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Nonlinear.hpp
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/*
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// Kokkos v. 2.0
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#ifndef HYBRIDFEM_NONLINEAR_HPP
#define HYBRIDFEM_NONLINEAR_HPP
#include <utility>
#include <iostream>
#include <iomanip>
#include <Kokkos_Core.hpp>
#include <SparseLinearSystem.hpp>
#include <SparseLinearSystemFill.hpp>
#include <NonlinearFunctors.hpp>
#include <FEMesh.hpp>
#include <HexElement.hpp>
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
namespace HybridFEM {
namespace Nonlinear {
struct PerformanceData {
double mesh_time ;
double graph_time ;
double elem_time ;
double matrix_gather_fill_time ;
double matrix_boundary_condition_time ;
double cg_iteration_time ;
size_t cg_iteration_count ;
size_t newton_iteration_count ;
double error_max ;
PerformanceData()
: mesh_time(0)
, graph_time(0)
, elem_time(0)
, matrix_gather_fill_time(0)
, matrix_boundary_condition_time(0)
, cg_iteration_time(0)
, cg_iteration_count(0)
, newton_iteration_count(0)
, error_max(0)
{}
void best( const PerformanceData & rhs )
{
mesh_time = std::min( mesh_time , rhs.mesh_time );
graph_time = std::min( graph_time , rhs.graph_time );
elem_time = std::min( elem_time , rhs.elem_time );
matrix_gather_fill_time = std::min( matrix_gather_fill_time , rhs.matrix_gather_fill_time );
matrix_boundary_condition_time = std::min( matrix_boundary_condition_time , rhs.matrix_boundary_condition_time );
cg_iteration_time = std::min( cg_iteration_time , rhs.cg_iteration_time );
cg_iteration_count = std::min( cg_iteration_count , rhs.cg_iteration_count );
newton_iteration_count = std::min( newton_iteration_count , rhs.newton_iteration_count );
error_max = std::min( error_max , rhs.error_max );
}
};
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
class ManufacturedSolution {
public:
// Manufactured solution for one dimensional nonlinear PDE
//
// -K T_zz + T^2 = 0 ; T(zmin) = T_zmin ; T(zmax) = T_zmax
//
// Has an analytic solution of the form:
//
// T(z) = ( a ( z - zmin ) + b )^(-2) where K = 1 / ( 6 a^2 )
//
// Given T_0 and T_L compute K for this analytic solution.
//
// Two analytic solutions:
//
// Solution with singularity:
// , a( ( 1.0 / sqrt(T_zmax) + 1.0 / sqrt(T_zmin) ) / ( zmax - zmin ) )
// , b( -1.0 / sqrt(T_zmin) )
//
// Solution without singularity:
// , a( ( 1.0 / sqrt(T_zmax) - 1.0 / sqrt(T_zmin) ) / ( zmax - zmin ) )
// , b( 1.0 / sqrt(T_zmin) )
const double zmin ;
const double zmax ;
const double T_zmin ;
const double T_zmax ;
const double a ;
const double b ;
const double K ;
ManufacturedSolution( const double arg_zmin ,
const double arg_zmax ,
const double arg_T_zmin ,
const double arg_T_zmax )
: zmin( arg_zmin )
, zmax( arg_zmax )
, T_zmin( arg_T_zmin )
, T_zmax( arg_T_zmax )
, a( ( 1.0 / std::sqrt(T_zmax) - 1.0 / std::sqrt(T_zmin) ) / ( zmax - zmin ) )
, b( 1.0 / std::sqrt(T_zmin) )
, K( 1.0 / ( 6.0 * a * a ) )
{}
double operator()( const double z ) const
{
const double tmp = a * ( z - zmin ) + b ;
return 1.0 / ( tmp * tmp );
}
};
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
template< typename Scalar , class FixtureType >
PerformanceData run( const typename FixtureType::FEMeshType & mesh ,
const int , // global_max_x ,
const int , // global_max_y ,
const int global_max_z ,
const bool print_error )
{
typedef Scalar scalar_type ;
typedef FixtureType fixture_type ;
typedef typename fixture_type::execution_space execution_space;
//typedef typename execution_space::size_type size_type ; // unused
typedef typename fixture_type::FEMeshType mesh_type ;
typedef typename fixture_type::coordinate_scalar_type coordinate_scalar_type ;
