This class provides a simple-to-use solver of the multi dimensional Poisson Equation on Sparse Grids. More...

#include <PoissonEquationSolver.hpp>

Inheritance diagram for sgpp::pde::PoissonEquationSolver:

Public Member Functions
void	constructGrid (sgpp::base::BoundingBox &myBoundingBox, size_t level)
	Use this routine the construct a regular grid to solve a PDE. More...

void	initGridWithExpHeat (sgpp::base::DataVector &alpha, double factor=1.0)
	Inits the grid with a heat distribution based on the e-function. More...

void	initGridWithExpHeatFullDomain (sgpp::base::DataVector &alpha, double factor=1.0)
	Inits the grid with a heat distribution based on the e-function. More...

void	initGridWithSmoothHeat (sgpp::base::DataVector &alpha, double mu, double sigma, double factor)
	Inits the grid with a smooth heat distribution (based on a std-normal distribution) on its boundaries. More...

void	initGridWithSmoothHeatFullDomain (sgpp::base::DataVector &alpha, double mu, double sigma, double factor)
	Inits the grid with a smooth heat distribution (based on a std-normal distribution) on its boundaries. More...

void	initScreen ()
	Inits the screen object. More...

	PoissonEquationSolver ()
	Std-Constructor of the solver. More...

void	solvePDE (sgpp::base::DataVector &alpha, sgpp::base::DataVector &rhs, size_t maxCGIterations, double epsilonCG, bool verbose=false)
	abstract method to solve an elliptic PDE. More...

void	storeInnerRHS (sgpp::base::DataVector &alpha, std::string tFilename)
	Routine to export the RHS of the inner system which has to be solved in order to solve the Poisson equation. More...

void	storeInnerSolution (sgpp::base::DataVector &alpha, size_t maxCGIterations, double epsilonCG, std::string tFilename)
	Routine to export the solution of the inner system which has been calculated by Up/Down scheme. More...

virtual	~PoissonEquationSolver ()
	Std-Destructor of the solver. More...

Public Member Functions inherited from sgpp::pde::EllipticPDESolver
	EllipticPDESolver ()
	Std-Constructor of the solver. More...

virtual	~EllipticPDESolver ()
	Std-Destructor of the solver. More...

Public Member Functions inherited from sgpp::pde::PDESolver
void	coarsenInitialGridSurplus (sgpp::base::DataVector &alpha, double dThreshold)
	Coarsens a grid by taking the grid's coefficients into account. More...

void	deleteGrid ()
	deletes the grid created within that solver More...

void	evaluateCuboid (sgpp::base::DataVector &alpha, sgpp::base::DataVector &FunctionValues, sgpp::base::DataMatrix &EvaluationPoints)
	Evaluates the sparse grid's function given by the stored grid and the alpha coefficients. More...

double	evaluatePoint (sgpp::base::DataVector &evalPoint, sgpp::base::DataVector &alpha)
	Determines the value of the function in the d-dimensional space. More...

std::string	getGrid () const
	gets the a string the describes the grid which is currently used to solve More...

size_t	getNumberDimensions () const
	use this the determine the number of dimensions that are currently used in the solver. More...

size_t	getNumberGridPoints () const
	use this to determine the number of grid points, used to solve the current problem More...

size_t	getNumberInnerGridPoints () const
	use this to determine the number of inner grid points, used to solve the current problem More...

	PDESolver ()
	Std-Constructor of the solver. More...

virtual void	printGrid (sgpp::base::DataVector &alpha, size_t PointesPerDimension, std::string tfilename) const
	This is some kind of debug functionality. More...

virtual void	printGridDomain (sgpp::base::DataVector &alpha, size_t PointesPerDimension, sgpp::base::BoundingBox &GridArea, std::string tfilename) const
	This is some kind of debug functionality. More...

virtual void	printLevelIndexGrid (std::string tfilename) const
	Prints the level,index pairs of the grid for each Gridpoint to a file. More...

virtual void	printSparseGrid (sgpp::base::DataVector &alpha, std::string tfilename, bool bSurplus) const
	Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus. More...

