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ElemFunctor.hpp
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/*
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// Kokkos v. 2.0
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#ifndef KOKKOS_EXAMPLE_FEINT_FUNCTORS_HPP
#define KOKKOS_EXAMPLE_FEINT_FUNCTORS_HPP
#include <cstdio>
#include <Kokkos_Core.hpp>
#include <BoxElemFixture.hpp>
namespace Kokkos {
namespace Example {
/** \brief Numerically integrate a function on a finite element mesh and
* project the integrated values to nodes.
*/
template< class FixtureType ,
class FunctionType ,
bool PerformScatterAddWithAtomic >
struct FiniteElementIntegration ;
// Specialized for an 'Example::BoxElemFixture' finite element mesh
template< class Device , BoxElemPart::ElemOrder ElemOrder , class GridMap ,
class FunctionType ,
bool PerformScatterAddWithAtomic >
struct FiniteElementIntegration<
Kokkos::Example::BoxElemFixture< Device , ElemOrder , GridMap > ,
FunctionType ,
PerformScatterAddWithAtomic >
{
// Element mesh types:
typedef Kokkos::Example::BoxElemFixture< Device , ElemOrder >
BoxFixtureType ;
typedef Kokkos::Example::HexElement_Data< BoxFixtureType::ElemNode >
HexElemDataType ;
enum { ElemNodeCount = HexElemDataType::element_node_count };
enum { IntegrationCount = HexElemDataType::integration_count };
enum { ValueCount = FunctionType::value_count };
// Dictionary of view types:
typedef View<int*, Device> ElemErrorType ;
typedef View<double*[ElemNodeCount][ValueCount],Device> ElemValueType ;
typedef View<double*[ValueCount], Device> NodeValueType ;
// Data members for this Functor:
const HexElemDataType m_hex_elem_data ; ///< Master element
const BoxFixtureType m_box_fixture ; ///< Unstructured mesh data
const FunctionType m_function ; ///< Function to integrate
const ElemErrorType m_elem_error ; ///< Flags for element errors
const ElemValueType m_elem_integral ; ///< Per-element quantities
const NodeValueType m_node_lumped ; ///< Quantities lumped to nodes
//----------------------------------------
FiniteElementIntegration(
const BoxFixtureType & box_fixture ,
const FunctionType & function )
: m_hex_elem_data()
, m_box_fixture( box_fixture ) // Shallow copy of the mesh fixture
, m_function( function )
, m_elem_error( "elem_error" , box_fixture.elem_count() )
, m_elem_integral( "elem_integral" , box_fixture.elem_count() )
, m_node_lumped( "node_lumped" , box_fixture.node_count() )
{}
//----------------------------------------
// Device for parallel dispatch.
typedef typename Device::execution_space execution_space;
// Value type for global parallel reduction.
struct value_type {
double value[ ValueCount ]; ///< Integrated quantitie
int error ; ///< Element inversion flag
};
//----------------------------------------
// Transform element interpolation function gradients and
// compute determinant of spatial jacobian.
KOKKOS_INLINE_FUNCTION
float transform_gradients(
const float grad[][ ElemNodeCount ] , // Gradient of bases master element
const double coord[][ ElemNodeCount ] ,
float dpsi[][ ElemNodeCount ] ) const
{
enum { TensorDim = 9 };
enum { j11 = 0 , j12 = 1 , j13 = 2 ,
j21 = 3 , j22 = 4 , j23 = 5 ,
j31 = 6 , j32 = 7 , j33 = 8 };
// Temporary for jacobian accumulation is double for summation accuracy.