enum { ElementNodeCount = fixture_type::element_node_count };
const comm::Machine machine = mesh.parallel_data_map.machine ;
const size_t element_count = mesh.elem_node_ids.dimension_0();
//------------------------------------
// The amount of nonlinearity is proportional to the ratio
// between T(zmax) and T(zmin). For the manufactured solution
// 0 < T(zmin) and 0 < T(zmax)
const ManufacturedSolution
exact_solution( /* zmin */ 0 ,
/* zmax */ global_max_z ,
/* T(zmin) */ 1 ,
/* T(zmax) */ 20 );
//-----------------------------------
// Convergence Criteria and perf data:
const size_t cg_iteration_limit = 200 ;
const double cg_tolerance = 1e-14 ;
const size_t newton_iteration_limit = 150 ;
const double newton_tolerance = 1e-14 ;
size_t cg_iteration_count_total = 0 ;
double cg_iteration_time = 0 ;
size_t newton_iteration_count = 0 ;
double residual_norm_init = 0 ;
double residual_norm = 0 ;
PerformanceData perf_data ;
//------------------------------------
// Sparse linear system types:
typedef Kokkos::View< scalar_type* , execution_space > vector_type ;
typedef Kokkos::CrsMatrix< scalar_type , execution_space > matrix_type ;
typedef typename matrix_type::graph_type matrix_graph_type ;
typedef typename matrix_type::coefficients_type matrix_coefficients_type ;
typedef GraphFactory< matrix_graph_type , mesh_type > graph_factory ;
//------------------------------------
// Problem setup types:
typedef ElementComputation < mesh_type , scalar_type > ElementFunctor ;
typedef DirichletSolution < mesh_type , scalar_type > DirichletSolutionFunctor ;
typedef DirichletResidual < mesh_type , scalar_type > DirichletResidualFunctor ;
typedef typename ElementFunctor::elem_matrices_type elem_matrices_type ;
typedef typename ElementFunctor::elem_vectors_type elem_vectors_type ;
typedef GatherFill< matrix_type ,
mesh_type ,
elem_matrices_type ,
elem_vectors_type > GatherFillFunctor ;
//------------------------------------
matrix_type jacobian ;
vector_type residual ;
vector_type delta ;
vector_type nodal_solution ;
typename graph_factory::element_map_type element_map ;
//------------------------------------
// Generate mesh and corresponding sparse matrix graph
Kokkos::Timer wall_clock ;
//------------------------------------
// Generate sparse matrix graph and element->graph map.
wall_clock.reset();
graph_factory::create( mesh , jacobian.graph , element_map );
execution_space::fence();
perf_data.graph_time = comm::max( machine , wall_clock.seconds() );
//------------------------------------
// Allocate linear system coefficients and rhs:
const size_t local_owned_length = jacobian.graph.row_map.dimension_0() - 1 ;
const size_t local_total_length = mesh.node_coords.dimension_0();
jacobian.coefficients =
matrix_coefficients_type( "jacobian_coeff" , jacobian.graph.entries.dimension_0() );
// Nonlinear residual for owned nodes:
residual = vector_type( "residual" , local_owned_length );
// Nonlinear solution for owned and ghosted nodes:
nodal_solution = vector_type( "solution" , local_total_length );
// Nonlinear solution update for owned nodes:
delta = vector_type( "delta" , local_owned_length );
//------------------------------------
// Allocation of arrays to fill the linear system
elem_matrices_type elem_matrices ; // Jacobian matrices
elem_vectors_type elem_vectors ; // Residual vectors
if ( element_count ) {
elem_matrices = elem_matrices_type( std::string("elem_matrices"), element_count );
elem_vectors = elem_vectors_type( std::string("elem_vectors"), element_count );
}
//------------------------------------
// For boundary condition set the correct values in the solution vector
// The 'zmin' face is assigned to 'T_zmin'.
// The 'zmax' face is assigned to 'T_zmax'.
// The resulting solution is one dimensional along the 'Z' axis.