virtual void	printSparseGridExpTransform (sgpp::base::DataVector &alpha, std::string tfilename, bool bSurplus) const
	Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus. More...

void	refineInitialGridSurplus (sgpp::base::DataVector &alpha, int numRefinePoints, double dThreshold)
	Refines a grid by taking the grid's coefficients into account. More...

void	refineInitialGridSurplusSubDomain (sgpp::base::DataVector &alpha, int numRefinePoints, double dThreshold, std::vector< double > &norm_mu, std::vector< double > &norm_sigma)
	Refines a grid by taking the grid's coefficients into account. More...

void	refineInitialGridSurplusToMaxLevel (sgpp::base::DataVector &alpha, double dThreshold, sgpp::base::level_t maxLevel)
	Refines a grid by taking the grid's coefficients into account. More...

void	refineInitialGridSurplusToMaxLevelSubDomain (sgpp::base::DataVector &alpha, double dThreshold, sgpp::base::level_t maxLevel, std::vector< double > &norm_mu, std::vector< double > &norm_sigma)
	Refines a grid by taking the grid's coefficients into account. More...

void	setGrid (const std::string &serializedGrid)
	Sets the grid used in this BlackScholes Solver by an given serialized string of the grid. More...

virtual	~PDESolver ()
	Std-Destructor of the solver. More...

Additional Inherited Members
Protected Member Functions inherited from sgpp::pde::PDESolver
virtual void	getGridNormalDistribution (sgpp::base::DataVector &alpha, std::vector< double > &norm_mu, std::vector< double > &norm_sigma)
	This function calculates for every grid point the value of a normal distribution given by norm_mu and norm_sigma. More...

Protected Attributes inherited from sgpp::pde::PDESolver
bool	bGridConstructed
	stores if the grid was created inside the solver More...

size_t	dim
	the dimension of the grid More...

int	levels
	the number of levels used for an regular grid More...

sgpp::base::BoundingBox *	myBoundingBox
	Stores Pointer to the sgpp::base::Grid's Bounding Box. More...

sgpp::base::Grid *	myGrid
	The Sparse sgpp::base::Grid needed in this classificator. More...

sgpp::base::GridStorage *	myGridStorage
	Stores Pointer to the Girs's Storage. More...

Detailed Description

This class provides a simple-to-use solver of the multi dimensional Poisson Equation on Sparse Grids.

The class's aim is, to hide all complex details of solving the Poisson Equation on Sparse Grids!

Constructor & Destructor Documentation

◆ PoissonEquationSolver()

sgpp::pde::PoissonEquationSolver::PoissonEquationSolver ( )

Std-Constructor of the solver.

References sgpp::pde::PDESolver::bGridConstructed.

◆ ~PoissonEquationSolver()

sgpp::pde::PoissonEquationSolver::~PoissonEquationSolver ( )

virtual

Std-Destructor of the solver.

Member Function Documentation

◆ constructGrid()

void sgpp::pde::PoissonEquationSolver::constructGrid	(	sgpp::base::BoundingBox &	myBoundingBox,
		size_t	level
	)

virtual

Use this routine the construct a regular grid to solve a PDE.

Parameters

myBoundingBox	reference to a bounding box that describes the grid
level	number of the regular's grid levels

Implements sgpp::pde::PDESolver.

References sgpp::pde::PDESolver::bGridConstructed, sgpp::pde::PDESolver::dim, sgpp::base::Grid::getBoundingBox(), sgpp::base::BoundingBox::getDimension(), sgpp::base::Grid::getGenerator(), sgpp::base::Grid::getStorage(), level, sgpp::pde::PDESolver::levels, sgpp::pde::PDESolver::myBoundingBox, sgpp::pde::PDESolver::myGrid, sgpp::pde::PDESolver::myGridStorage, and sgpp::base::GridGenerator::regular().

◆ initGridWithExpHeat()

void sgpp::pde::PoissonEquationSolver::initGridWithExpHeat	(	sgpp::base::DataVector &	alpha,
		double	factor = `1.0`
	)

Inits the grid with a heat distribution based on the e-function.

