S_ZZ] * grad_z[inode] ;
element_force(ielem, 2, inode) = fz ;
internal_energy_inc +=
fx * vx[inode] +
fy * vy[inode] +
fz * vz[inode] ;
}
internal_energy(ielem) = internal_energy_inc ;
}
//----------------------------------------------------------------------------
KOKKOS_INLINE_FUNCTION
void get_stress(int ielem , Scalar * const s_n ) const
{
const int kxx = 0;
const int kyy = 1;
const int kzz = 2;
const int kxy = 3;
const int kyz = 4;
const int kzx = 5;
const Scalar e = (rot_stretch(ielem,kxx)+rot_stretch(ielem,kyy)+rot_stretch(ielem,kzz))/3.0;
s_n[kxx] = stress_new(ielem,kxx) += *dt * (two_mu * (rot_stretch(ielem,kxx)-e)+3*bulk_modulus*e);
s_n[kyy] = stress_new(ielem,kyy) += *dt * (two_mu * (rot_stretch(ielem,kyy)-e)+3*bulk_modulus*e);
s_n[kzz] = stress_new(ielem,kzz) += *dt * (two_mu * (rot_stretch(ielem,kzz)-e)+3*bulk_modulus*e);
s_n[kxy] = stress_new(ielem,kxy) += *dt * two_mu * rot_stretch(ielem,kxy);
s_n[kyz] = stress_new(ielem,kyz) += *dt * two_mu * rot_stretch(ielem,kyz);
s_n[kzx] = stress_new(ielem,kzx) += *dt * two_mu * rot_stretch(ielem,kzx);
}
//----------------------------------------------------------------------------
KOKKOS_INLINE_FUNCTION
void operator()( int ielem, value_type & update )const
{
const Scalar ONE12TH = 1.0 / 12.0 ;
Scalar x[8], y[8], z[8] ;
Scalar vx[8], vy[8], vz[8];
Scalar grad_x[8], grad_y[8], grad_z[8];
// Position and velocity:
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
const int n = elem_node_connectivity(ielem,i);
x[i] = model_coords(n, 0) + displacement(n, 0, current_state) ;
y[i] = model_coords(n, 1) + displacement(n, 1, current_state) ;
z[i] = model_coords(n, 2) + displacement(n, 2, current_state) ;
vx[i] = velocity(n, 0, current_state);
vy[i] = velocity(n, 1, current_state);
vz[i] = velocity(n, 2, current_state);
}
// Gradient:
comp_grad<Scalar,execution_space>( x , y , z , grad_x , grad_y , grad_z );
const Scalar mid_vol = dot8<Scalar,execution_space>( x , grad_x );
const Scalar shr = two_mu ;
const Scalar dil = bulk_modulus + ((2.0*shr)/3.0);
const Scalar aspect = 6.0 * mid_vol /
( dot8<Scalar,execution_space>( grad_x , grad_x ) +
dot8<Scalar,execution_space>( grad_y , grad_y ) +
dot8<Scalar,execution_space>( grad_z , grad_z ) );
const Scalar dtrial = std::sqrt(elem_mass(ielem) * aspect / dil);
const Scalar traced = (rot_stretch(ielem, 0) + rot_stretch(ielem, 1) + rot_stretch(ielem, 2));
const Scalar eps = traced < 0 ? (lin_bulk_visc - quad_bulk_visc * traced * dtrial) : lin_bulk_visc ;
const Scalar bulkq = eps * dil * dtrial * traced;
Scalar cur_time_step = dtrial * ( std::sqrt( 1.0 + eps * eps) - eps);
// force fixed time step if input
cur_time_step = user_dt > 0 ? user_dt : cur_time_step;
update = update < cur_time_step ? update : cur_time_step;
Scalar s_n[ 6 ];
get_stress( ielem, s_n );
Scalar total_stress12th[6];
// Get rotated stress:
rotate_tensor_backward(ielem, s_n , total_stress12th );
total_stress12th[0] = ONE12TH*( total_stress12th[ 0 ] + bulkq );
total_stress12th[1] = ONE12TH*( total_stress12th[ 1 ] + bulkq );
total_stress12th[2] = ONE12TH*( total_stress12th[ 2 ] + bulkq );
total_stress12th[3] = ONE12TH*( total_stress12th[ 3 ] );
total_stress12th[4] = ONE12TH*( total_stress12th[ 4 ] );
total_stress12th[5] = ONE12TH*( total_stress12th[ 5 ] );
comp_force(ielem, vx, vy, vz,
grad_x, grad_y, grad_z, total_stress12th);
}
};
//----------------------------------------------------------------------------
template<typename Scalar, class DeviceType >
struct nodal_step
{
typedef DeviceType execution_space ;
typedef typename execution_space::size_type size_type;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
const typename Fields::scalar_type dt ;