DirichletSolutionFunctor::apply( nodal_solution , mesh ,
exact_solution.zmin ,
exact_solution.zmax ,
exact_solution.T_zmin ,
exact_solution.T_zmax );
for(;;) { // Nonlinear loop
#if defined( KOKKOS_ENABLE_MPI )
{ //------------------------------------
// Import off-processor nodal solution values
// for residual and jacobian computations
Kokkos::AsyncExchange< typename vector_type::value_type , execution_space ,
Kokkos::ParallelDataMap >
exchange( mesh.parallel_data_map , 1 );
Kokkos::PackArray< vector_type >
::pack( exchange.buffer() ,
mesh.parallel_data_map.count_interior ,
mesh.parallel_data_map.count_send ,
nodal_solution );
exchange.setup();
exchange.send_receive();
Kokkos::UnpackArray< vector_type >
::unpack( nodal_solution , exchange.buffer() ,
mesh.parallel_data_map.count_owned ,
mesh.parallel_data_map.count_receive );
}
#endif
//------------------------------------
// Compute element matrices and vectors:
wall_clock.reset();
ElementFunctor( mesh ,
elem_matrices ,
elem_vectors ,
nodal_solution ,
exact_solution.K );
execution_space::fence();
perf_data.elem_time += comm::max( machine , wall_clock.seconds() );
//------------------------------------
// Fill linear system coefficients:
wall_clock.reset();
fill( jacobian.coefficients.dimension_0(), 0 , jacobian.coefficients );
fill( residual.dimension_0() , 0 , residual );
GatherFillFunctor::apply( jacobian ,
residual ,
mesh ,
element_map ,
elem_matrices ,
elem_vectors );
execution_space::fence();
perf_data.matrix_gather_fill_time += comm::max( machine , wall_clock.seconds() );
// Apply boundary conditions:
wall_clock.reset();
// Updates jacobian matrix to 1 on the diagonal, zero elsewhere,
// and 0 in the residual due to the solution vector having the correct value
DirichletResidualFunctor::apply( jacobian, residual, mesh ,
exact_solution.zmin ,
exact_solution.zmax );
execution_space::fence();
perf_data.matrix_boundary_condition_time +=
comm::max( machine , wall_clock.seconds() );
//------------------------------------
// Has the residual converged?
residual_norm = norm2( mesh.parallel_data_map.count_owned,
residual,
mesh.parallel_data_map.machine );
if ( 0 == newton_iteration_count ) {
residual_norm_init = residual_norm ;
}
if ( residual_norm / residual_norm_init < newton_tolerance ) {
break ;
}
//------------------------------------
// Solve linear sytem
size_t cg_iteration_count = 0 ;
double cg_residual_norm = 0 ;
cgsolve( mesh.parallel_data_map ,
jacobian , residual , delta ,
cg_iteration_count ,
cg_residual_norm ,
cg_iteration_time ,
cg_iteration_limit , cg_tolerance ) ;
perf_data.cg_iteration_time += cg_iteration_time ;
cg_iteration_count_total += cg_iteration_count ;
// Update non-linear solution with delta...
// delta is : - Dx = [Jacobian]^1 * Residual which is the negative update
// LaTeX:
// \vec {x}_{n+1} = \vec {x}_{n} - ( - \Delta \vec{x}_{n} )
// text:
// x[n+1] = x[n] + Dx
axpy( mesh.parallel_data_map.count_owned ,
-1.0, delta, nodal_solution);
++newton_iteration_count ;
if ( newton_iteration_limit < newton_iteration_count ) {
break ;
}
};
if ( newton_iteration_count ) {
perf_data.elem_time /= newton_iteration_count ;
perf_data.matrix_gather_fill_time /= newton_iteration_count ;
perf_data.matrix_boundary_condition_time /= newton_iteration_count ;
}
if ( cg_iteration_count_total ) {
perf_data.cg_iteration_time /= cg_iteration_count_total ;
}
perf_data.newton_iteration_count = newton_iteration_count ;
perf_data.cg_iteration_count = cg_iteration_count_total ;
//------------------------------------
{
// For extracting the nodal solution and its coordinates:
typename mesh_type::node_coords_type::HostMirror node_coords_host =
Kokkos::create_mirror( mesh.node_coords );
typename vector_type::HostMirror nodal_solution_host =