The e-function is shifted in that way the right boundary values becomes 1 (in case of factor = 1)

Parameters

alpha	reference to the coefficient's vector
factor	a constant factor used to enlarge the exp-functions input parameter

References sgpp::pde::PDESolver::bGridConstructed, sgpp::op_factory::createOperationHierarchisation(), sgpp::pde::PDESolver::dim, sgpp::base::OperationHierarchisation::doHierarchisation(), sgpp::base::BoundingBox::getBoundary(), sgpp::base::Grid::getBoundingBox(), sgpp::base::HashGridStorage::getCoordinates(), sgpp::base::HashGridStorage::getPoint(), sgpp::base::Grid::getSize(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, sgpp::base::BoundingBox1D::leftBoundary, sgpp::pde::PDESolver::myBoundingBox, sgpp::pde::PDESolver::myGrid, sgpp::pde::PDESolver::myGridStorage, sgpp::base::BoundingBox1D::rightBoundary, and analyse_erg::tmp.

◆ initGridWithExpHeatFullDomain()

void sgpp::pde::PoissonEquationSolver::initGridWithExpHeatFullDomain	(	sgpp::base::DataVector &	alpha,
		double	factor = `1.0`
	)

Inits the grid with a heat distribution based on the e-function.

The e-function is shifted in that way the right boundary values becomes 1 (in case of factor = 1)

Parameters

alpha	reference to the coefficient's vector
factor	a constant factor used to enlarge the exp-functions input parameter

References sgpp::pde::PDESolver::bGridConstructed, sgpp::op_factory::createOperationHierarchisation(), sgpp::pde::PDESolver::dim, sgpp::base::OperationHierarchisation::doHierarchisation(), sgpp::base::BoundingBox::getBoundary(), sgpp::base::Grid::getBoundingBox(), sgpp::base::HashGridStorage::getCoordinates(), sgpp::base::HashGridStorage::getPoint(), sgpp::base::Grid::getSize(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, sgpp::pde::PDESolver::myGrid, sgpp::pde::PDESolver::myGridStorage, and analyse_erg::tmp.

◆ initGridWithSmoothHeat()

void sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeat	(	sgpp::base::DataVector &	alpha,
		double	mu,
		double	sigma,
		double	factor
	)

Inits the grid with a smooth heat distribution (based on a std-normal distribution) on its boundaries.

Coefficients of inner grid points are set to zero since an elliptical PDE is solved

Parameters

alpha	reference to the coefficients vector
mu	the exspected value of the normal distribution
sigma	the sigma of the normal distribution
factor	a factor that is used to stretch the function values

References sgpp::pde::PDESolver::bGridConstructed, sgpp::op_factory::createOperationHierarchisation(), sgpp::pde::PDESolver::dim, sgpp::base::OperationHierarchisation::doHierarchisation(), sgpp::base::BoundingBox::getBoundary(), sgpp::base::HashGridStorage::getCoordinates(), sgpp::base::HashGridStorage::getPoint(), sgpp::base::Grid::getSize(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, sgpp::base::BoundingBox1D::leftBoundary, mu, sgpp::pde::PDESolver::myBoundingBox, sgpp::pde::PDESolver::myGrid, sgpp::pde::PDESolver::myGridStorage, sgpp::base::BoundingBox1D::rightBoundary, and analyse_erg::tmp.

◆ initGridWithSmoothHeatFullDomain()

void sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeatFullDomain	(	sgpp::base::DataVector &	alpha,
		double	mu,
		double	sigma,
		double	factor
	)

Inits the grid with a smooth heat distribution (based on a std-normal distribution) on its boundaries.

Coefficients of inner grid points aren't set to zero since they are used to hint an adaptive refinement of the grid BEFORE solving the PDE.

