Defines a System that is used to solve parabolic partial differential equations. More...

#include <OperationParabolicPDESolverSystemDirichlet.hpp>

Inheritance diagram for sgpp::pde::OperationParabolicPDESolverSystemDirichlet:

Public Member Functions
virtual sgpp::base::DataVector *	generateRHS ()
	generates the right hand side of the system More...

virtual sgpp::base::DataVector *	getGridCoefficientsForCG ()
	gets a pointer to the sparse grids coefficients used in the CG method to solve one timestep. More...

virtual void	mult (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)
	Multiplicates a vector with the matrix. More...

	OperationParabolicPDESolverSystemDirichlet ()
	Constructor. More...

virtual	~OperationParabolicPDESolverSystemDirichlet ()
	Destructor. More...

Public Member Functions inherited from sgpp::solver::OperationParabolicPDESolverSystem
void	abortTimestep ()
	aborts the current timestep execution More...

virtual void	coarsenAndRefine (bool isLastTimestep=false)=0

virtual void	finishTimestep ()=0
	performs some action that might be needed after a timestep has be finished in the ODE Solver, e.g. More...

sgpp::base::Grid *	getGrid ()
	get the pointer to the underlying grid object More...

sgpp::base::DataVector *	getGridCoefficients ()
	gets a pointer to the sparse grids coefficients with evtl. More...

void	getGridCoefficientsForSC (sgpp::base::DataVector &Values)
	stores the values of the (dehierarchized) grid in the sgpp::base::DataVector Values used by time step size control methods More...

sgpp::base::GridStorage *	getGridStorage ()

std::string	getODESolver ()
	Returns the specified ODE solver for this instance. More...

sgpp::base::GridStorage *	getOldGridStorage ()

sgpp::base::GridStorage *	getSecondGridStorage ()

size_t	getSumGridPointsComplete ()
	Returns the number of average grid points for the complete grid. More...

size_t	getSumGridPointsInner ()
	Returns the number of average grid points for the inner grid. More...

	OperationParabolicPDESolverSystem ()
	Constructor. More...

void	saveAlpha ()
	stores the current alpha_complete into alpha_complete_old to be available in the next timestep More...

void	setODESolver (std::string ode)
	defines the used ODE Solver for this instance, this is important because the implementation of mult and generateRHS depends on the used ODE solver More...

void	setTimestepSize (double newTimestepSize)
	set the size of the new timestep More...

virtual void	startTimestep ()=0
	Implements some start jobs of every timestep, e.g.discounting boundaries. More...

virtual	~OperationParabolicPDESolverSystem ()
	Destructor. More...

Public Member Functions inherited from sgpp::base::OperationMatrix
	OperationMatrix ()
	Constructor. More...

virtual	~OperationMatrix ()
	Destructor. More...

Protected Member Functions
virtual void	applyLOperatorComplete (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)=0
	applies the PDE's system matrix, on complete grid - with boundaries More...

virtual void	applyLOperatorInner (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)=0
	applies the PDE's system matrix, on inner grid only More...

virtual void	applyMassMatrixComplete (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)=0
	applies the PDE's mass matrix, on complete grid - with boundaries More...

virtual void	applyMassMatrixInner (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)=0
	applies the PDE's mass matrix, on inner grid only More...

Protected Attributes
sgpp::base::DataVector *	alpha_inner
	Pointer to the alphas (ansatzfunctions' coefficients; inner points only) More...

sgpp::base::DirichletUpdateVector *	BoundaryUpdate
	Routine to modify the boundaries/inner points of the grid. More...

sgpp::base::DirichletGridConverter *	GridConverter
	Class that allows a simple conversion between a grid with and a without boundary points. More...

sgpp::base::Grid *	InnerGrid
	Pointer to the inner grid object. More...

