ElemFunctor.hpp
178eff237bc3master

ElemFunctor.hpp
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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 */

lammps/lib/kokkos/example/feint/ElemFunctor.hpp178eff237bc3master

ElemFunctor.hppView Options

lammps/lib/kokkos/example/feint/ElemFunctor.hpp
178eff237bc3master

ElemFunctor.hpp
View Options