const typename Fields::scalar_type prev_dt ;
const typename Fields::node_elem_ids_type node_elem_connectivity ;
const typename Fields::node_coords_type model_coords ;
const typename Fields::array_type nodal_mass ;
const typename Fields::geom_state_array_type displacement ;
const typename Fields::geom_state_array_type velocity ;
const typename Fields::geom_array_type acceleration ;
const typename Fields::geom_array_type internal_force ;
const typename Fields::elem_node_geom_type element_force ;
const Scalar x_bc;
const int current_state;
const int next_state;
nodal_step( const Fields & mesh_fields ,
const Scalar arg_x_bc,
const int arg_current_state,
const int arg_next_state)
: dt( mesh_fields.dt )
, prev_dt( mesh_fields.prev_dt )
, node_elem_connectivity( mesh_fields.node_elem_connectivity )
, model_coords( mesh_fields.model_coords )
, nodal_mass( mesh_fields.nodal_mass )
, displacement( mesh_fields.displacement )
, velocity( mesh_fields.velocity )
, acceleration( mesh_fields.acceleration )
, internal_force( mesh_fields.internal_force )
, element_force( mesh_fields.element_force )
, x_bc( arg_x_bc )
, current_state( arg_current_state )
, next_state( arg_next_state )
{
//std::cout << "finish_step dt: " << dt << std::endl;
//std::cout << "finish_step prev_dt: " << prev_dt << std::endl;
}
static void apply( const Fields & mesh_fields ,
const Scalar arg_x_bc ,
const int arg_current_state ,
const int arg_next_state )
{
nodal_step op( mesh_fields, arg_x_bc, arg_current_state, arg_next_state );
// Only update the owned nodes:
Kokkos::parallel_for( mesh_fields.num_nodes_owned , op );
}
KOKKOS_INLINE_FUNCTION
void operator()(int inode) const
{
// Getting count as per 'CSR-like' data structure
const int begin = node_elem_connectivity.row_map[inode];
const int end = node_elem_connectivity.row_map[inode+1];
double local_force[] = {0.0, 0.0, 0.0};
// Gather-sum internal force from
// each element that a node is attached to.
for ( int i = begin; i < end ; ++i ){
// node_elem_offset is a cumulative structure, so
// node_elem_offset(inode) should be the index where
// a particular row's elem_IDs begin
const int nelem = node_elem_connectivity.entries( i, 0);
// find the row in an element's stiffness matrix
// that corresponds to inode
const int elem_node_index = node_elem_connectivity.entries( i, 1);
local_force[0] += element_force(nelem, 0, elem_node_index);
local_force[1] += element_force(nelem, 1, elem_node_index);
local_force[2] += element_force(nelem, 2, elem_node_index);
}
internal_force(inode, 0) = local_force[0];
internal_force(inode, 1) = local_force[1];
internal_force(inode, 2) = local_force[2];
// Acceleration:
Scalar v_new[3];
Scalar a_current[3];
const Scalar tol = 1.0e-7;
// If not on the boundary then: a = F / m
if ( tol < fabs(model_coords(inode,0)-x_bc) ) {
const Scalar m = nodal_mass( inode );
acceleration(inode,0) = a_current[0] = -local_force[0] / m ;
acceleration(inode,1) = a_current[1] = -local_force[1] / m ;
acceleration(inode,2) = a_current[2] = -local_force[2] / m ;
}
else { //enforce fixed BC
acceleration(inode,0) = a_current[0] = 0;
acceleration(inode,1) = a_current[1] = 0;
acceleration(inode,2) = a_current[2] = 0;
}
// Central difference time integration:
const Scalar dt_disp = *dt ;
const Scalar dt_vel = ( *dt + *prev_dt ) / 2.0 ;
velocity(inode,0,next_state) = v_new[0] =
velocity(inode,0,current_state) + dt_vel * a_current[0];
velocity(inode,1,next_state) = v_new[1] =
velocity(inode,1,current_state) + dt_vel * a_current[1];
velocity(inode,2,next_state) = v_new[2] =
velocity(inode,2,current_state) + dt_vel * a_current[2];
displacement(inode,0,next_state) =
