TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true > Struct Template Reference

Inheritance diagram for TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >:

Collaboration diagram for TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >:

Public Types
using	IndexType = std::size_t
	Type for indexing.
using	RealType = GetValueType_t< Vector >
	Type of floating-point arithemtics.
using	SolverMonitorType = SolverMonitor
	Type of object used for monitoring the convergence.
using	ValueType = typename VectorType::ValueType
using	VectorType = Vector
Public Types inherited from TNL::Solvers::ODE::StaticExplicitSolver< GetValueType_t< Vector >, std::size_t >
using	IndexType
	Indexing type.
using	RealType
	Type of the floating-point arithmetics or static vector.

Public Member Functions
__cuda_callable__	ODESolver ()
	Default constructor.
__cuda_callable__	ODESolver (const ODESolver &solver)
__cuda_callable__ RealType	getAdaptivity () const
	Getter of the parameter controlling the adaptive choice of the integration time step.
__cuda_callable__ Method &	getMethod ()
	Gives reference to the underlying method.
__cuda_callable__ const Method &	getMethod () const
	Gives constant reference to the underlying method.
void __cuda_callable__	init (const VectorType &u)
	Setup auxiliary vectors of the solver.
template<typename RHSFunction , typename... Params>
void __cuda_callable__	iterate (VectorType &u, RealType &time, RealType &tau, RHSFunction &&f, Params &&... params)
	Performs one iteration of the solver.
void __cuda_callable__	reset ()
	This method is just for consistency with the ODE solver for dynamic vectors.
__cuda_callable__ void	setAdaptivity (const RealType &adaptivity)
	Setter of the parameter controlling the adaptive choice of the integration time step.
bool	setup (const Config::ParameterContainer &parameters, const String &prefix="")
	Method for setup of the explicit solver based on configuration parameters.
template<typename RHSFunction , typename... Params>
__cuda_callable__ bool	solve (VectorType &u, RHSFunction &&f, Params &&... params)
	Solve ODE given by a lambda function.
Public Member Functions inherited from TNL::Solvers::ODE::StaticExplicitSolver< GetValueType_t< Vector >, std::size_t >
__cuda_callable__	StaticExplicitSolver ()=default
	Default constructor.
bool __cuda_callable__	checkNextIteration ()
	Checks if the solver is allowed to do the next iteration.
__cuda_callable__ const RealType &	getMaxTau () const
	Getter of maximal value of the time step.
__cuda_callable__ const RealType &	getStopTime () const
	Getter of the time where the evolution computation shall by stopped.
__cuda_callable__ const RealType &	getTau () const
	Getter of the time step used for the computation.
__cuda_callable__ const RealType &	getTime () const
	Getter of the current time of the evolution computed by the solver.
__cuda_callable__ void	setMaxTau (const RealType &maxTau)
	Setter of maximal value of the time step.
__cuda_callable__ void	setStopTime (const RealType &stopTime)
	Setter of the time where the evolution computation shall by stopped.
__cuda_callable__ void	setTau (const RealType &tau)
	Setter of the time step used for the computation.
__cuda_callable__ void	setTestingMode (bool testingMode)
__cuda_callable__ void	setTime (const RealType &t)
	Settter of the current time of the evolution computed by the solver.
bool	setup (const Config::ParameterContainer &parameters, const std::string &prefix="")
	Method for setup of the iterative solver based on configuration parameters.
Public Member Functions inherited from TNL::Solvers::StaticIterativeSolver< GetValueType_t< Vector >, std::size_t >
__cuda_callable__	StaticIterativeSolver ()=default
	Default constructor.
__cuda_callable__ bool	checkConvergence ()
	Checks whether the convergence occurred already.
__cuda_callable__ bool	checkNextIteration ()
	Checks if the solver is allowed to do the next iteration.
__cuda_callable__ const GetValueType_t< Vector > &	getConvergenceResidue () const
	Gets the the convergence threshold.
__cuda_callable__ const GetValueType_t< Vector > &	getDivergenceResidue () const
	Gets the limit for the divergence criterion.
__cuda_callable__ const std::size_t &	getIterations () const
	Gets the number of iterations performed by the solver so far.
__cuda_callable__ const std::size_t &	getMaxIterations () const
	Gets the maximal number of iterations the solver is allowed to perform.
__cuda_callable__ const std::size_t &	getMinIterations () const
	Gets the minimal number of iterations the solver is supposed to do.
__cuda_callable__ const GetValueType_t< Vector > &	getResidue () const
	Gets the residue reached at the current iteration.
__cuda_callable__ bool	nextIteration ()
	Proceeds to the next iteration.
__cuda_callable__ void	resetIterations ()
	Sets the the number of the current iterations to zero.
__cuda_callable__ void	setConvergenceResidue (const GetValueType_t< Vector > &convergenceResidue)
	Sets the threshold for the convergence.
__cuda_callable__ void	setDivergenceResidue (const GetValueType_t< Vector > &divergenceResidue)
	Sets the residue limit for the divergence criterion.
__cuda_callable__ void	setMaxIterations (const std::size_t &maxIterations)
	Sets the maximal number of iterations the solver is allowed to perform.
__cuda_callable__ void	setMinIterations (const std::size_t &minIterations)
	Sets the minimal number of iterations the solver is supposed to do.
__cuda_callable__ void	setResidue (const GetValueType_t< Vector > &residue)
	Sets the residue reached at the current iteration.
bool	setup (const Config::ParameterContainer &parameters, const std::string &prefix="")
	Method for setup of the iterative solver based on configuration parameters.