double J[ TensorDim ] = { 0, 0, 0, 0, 0, 0, 0, 0, 0 };
for( int i = 0; i < ElemNodeCount ; ++i ) {
J[j11] += grad[0][i] * coord[0][i] ;
J[j12] += grad[0][i] * coord[1][i] ;
J[j13] += grad[0][i] * coord[2][i] ;
J[j21] += grad[1][i] * coord[0][i] ;
J[j22] += grad[1][i] * coord[1][i] ;
J[j23] += grad[1][i] * coord[2][i] ;
J[j31] += grad[2][i] * coord[0][i] ;
J[j32] += grad[2][i] * coord[1][i] ;
J[j33] += grad[2][i] * coord[2][i] ;
}
// Inverse jacobian, compute as double and store as float.
float invJ[ TensorDim ] = {
float( J[j22] * J[j33] - J[j23] * J[j32] ) ,
float( J[j13] * J[j32] - J[j12] * J[j33] ) ,
float( J[j12] * J[j23] - J[j13] * J[j22] ) ,
float( J[j23] * J[j31] - J[j21] * J[j33] ) ,
float( J[j11] * J[j33] - J[j13] * J[j31] ) ,
float( J[j13] * J[j21] - J[j11] * J[j23] ) ,
float( J[j21] * J[j32] - J[j22] * J[j31] ) ,
float( J[j12] * J[j31] - J[j11] * J[j32] ) ,
float( J[j11] * J[j22] - J[j12] * J[j21] ) };
const float detJ = J[j11] * invJ[j11] +
J[j21] * invJ[j12] +
J[j31] * invJ[j13] ;
{
const float detJinv = 1.0 / detJ ;
for ( int i = 0 ; i < TensorDim ; ++i ) { invJ[i] *= detJinv ; }
}
// Transform gradients:
for ( int i = 0; i < ElemNodeCount ; ++i ) {
dpsi[0][i] = grad[0][i] * invJ[j11] +
grad[1][i] * invJ[j12] +
grad[2][i] * invJ[j13];
dpsi[1][i] = grad[0][i] * invJ[j21] +
grad[1][i] * invJ[j22] +
grad[2][i] * invJ[j23];
dpsi[2][i] = grad[0][i] * invJ[j31] +
grad[1][i] * invJ[j32] +
grad[2][i] * invJ[j33];
}
return detJ ;
}
// Functor's function called for each element in the mesh
// to numerically integrate the function and add element quantities
// to the global integral.
KOKKOS_INLINE_FUNCTION
void operator()( const int ielem , value_type & update ) const
{
// Local temporaries for gathering nodal data.
double node_coord[3][ ElemNodeCount ];
int inode[ ElemNodeCount ] ;
// Gather indices of element's node from global memory to local memory.
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
inode[i] = m_box_fixture.elem_node( ielem , i );
}
// Gather coordinates of element's nodes from global memory to local memory.
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
node_coord[0][i] = m_box_fixture.node_coord( inode[i] , 0 );
node_coord[1][i] = m_box_fixture.node_coord( inode[i] , 1 );
node_coord[2][i] = m_box_fixture.node_coord( inode[i] , 2 );
}
// Local temporary to accumulate numerical integration
// of vector valued function.
double accum[ ValueCount ];
for ( int j = 0 ; j < ValueCount ; ++j ) { accum[j] = 0 ; }
int error = 0 ;
// Numerical integration loop for this element:
for ( int k = 0 ; k < IntegrationCount ; ++k ) {
// Integration point in space as interpolated from nodal coordinates:
double point[3] = { 0 , 0 , 0 };
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
point[0] += node_coord[0][i] * m_hex_elem_data.values[k][i] ;
point[1] += node_coord[1][i] * m_hex_elem_data.values[k][i] ;
point[2] += node_coord[2][i] * m_hex_elem_data.values[k][i] ;
}
// Example function vector value at cubature point:
double val_at_pt[ ValueCount ];
m_function( point , val_at_pt );
// Temporary array for transformed element basis functions' gradient.