Protected Attributes inherited from sgpp::solver::OperationParabolicPDESolverSystem
sgpp::base::DataVector *	alpha_complete
	Pointer to the alphas (ansatzfunctions' coefficients) More...

sgpp::base::DataVector *	alpha_complete_old
	Pointer to the alphas from the last timestep, needed when using variable timestep sizes. More...

sgpp::base::DataVector *	alpha_complete_tmp
	Pointer to temporary alphas, needed when using variable timestep sizes. More...

bool	bnewODESolver
	checks whether a new ODE solver has been selected after creation More...

sgpp::base::Grid *	BoundGrid
	Pointer to the grid object. More...

size_t	numSumGridpointsComplete
	Stores number of average gridpoints, complete grid. More...

size_t	numSumGridpointsInner
	Stores number of average gridpoints, inner grid. More...

sgpp::base::GridStorage *	oldGridStorage
	Pointer to the grid from the last iteration. More...

sgpp::base::DataVector *	rhs

sgpp::base::GridStorage *	secondGridStorage
	Pointer to the grid from the last aborted iteration. More...

double	TimestepSize
	the size of one timestep used in the ODE Solver More...

double	TimestepSize_old
	the size of the last timestep More...

std::string	tOperationMode
	specifies in which solver this matrix is used, valid values are: ExEul for explicit Euler ImEul for implicit Euler CrNic for Crank Nicolson solver More...

Detailed Description

Defines a System that is used to solve parabolic partial differential equations.

So an instance of this class has to pass to any ODE Solver used in SGpp.

\(A \dot{u} = L \vec{u}\)

A: mass matrix L: space discretization (L-Operator)

This class defines an elliptic problem in every timestep which is solved using an iterative SLE solver, that solving step is integrated in the ODE Solver.

This class is a specialized version of OperationParabolicPDESolverSystem which exploit Dirichlet boundary conditions. Hence there are no degrees of freedom on on the boundaries the iterative solver (CG or BiCGSTAB) has only to take inner grid points into account.

Constructor & Destructor Documentation

◆ OperationParabolicPDESolverSystemDirichlet()

sgpp::pde::OperationParabolicPDESolverSystemDirichlet::OperationParabolicPDESolverSystemDirichlet ( )

Constructor.

References sgpp::solver::OperationParabolicPDESolverSystem::numSumGridpointsComplete, and sgpp::solver::OperationParabolicPDESolverSystem::numSumGridpointsInner.

◆ ~OperationParabolicPDESolverSystemDirichlet()

sgpp::pde::OperationParabolicPDESolverSystemDirichlet::~OperationParabolicPDESolverSystemDirichlet ( )

virtual

Destructor.

Member Function Documentation

◆ applyLOperatorComplete()

virtual void sgpp::pde::OperationParabolicPDESolverSystemDirichlet::applyLOperatorComplete	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

protectedpure virtual

applies the PDE's system matrix, on complete grid - with boundaries

Parameters

alpha	the coefficients of the sparse grid's ansatzfunctions
result	reference to the sgpp::base::DataVector into which the result is written

Implemented in sgpp::pde::HeatEquationParabolicPDESolverSystemParallelOMP.

Referenced by generateRHS().

◆ applyLOperatorInner()

virtual void sgpp::pde::OperationParabolicPDESolverSystemDirichlet::applyLOperatorInner	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

protectedpure virtual

applies the PDE's system matrix, on inner grid only

Parameters

alpha	the coefficients of the sparse grid's ansatzfunctions
result	reference to the sgpp::base::DataVector into which the result is written

Implemented in sgpp::pde::HeatEquationParabolicPDESolverSystemParallelOMP.

Referenced by mult().

◆ applyMassMatrixComplete()

virtual void sgpp::pde::OperationParabolicPDESolverSystemDirichlet::applyMassMatrixComplete	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

protectedpure virtual

applies the PDE's mass matrix, on complete grid - with boundaries

Parameters

alpha	the coefficients of the sparse grid's ansatzfunctions
result	reference to the sgpp::base::DataVector into which the result is written

Implemented in sgpp::pde::HeatEquationParabolicPDESolverSystemParallelOMP.

Referenced by generateRHS().

◆ applyMassMatrixInner()

virtual void sgpp::pde::OperationParabolicPDESolverSystemDirichlet::applyMassMatrixInner	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

protectedpure virtual

applies the PDE's mass matrix, on inner grid only

Parameters

alpha	the coefficients of the sparse grid's ansatzfunctions
result	reference to the sgpp::base::DataVector into which the result is written

Implemented in sgpp::pde::HeatEquationParabolicPDESolverSystemParallelOMP.