Static Public Member Functions
static void	configSetup (Config::ConfigDescription &config, const String &prefix="")
	Static method for setup of configuration parameters.
static constexpr bool	isStatic ()
Static Public Member Functions inherited from TNL::Solvers::ODE::StaticExplicitSolver< GetValueType_t< Vector >, std::size_t >
static void	configSetup (Config::ConfigDescription &config, const std::string &prefix="")
	This method defines configuration entries for setup of the iterative solver.
Static Public Member Functions inherited from TNL::Solvers::StaticIterativeSolver< GetValueType_t< Vector >, std::size_t >
static void	configSetup (Config::ConfigDescription &config, const std::string &prefix="")
	This method defines configuration entries for setup of the iterative solver.

Static Public Attributes
static constexpr int	Stages = Method::getStages()

Protected Attributes
RealType	adaptivity = 0.00001
std::array< VectorType, Stages >	k_vectors
VectorType	kAux
Method	method
Protected Attributes inherited from TNL::Solvers::ODE::StaticExplicitSolver< GetValueType_t< Vector >, std::size_t >
RealType	maxTau
bool	stopOnSteadyState
RealType	stopTime
RealType	tau
bool	testingMode
RealType	time
Protected Attributes inherited from TNL::Solvers::StaticIterativeSolver< GetValueType_t< Vector >, std::size_t >
GetValueType_t< Vector >	convergenceResidue
std::size_t	currentIteration
GetValueType_t< Vector >	currentResidue
GetValueType_t< Vector >	divergenceResidue
std::size_t	maxIterations
std::size_t	minIterations
std::size_t	refreshRate

Member Typedef Documentation

SolverMonitorType

template<typename Method , typename Vector , typename SolverMonitor >

using TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::SolverMonitorType = SolverMonitor

Type of object used for monitoring the convergence.

Can be TNL::Solvers::IterativeSolverMonitor.

Member Function Documentation

configSetup()

template<typename Method , typename Vector , typename SolverMonitor >

static void TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::configSetup ( Config::ConfigDescription & config, const String & prefix = "" )

static

Static method for setup of configuration parameters.

Parameters

config	is the config description.
prefix	is the prefix of the configuration parameters for this solver.

getAdaptivity()

template<typename Method , typename Vector , typename SolverMonitor >

__cuda_callable__ RealType TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::getAdaptivity ( ) const

inline

Getter of the parameter controlling the adaptive choice of the integration time step.