displacement(inode,0,current_state) + dt_disp * v_new[0];
displacement(inode,1,next_state) =
displacement(inode,1,current_state) + dt_disp * v_new[1];
displacement(inode,2,next_state) =
displacement(inode,2,current_state) + dt_disp * v_new[2];
}
};
//----------------------------------------------------------------------------
template< typename Scalar , class DeviceType >
struct pack_state
{
typedef DeviceType execution_space ;
typedef typename execution_space::size_type size_type ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
typedef typename Fields::geom_state_array_type::value_type value_type ;
typedef Kokkos::View< value_type* , execution_space > buffer_type ;
static const unsigned value_count = 6 ;
const typename Fields::geom_state_array_type displacement ;
const typename Fields::geom_state_array_type velocity ;
const buffer_type output ;
const size_type inode_base ;
const size_type state_next ;
pack_state( const buffer_type & arg_output ,
const Fields & mesh_fields ,
const size_type arg_begin ,
const size_type arg_state )
: displacement( mesh_fields.displacement )
, velocity( mesh_fields.velocity )
, output( arg_output )
, inode_base( arg_begin )
, state_next( arg_state )
{}
static void apply( const buffer_type & arg_output ,
const size_type arg_begin ,
const size_type arg_count ,
const Fields & mesh_fields ,
const size_type arg_state )
{
pack_state op( arg_output , mesh_fields , arg_begin , arg_state );
Kokkos::parallel_for( arg_count , op );
}
KOKKOS_INLINE_FUNCTION
void operator()( const size_type i ) const
{
const size_type inode = inode_base + i ;
size_type j = i * value_count ;
output[j++] = displacement( inode , 0 , state_next );
output[j++] = displacement( inode , 1 , state_next );
output[j++] = displacement( inode , 2 , state_next );
output[j++] = velocity( inode , 0 , state_next );
output[j++] = velocity( inode , 1 , state_next );
output[j++] = velocity( inode , 2 , state_next );
}
};
template< typename Scalar , class DeviceType >
struct unpack_state
{
typedef DeviceType execution_space ;
typedef typename execution_space::size_type size_type ;
typedef Explicit::Fields< Scalar , execution_space > Fields ;
typedef typename Fields::geom_state_array_type::value_type value_type ;
typedef Kokkos::View< value_type* , execution_space > buffer_type ;
static const unsigned value_count = 6 ;
const typename Fields::geom_state_array_type displacement ;
const typename Fields::geom_state_array_type velocity ;
const buffer_type input ;
const size_type inode_base ;
const size_type state_next ;
unpack_state( const buffer_type & arg_input ,
const Fields & mesh_fields ,
const size_type arg_begin ,
const size_type arg_state )
: displacement( mesh_fields.displacement )
, velocity( mesh_fields.velocity )
, input( arg_input )
, inode_base( arg_begin )
, state_next( arg_state )
{}
static void apply( const Fields & mesh_fields ,
const size_type arg_state ,
const buffer_type & arg_input ,
const size_type arg_begin ,
const size_type arg_count )
{
unpack_state op( arg_input , mesh_fields , arg_begin , arg_state );
Kokkos::parallel_for( arg_count , op );
}
KOKKOS_INLINE_FUNCTION
void operator()( const size_type i ) const
{
const size_type inode = inode_base + i ;
size_type j = i * value_count ;
displacement( inode , 0 , state_next ) = input[j++] ;
displacement( inode , 1 , state_next ) = input[j++] ;
displacement( inode , 2 , state_next ) = input[j++] ;
velocity( inode , 0 , state_next ) = input[j++] ;
velocity( inode , 1 , state_next ) = input[j++] ;
velocity( inode , 2 , state_next ) = input[j++] ;
}
};
} /* namespace Explicit */
#endif /* #ifndef KOKKOS_EXPLICITFUNCTORS_HPP */

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