Referenced by mult().

◆ generateRHS()

sgpp::base::DataVector * sgpp::pde::OperationParabolicPDESolverSystemDirichlet::generateRHS ( )

virtual

generates the right hand side of the system

Returns: returns the rhs

Implements sgpp::solver::OperationParabolicPDESolverSystem.

Reimplemented in sgpp::pde::HeatEquationParabolicPDESolverSystemParallelOMP.

Referenced by sgpp::pde::HeatEquationSolver::storeInnerRHS().

◆ getGridCoefficientsForCG()

sgpp::base::DataVector * sgpp::pde::OperationParabolicPDESolverSystemDirichlet::getGridCoefficientsForCG ( )

virtual

gets a pointer to the sparse grids coefficients used in the CG method to solve one timestep.

This is useful because (direchlet) boundaries can be skipped when solving the system.

Returns: alpha vector for CG method

Implements sgpp::solver::OperationParabolicPDESolverSystem.

References sgpp::solver::OperationParabolicPDESolverSystem::alpha_complete, alpha_inner, sgpp::base::DirichletGridConverter::calcInnerCoefs(), and GridConverter.

Referenced by sgpp::pde::HeatEquationSolver::storeInnerSolution().

◆ mult()

void sgpp::pde::OperationParabolicPDESolverSystemDirichlet::mult	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

virtual

Multiplicates a vector with the matrix.

Parameters

alpha	sgpp::base::DataVector that contains the ansatzfunctions' coefficients
result	sgpp::base::DataVector into which the result of the space discretization operation is stored

Implements sgpp::solver::OperationParabolicPDESolverSystem.

Reimplemented in sgpp::pde::HeatEquationParabolicPDESolverSystemParallelOMP.

References sgpp::base::DataVector::add(), applyLOperatorInner(), applyMassMatrixInner(), sgpp::base::DataVector::axpy(), sgpp::base::DataVector::getSize(), sgpp::base::DataVector::mult(), sgpp::base::DataVector::setAll(), sgpp::solver::OperationParabolicPDESolverSystem::TimestepSize, sgpp::solver::OperationParabolicPDESolverSystem::TimestepSize_old, and sgpp::solver::OperationParabolicPDESolverSystem::tOperationMode.

Member Data Documentation

◆ alpha_inner

sgpp::base::DataVector* sgpp::pde::OperationParabolicPDESolverSystemDirichlet::alpha_inner

protected

Pointer to the alphas (ansatzfunctions' coefficients; inner points only)

◆ BoundaryUpdate

sgpp::base::DirichletUpdateVector* sgpp::pde::OperationParabolicPDESolverSystemDirichlet::BoundaryUpdate

protected

Routine to modify the boundaries/inner points of the grid.

◆ GridConverter

sgpp::base::DirichletGridConverter* sgpp::pde::OperationParabolicPDESolverSystemDirichlet::GridConverter

protected

Class that allows a simple conversion between a grid with and a without boundary points.

◆ InnerGrid

sgpp::base::Grid* sgpp::pde::OperationParabolicPDESolverSystemDirichlet::InnerGrid

protected

Pointer to the inner grid object.

The documentation for this class was generated from the following files:

pde/src/sgpp/pde/operation/hash/OperationParabolicPDESolverSystemDirichlet.hpp
pde/src/sgpp/pde/operation/hash/OperationParabolicPDESolverSystemDirichlet.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ OperationParabolicPDESolverSystemDirichlet()

◆ ~OperationParabolicPDESolverSystemDirichlet()

Member Function Documentation

◆ applyLOperatorComplete()

◆ applyLOperatorInner()

◆ applyMassMatrixComplete()

◆ applyMassMatrixInner()

◆ generateRHS()

◆ getGridCoefficientsForCG()

◆ mult()

Member Data Documentation

◆ alpha_inner

◆ BoundaryUpdate

◆ GridConverter

◆ InnerGrid