Returns

the current value of the parameter controlling the adaptive choice of integration time step.

getMethod() [1/2]

template<typename Method , typename Vector , typename SolverMonitor >

__cuda_callable__ Method & TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::getMethod

(

)

Gives reference to the underlying method.

Returns

reference to the underlying method.

getMethod() [2/2]

template<typename Method , typename Vector , typename SolverMonitor >

__cuda_callable__ const Method & TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::getMethod

(

)

const

Gives constant reference to the underlying method.

Returns

constant reference to the underlying method.

init()

template<typename Method , typename Vector , typename SolverMonitor >

void __cuda_callable__ TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::init

(

const VectorType &

u

)

Setup auxiliary vectors of the solver.

This method is supposed to be called before the first call of the method iterate. It is not necessary to call this method before the method solve is used.

Parameters

u	this parameter is only for consistency with the ODE solver for dynamic vectors.

iterate()

template<typename Method , typename Vector , typename SolverMonitor >

template<typename RHSFunction , typename... Params>

void __cuda_callable__ TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::iterate	(	VectorType &	u,
		RealType &	time,
		RealType &	tau,
		RHSFunction &&	f,
		Params &&...	params )

Performs one iteration of the solver.

This method can be used for hybrid solvers which combine various ODE solvers. Otherwise, use of solve is recommended. Before the first call of this method, the method init has to be called.

Template Parameters

RHSFunction	is type of a lambda function representing the right-hand side of the ODE system.
Params	are the parameters which are supposed to be passed to the lambda function f.

Parameters

u	is a variable/static vector representing the solution of the ODE system at current time.
time	is the current time of the evolution. The variable is increased by tau.
tau	is the current time step. It can be changed by the solver if the adaptive time step control is used.
f	is the lambda function representing the right-hand side of the ODE system. The definition of the lambda function is the same as in the method solve.
params	are the parameters which are supposed to be passed to the lambda function f.

Example

#include <iostream>
#include <TNL/Solvers/ODE/ODESolver.h>
#include <TNL/Solvers/ODE/Methods/Euler.h>
 
using Real = double;
 
int
main( int argc, char* argv[] )
{
   using Vector = TNL::Containers::StaticVector< 1, Real >;
   using Method = TNL::Solvers::ODE::Methods::Euler< Real >;
   using ODESolver = TNL::Solvers::ODE::ODESolver< Method, Vector >;
 
   const Real final_time = 10.0;
   const Real output_time_step = 0.25;
   Real next_output_time = TNL::min( output_time_step, final_time );
   Real tau = 0.001;
   Real time = 0.0;
   Real current_tau = tau;
 
   Vector u = 0.0;
   ODESolver solver;
   solver.init( u );
 
   while( time < final_time ) {
      auto f = []( const Real& t, const Real& current_tau, const Vector& u, Vector& fu )
      {
         fu = t * sin( t );
      };
      solver.iterate( u, time, current_tau, f );
      if( time >= next_output_time ) {
         std::cout << time << " " << u[ 0 ] << std::endl;
         next_output_time += output_time_step;
         if( next_output_time > final_time )
            next_output_time = final_time;
      }
      if( time + current_tau > next_output_time )
         current_tau = next_output_time - time;
      else
         current_tau = tau;
   }
}

setAdaptivity()

template<typename Method , typename Vector , typename SolverMonitor >

__cuda_callable__ void TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::setAdaptivity ( const RealType & adaptivity )

inline

Setter of the parameter controlling the adaptive choice of the integration time step.

The smaller the parameter is the smaller the integration time step tends to be. Reasonable values for this parameters are approximately from interval \( [10^{-12},10^{-2}] \).