Kokkos::create_mirror( nodal_solution );
Kokkos::deep_copy( node_coords_host , mesh.node_coords );
Kokkos::deep_copy( nodal_solution_host , nodal_solution );
double tmp = 0 ;
for ( size_t i = 0 ; i < mesh.parallel_data_map.count_owned ; ++i ) {
const coordinate_scalar_type x = node_coords_host(i,0);
const coordinate_scalar_type y = node_coords_host(i,1);
const coordinate_scalar_type z = node_coords_host(i,2);
const double Tx = exact_solution(z);
const double Ts = nodal_solution_host(i);
const double Te = std::abs( Tx - Ts ) / std::abs( Tx );
tmp = std::max( tmp , Te );
if ( print_error && 0.02 < Te ) {
std::cout << " node( " << x << " " << y << " " << z << " ) = "
<< Ts << " != exact_solution " << Tx
<< std::endl ;
}
}
perf_data.error_max = comm::max( machine , tmp );
}
return perf_data ;
}
//----------------------------------------------------------------------------
template< typename Scalar , class Device , class FixtureElement >
void driver( const char * const label ,
comm::Machine machine ,
const int gang_count ,
const int elem_count_beg ,
const int elem_count_end ,
const int runs )
{
typedef Scalar scalar_type ;
typedef Device execution_space ;
typedef double coordinate_scalar_type ;
typedef FixtureElement fixture_element_type ;
typedef BoxMeshFixture< coordinate_scalar_type ,
execution_space ,
fixture_element_type > fixture_type ;
typedef typename fixture_type::FEMeshType mesh_type ;
const size_t proc_count = comm::size( machine );
const size_t proc_rank = comm::rank( machine );
if ( elem_count_beg == 0 || elem_count_end == 0 || runs == 0 ) return ;
if ( comm::rank( machine ) == 0 ) {
std::cout << std::endl ;
std::cout << "\"Kokkos::HybridFE::Nonlinear " << label << "\"" << std::endl;
std::cout
<< "\"Size\" , \"Size\" , \"Graphing\" , \"Element\" , \"Fill\" , \"Boundary\" , \"CG-Iter\" , \"CG-Iter\" , \"Newton-Iter\" , \"Max-node-error\""
<< std::endl
<< "\"elems\" , \"nodes\" , \"millisec\" , \"millisec\" , \"millisec\" , \"millisec\" , \"millisec\" , \"total-count\" , \"total-count\" , \"ratio\""
<< std::endl ;
}
const bool print_sample = 0 ;
const double x_curve = 1.0 ;
const double y_curve = 1.0 ;
const double z_curve = 0.8 ;
for(int i = elem_count_beg ; i < elem_count_end ; i *= 2 )
{
const int ix = std::max( 1 , (int) cbrt( ((double) i) / 2.0 ) );
const int iy = 1 + ix ;
const int iz = 2 * iy ;
const int global_elem_count = ix * iy * iz ;
const int global_node_count = ( 2 * ix + 1 ) *
( 2 * iy + 1 ) *
( 2 * iz + 1 );
mesh_type mesh =
fixture_type::create( proc_count , proc_rank , gang_count ,
ix , iy , iz ,
x_curve , y_curve , z_curve );
mesh.parallel_data_map.machine = machine ;
PerformanceData perf_data , perf_best ;
for(int j = 0; j < runs; j++){
perf_data = run<scalar_type,fixture_type>(mesh,ix,iy,iz, print_sample );
if( j == 0 ) {
perf_best = perf_data ;
}
else {
perf_best.best( perf_data );
}
}
if ( comm::rank( machine ) == 0 ) {
std::cout << std::setw(8) << global_elem_count << " , "
<< std::setw(8) << global_node_count << " , "
<< std::setw(10) << perf_best.graph_time * 1000 << " , "
<< std::setw(10) << perf_best.elem_time * 1000 << " , "
<< std::setw(10) << perf_best.matrix_gather_fill_time * 1000 << " , "
<< std::setw(10) << perf_best.matrix_boundary_condition_time * 1000 << " , "
<< std::setw(10) << perf_best.cg_iteration_time * 1000 << " , "
<< std::setw(7) << perf_best.cg_iteration_count << " , "
<< std::setw(3) << perf_best.newton_iteration_count << " , "
<< std::setw(10) << perf_best.error_max
<< std::endl ;
}
}
}
//----------------------------------------------------------------------------
} /* namespace Nonlinear */
} /* namespace HybridFEM */
#endif /* #ifndef HYBRIDFEM_IMPLICIT_HPP */

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