// Not used in this example, but computed anyway by the more general
// deformation function.
float dpsi[3][ ElemNodeCount ];
// Compute deformation jacobian, transform basis function gradient,
// and return determinant of deformation jacobian.
float detJ = transform_gradients( m_hex_elem_data.gradients[k] ,
node_coord , dpsi );
// Check for inverted spatial jacobian
if ( detJ <= 0 ) { error = 1 ; detJ = 0 ; }
// Integration weight.
const float w = m_hex_elem_data.weights[k] * detJ ;
// Cubature of function.
for ( int j = 0 ; j < ValueCount ; ++j ) {
accum[j] += val_at_pt[j] * w ;
}
}
m_elem_error(ielem) = error ;
// Element contribution to global integral:
if ( error ) { update.error = 1 ; }
for ( int j = 0 ; j < ValueCount ; ++j ) { update.value[j] += accum[j] ; }
// Element-node quantity for lumping to nodes:
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
for ( int j = 0 ; j < ValueCount ; ++j ) {
// Save element's integral apportionment to nodes to global memory
m_elem_integral( ielem , i , j ) = accum[j] / ElemNodeCount ;
}
}
if ( PerformScatterAddWithAtomic ) {
// Option to immediately scatter-add the integrated quantities to nodes.
// This is a race condition as two or more threads could attempt
// concurrent update of nodal values. The atomic_fetch_add (+=)
// function guarantees that the summation will occur correctly;
// however, there can be no guarantee for the order of summation.
// Due to non-associativity of floating point arithmetic the result
// is non-deterministic within bounds of floating point round-off.
for ( int i = 0 ; i < ElemNodeCount ; ++i ) {
for ( int j = 0 ; j < ValueCount ; ++j ) {
Kokkos::atomic_fetch_add( & m_node_lumped( inode[i] , j ) ,
m_elem_integral( ielem , i , j ) );
}
}
}
}
//--------------------------------------------------------------------------
// Initialization of the global reduction value.
KOKKOS_INLINE_FUNCTION
void init( value_type & update ) const
{
for ( int j = 0 ; j < ValueCount ; ++j ) update.value[j] = 0 ;
update.error = 0 ;
}
// Join two contributions to global reduction value.
KOKKOS_INLINE_FUNCTION
void join( volatile value_type & update ,
volatile const value_type & input ) const
{
for ( int j = 0 ; j < ValueCount ; ++j ) update.value[j] += input.value[j] ;
if ( input.error ) update.error = 1 ;
}
};
} /* namespace Example */
} /* namespace Kokkos */
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
namespace Kokkos {
namespace Example {
template< class ViewElemNode ,
class ViewNodeScan ,
class ViewNodeElem >
void map_node_to_elem( const ViewElemNode & elem_node ,
const ViewNodeScan & node_scan ,
const ViewNodeElem & node_elem );
/** \brief Functor to gather-sum elements' per-node quantities
* to element nodes. Gather-sum is thread safe and
* does not require atomic updates.
*/
template< class ViewNodeValue ,
class ViewElemValue ,
bool AlreadyUsedAtomic >
struct LumpElemToNode {
typedef typename ViewElemValue::execution_space execution_space ;
// In this example we know that the ViewElemValue
// array specification is < double*[nNode][nValue] >
enum { value_count = ViewElemValue::dimension::N2 };
ViewNodeValue m_node_value ; ///< Integrated values at nodes
ViewElemValue m_elem_value ; ///< Values apportioned to nodes
View<int*, execution_space> m_node_scan ; ///< Offsets for nodes->element
View<int*[2],execution_space> m_node_elem ; ///< Node->element connectivity
// Only allocate node->element connectivity if have
// not already used atomic updates for the nodes.
template< class ViewElemNode >
LumpElemToNode( const ViewNodeValue & node_value ,
const ViewElemValue & elem_value ,
const ViewElemNode & elem_node )
: m_node_value( node_value )
, m_elem_value( elem_value )
, m_node_scan( "node_scan" ,
AlreadyUsedAtomic ? 0 : node_value.dimension_0() + 1 )
, m_node_elem( "node_elem" ,
AlreadyUsedAtomic ? 0 : elem_node.dimension_0() *
elem_node.dimension_1() )
{
if ( ! AlreadyUsedAtomic ) {
map_node_to_elem( elem_node , m_node_scan , m_node_elem );
}
}
//----------------------------------------
struct value_type { double value[ value_count ]; };
KOKKOS_INLINE_FUNCTION
void operator()( const int inode , value_type & update ) const
{
if ( ! AlreadyUsedAtomic ) {
// Sum element quantities to a local variable.