Parameters

adaptivity

new value of the parameter controlling the adaptive choice of integration time step.

setup()

template<typename Method , typename Vector , typename SolverMonitor >

bool TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::setup	(	const Config::ParameterContainer &	parameters,
		const String &	prefix = "" )

Method for setup of the explicit solver based on configuration parameters.

Parameters

parameters	is the container for configuration parameters.
prefix	is the prefix of the configuration parameters for this solver.

Returns

true if the parameters where parsed successfully.

false if the method did not succeed to read the configuration parameters.

solve()

template<typename Method , typename Vector , typename SolverMonitor >

template<typename RHSFunction , typename... Params>

__cuda_callable__ bool TNL::Solvers::ODE::ODESolver< Method, Vector, SolverMonitor, true >::solve	(	VectorType &	u,
		RHSFunction &&	f,
		Params &&...	params )

Solve ODE given by a lambda function.

Template Parameters

RHSFunction

is type of a lambda function representing the right-hand side of the ODE system. The definition of the lambda function reads as: auto f = [=] ( const Real& t, const Real& tau, const VectorType& u, VectorType& fu ) {...} where t is the current time of the evolution, tau is the current time step, u is the solution at the current time, fu is variable/static vector into which the lambda function is suppsed to evaluate the function \( f(t, \vec x) \) at the current time \( t \).

Parameters

u	is a variable/static vector representing the solution of the ODE system at current time.
f	is the lambda function representing the right-hand side of the ODE system.
params	are the parameters which are supposed to be passed to the lambda function f. This is due to the fact that the CUDA compiler does not allow nested lambda functions: "An extended __host__ __device__ lambda cannot be defined inside an extended __host__ __device__ lambda expression".

Returns

true if steady state solution has been reached, false` otherwise.

Example

#include <iostream>
#include <TNL/Solvers/ODE/ODESolver.h>
#include <TNL/Solvers/ODE/Methods/Euler.h>
 
using Real = double;
 
int
main( int argc, char* argv[] )
{
   using Vector = TNL::Containers::StaticVector< 1, Real >;
   using Method = TNL::Solvers::ODE::Methods::Euler< Real >;
   using ODESolver = TNL::Solvers::ODE::ODESolver< Method, Vector >;
 
   const Real final_t = 10.0;
   const Real tau = 0.001;
   const Real output_time_step = 0.25;
 
   ODESolver solver;
   solver.setTau( tau );
   solver.setTime( 0.0 );
   Vector u = 0.0;
 
   while( solver.getTime() < final_t ) {
      solver.setStopTime( TNL::min( solver.getTime() + output_time_step, final_t ) );
      auto f = []( const Real& t, const Real& tau, const Vector& u, Vector& fu )
      {
         fu = t * sin( t );
      };
      solver.solve( u, f );
      std::cout << solver.getTime() << " " << u[ 0 ] << std::endl;
   }
}

#include <iostream>
#include <fstream>
#include <TNL/Containers/Vector.h>
#include <TNL/Algorithms/parallelFor.h>
#include <TNL/Containers/StaticVector.h>
#include <TNL/Solvers/ODE/ODESolver.h>
#include <TNL/Solvers/ODE/Methods/Euler.h>
 
using MultiIndex = TNL::Containers::StaticArray< 3, int >;
using Real = double;
 
template< typename Device >
void
solveParallelODEs( const char* file_name )
{
   using StaticVector = TNL::Containers::StaticVector< 3, Real >;
   using Method = TNL::Solvers::ODE::Methods::Euler< Real >;
   using ODESolver = TNL::Solvers::ODE::ODESolver< Method, StaticVector >;
 
   const Real final_t = 50.0;
   const Real tau = 0.001;
   const Real output_time_step = 0.005;
 
   const Real sigma_min( 10.0 ), rho_min( 15.0 ), beta_min( 1.0 );
   const int parametric_steps = 4;
   const Real sigma_step = 30.0 / ( parametric_steps - 1 );
   const Real rho_step = 21.0 / ( parametric_steps - 1 );
   const Real beta_step = 15.0 / ( parametric_steps - 1 );
   const int output_time_steps = ceil( final_t / output_time_step ) + 1;
 