Parameters

alpha	reference to the coefficients vector
mu	the exspected value of the normal distribution
sigma	the sigma of the normal distribution
factor	a factor that is used to stretch the function values

References sgpp::pde::PDESolver::bGridConstructed, sgpp::op_factory::createOperationHierarchisation(), sgpp::pde::PDESolver::dim, sgpp::base::OperationHierarchisation::doHierarchisation(), sgpp::base::HashGridStorage::getCoordinates(), sgpp::base::HashGridStorage::getPoint(), sgpp::base::Grid::getSize(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, mu, sgpp::pde::PDESolver::myGrid, sgpp::pde::PDESolver::myGridStorage, and analyse_erg::tmp.

◆ initScreen()

void sgpp::pde::PoissonEquationSolver::initScreen ( )

Inits the screen object.

References sgpp::base::ScreenOutput::writeTitle().

◆ solvePDE()

void sgpp::pde::PoissonEquationSolver::solvePDE	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	rhs,
		size_t	maxCGIterations,
		double	epsilonCG,
		bool	verbose = `false`
	)

virtual

abstract method to solve an elliptic PDE.

All solver of elliptic PDEs have to implement this method.

Parameters

alpha	the coefficients of the Sparse Gird's basis functions will be in this vector after solving
rhs	the right hand side of the SLE
maxCGIterations	the maximum of interation in the CG solver
epsilonCG	the epsilon used in the CG
verbose	enables verbose output during solving

Implements sgpp::pde::EllipticPDESolver.

References sgpp::pde::OperationEllipticPDESolverSystemDirichlet::generateRHS(), sgpp::pde::OperationEllipticPDESolverSystemDirichlet::getGridCoefficientsForCG(), sgpp::pde::OperationEllipticPDESolverSystem::getNumGridPointsComplete(), sgpp::pde::OperationEllipticPDESolverSystem::getNumGridPointsInner(), sgpp::pde::OperationEllipticPDESolverSystemDirichlet::getSolutionBoundGrid(), sgpp::pde::PDESolver::myGrid, sgpp::solver::ConjugateGradients::solve(), sgpp::base::SGppStopwatch::start(), and sgpp::base::SGppStopwatch::stop().

◆ storeInnerRHS()

void sgpp::pde::PoissonEquationSolver::storeInnerRHS	(	sgpp::base::DataVector &	alpha,
		std::string	tFilename
	)

Routine to export the RHS of the inner system which has to be solved in order to solve the Poisson equation.

Parameters

alpha	the start solution
tFilename	file into which the rhs is written

References sgpp::pde::OperationEllipticPDESolverSystemDirichlet::generateRHS(), sgpp::base::DataVector::get(), sgpp::base::DataVector::getSize(), python.statsfileInfo::i, sgpp::pde::PDESolver::myGrid, sgpp::base::SGppStopwatch::start(), and sgpp::base::SGppStopwatch::stop().

◆ storeInnerSolution()

void sgpp::pde::PoissonEquationSolver::storeInnerSolution	(	sgpp::base::DataVector &	alpha,
		size_t	maxCGIterations,
		double	epsilonCG,
		std::string	tFilename
	)

Routine to export the solution of the inner system which has been calculated by Up/Down scheme.

Parameters

alpha	the start solution
maxCGIterations	the maximum of interation in the CG solver
epsilonCG	the epsilon used in the C
tFilename	file into which the rhs is written

References sgpp::pde::OperationEllipticPDESolverSystemDirichlet::generateRHS(), sgpp::base::DataVector::get(), sgpp::pde::OperationEllipticPDESolverSystemDirichlet::getGridCoefficientsForCG(), sgpp::base::DataVector::getSize(), python.statsfileInfo::i, sgpp::pde::PDESolver::myGrid, and sgpp::solver::ConjugateGradients::solve().

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

pde/src/sgpp/pde/application/PoissonEquationSolver.hpp
pde/src/sgpp/pde/application/PoissonEquationSolver.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PoissonEquationSolver()

◆ ~PoissonEquationSolver()

Member Function Documentation

◆ constructGrid()

◆ initGridWithExpHeat()

◆ initGridWithExpHeatFullDomain()

◆ initGridWithSmoothHeat()

◆ initGridWithSmoothHeatFullDomain()

◆ initScreen()

◆ solvePDE()

◆ storeInnerRHS()

◆ storeInnerSolution()