value_type local ;
for ( int j = 0 ; j < value_count ; ++j ) { local.value[j] = 0 ; }
{
// nodes' element ids span [i,end)
int i = m_node_scan(inode);
const int end = m_node_scan(inode+1);
for ( ; i < end ; ++i ) {
// element #ielem , local node #ielem_node is this node:
const int ielem = m_node_elem(i,0);
const int ielem_node = m_node_elem(i,1);
// Sum the vector-values quantity
for ( int j = 0 ; j < value_count ; ++j ) {
local.value[j] += m_elem_value( ielem , ielem_node , j );
}
}
}
// Assign nodal quantity (no race condition).
// Sum global value.
for ( int j = 0 ; j < value_count ; ++j ) {
m_node_value( inode , j ) = local.value[j] ;
update.value[j] += local.value[j] ;
}
}
else {
// Already used atomic update of the nodal quantity,
// query and sum the value.
for ( int j = 0 ; j < value_count ; ++j ) {
update.value[j] += m_node_value( inode , j );
}
}
}
KOKKOS_INLINE_FUNCTION
void init( value_type & update ) const
{ for ( int j = 0 ; j < value_count ; ++j ) { update.value[j] = 0 ; } }
KOKKOS_INLINE_FUNCTION
void join( volatile value_type & update ,
volatile const value_type & input ) const
{
for ( int j = 0 ; j < value_count ; ++j ) {
update.value[j] += input.value[j] ;
}
}
};
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
template< class ViewElemNode ,
class ViewNodeScan ,
class ViewNodeElem >
void map_node_to_elem( const ViewElemNode & elem_node ,
const ViewNodeScan & node_scan ,
const ViewNodeElem & node_elem )
{
typedef typename ViewElemNode::host_mirror_space host_mirror_space ;
const typename ViewElemNode::HostMirror host_elem_node =
Kokkos::create_mirror_view(elem_node);
const typename ViewNodeScan::HostMirror host_node_scan =
Kokkos::create_mirror_view(node_scan);
const typename ViewNodeElem::HostMirror host_node_elem =
Kokkos::create_mirror_view(node_elem);
const int elem_count = host_elem_node.dimension_0();
const int elem_node_count = host_elem_node.dimension_1();
const int node_count = host_node_scan.dimension_0() - 1 ;
const View<int*, host_mirror_space >
node_elem_count( "node_elem_count" , node_count );
Kokkos::deep_copy( host_elem_node , elem_node );
for ( int i = 0 ; i < elem_count ; ++i ) {
for ( int j = 0 ; j < elem_node_count ; ++j ) {
++node_elem_count( host_elem_node(i,j) );
}
}
for ( int i = 0 ; i < node_count ; ++i ) {
host_node_scan(i+1) += host_node_scan(i) + node_elem_count(i);
node_elem_count(i) = 0 ;
}
for ( int i = 0 ; i < elem_count ; ++i ) {
for ( int j = 0 ; j < elem_node_count ; ++j ) {
const int inode = host_elem_node(i,j);
const int offset = host_node_scan(inode) + node_elem_count(inode);
host_node_elem( offset , 0 ) = i ;
host_node_elem( offset , 1 ) = j ;
++node_elem_count(inode);
}
}
Kokkos::deep_copy( node_scan , host_node_scan );
Kokkos::deep_copy( node_elem , host_node_elem );
}
} /* namespace Example */
} /* namespace Kokkos */
#endif /* #ifndef KOKKOS_EXAMPLE_FEINT_FUNCTORS_HPP */

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