   const int results_size( output_time_steps * parametric_steps * parametric_steps * parametric_steps );
   TNL::Containers::Vector< StaticVector, Device > results( results_size, 0.0 );
   auto results_view = results.getView();
 
   auto f = [ = ] __cuda_callable__( const Real& t,
                                     const Real& tau,
                                     const StaticVector& u,
                                     StaticVector& fu,
                                     const Real& sigma_i,
                                     const Real& rho_j,
                                     const Real& beta_k )
   {
      const Real& x = u[ 0 ];
      const Real& y = u[ 1 ];
      const Real& z = u[ 2 ];
      fu[ 0 ] = sigma_i * ( y - x );
      fu[ 1 ] = rho_j * x - y - x * z;
      fu[ 2 ] = -beta_k * z + x * y;
   };
 
   auto solve = [ = ] __cuda_callable__( const MultiIndex& idx ) mutable
   {
      const Real sigma_i = sigma_min + idx[ 0 ] * sigma_step;
      const Real rho_j = rho_min + idx[ 1 ] * rho_step;
      const Real beta_k = beta_min + idx[ 2 ] * beta_step;
 
      ODESolver solver;
      solver.setTau( tau );
      solver.setTime( 0.0 );
      StaticVector u( 1.0, 1.0, 1.0 );
      int time_step( 1 );
      results_view[ ( idx[ 0 ] * parametric_steps + idx[ 1 ] ) * parametric_steps + idx[ 2 ] ] = u;
 
      while( time_step < output_time_steps ) {
         solver.setStopTime( TNL::min( solver.getTime() + output_time_step, final_t ) );
         solver.solve( u, f, sigma_i, rho_j, beta_k );
         const int k =
            ( ( time_step++ * parametric_steps + idx[ 0 ] ) * parametric_steps + idx[ 1 ] ) * parametric_steps + idx[ 2 ];
         results_view[ k ] = u;
      }
   };
 
   const MultiIndex begin = { 0, 0, 0 };
   const MultiIndex end = { parametric_steps, parametric_steps, parametric_steps };
   TNL::Algorithms::parallelFor< Device >( begin, end, solve );
 
   std::fstream file;
   file.open( file_name, std::ios::out );
   for( int sigma_idx = 0; sigma_idx < parametric_steps; sigma_idx++ )
      for( int rho_idx = 0; rho_idx < parametric_steps; rho_idx++ )
         for( int beta_idx = 0; beta_idx < parametric_steps; beta_idx++ ) {
            Real sigma = sigma_min + sigma_idx * sigma_step;
            Real rho = rho_min + rho_idx * rho_step;
            Real beta = beta_min + beta_idx * beta_step;
            file << "# sigma " << sigma << " rho " << rho << " beta " << beta << std::endl;
            for( int i = 0; i < output_time_steps - 1; i++ ) {
               int offset = ( ( i * parametric_steps + sigma_idx ) * parametric_steps + rho_idx ) * parametric_steps + beta_idx;
               auto u = results.getElement( offset );
               file << u[ 0 ] << " " << u[ 1 ] << " " << u[ 2 ] << std::endl;
            }
            file << std::endl;
         }
}
 
int
main( int argc, char* argv[] )
{
   if( argc != 2 ) {
      std::cout << "Usage: " << argv[ 0 ] << " <path to output directory>" << std::endl;
      return EXIT_FAILURE;
   }
   TNL::String file_name( argv[ 1 ] );
   file_name += "/StaticODESolver-LorenzParallelExample-result.out";
 
   solveParallelODEs< TNL::Devices::Host >( file_name.getString() );
#ifdef __CUDACC__
   solveParallelODEs< TNL::Devices::Cuda >( file_name.getString() );
#endif
}

.

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The documentation for this struct was generated from the following file:

• src/TNL/Solvers/ODE/ODESolver.h