This class provides a simple-to-use solver of the multi dimensional Heat Equation that uses Sparse Grids. More...

#include <HeatEquationSolverWithStretching.hpp>

Inheritance diagram for sgpp::pde::HeatEquationSolverWithStretching:

Public Member Functions
void	constructGrid (sgpp::base::Stretching &myStretching, size_t level)

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

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

void	initGridWithSmoothHeat (sgpp::base::DataVector &alpha, double mu, double sigma, double factor)
	Inits the grid in the middle of the whole domain with one single heat. More...

void	initScreen ()
	Inits the grid with a constant heat. More...

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

void	printGridDomain (sgpp::base::DataVector &alpha, size_t PointesPerDimension, sgpp::base::BoundingBox &GridArea, std::string tfilename) const
	This function is a placeholder, is not used. More...

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

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...

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	setHeatCoefficient (double a)
	This method sets the heat coefficient of the regarded material. More...

void	solveCrankNicolson (size_t numTimesteps, double timestepsize, size_t maxCGIterations, double epsilonCG, sgpp::base::DataVector &alpha, size_t NumImEul=0)
	Call this routine to use the Crank Nicolson algorithm to solve the parabolic PDE. More...

void	solveExplicitEuler (size_t numTimesteps, double timestepsize, size_t maxCGIterations, double epsilonCG, sgpp::base::DataVector &alpha, bool verbose=false, bool generateAnimation=false)
	Call this routine to use an explicit Euler algorithm to solve the parabolic PDE. More...

void	solveImplicitEuler (size_t numTimesteps, double timestepsize, size_t maxCGIterations, double epsilonCG, sgpp::base::DataVector &alpha, bool verbose=false, bool generateAnimation=false)
	Call this routine to use an explicit Euler algorithm to solve the parabolic PDE. More...

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

Public Member Functions inherited from sgpp::pde::ParabolicPDESolver
	ParabolicPDESolver ()
	the size of one timestep More...

virtual	~ParabolicPDESolver ()
	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	printLevelIndexGrid (std::string tfilename) const
	Prints the level,index pairs of the grid for each Gridpoint to a file. 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 Heat Equation that uses Sparse Grids.

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

Constructor & Destructor Documentation

◆ HeatEquationSolverWithStretching()

sgpp::pde::HeatEquationSolverWithStretching::HeatEquationSolverWithStretching ( )

Std-Constructor of the solver.

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

◆ ~HeatEquationSolverWithStretching()

sgpp::pde::HeatEquationSolverWithStretching::~HeatEquationSolverWithStretching ( )

virtual

Std-Destructor of the solver.

Member Function Documentation

◆ constructGrid() [1/2]

void sgpp::pde::HeatEquationSolverWithStretching::constructGrid	(	sgpp::base::Stretching &	myStretching,
		size_t	level
	)

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

◆ constructGrid() [2/2]

void sgpp::pde::HeatEquationSolverWithStretching::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.

◆ initGridWithSmoothHeat()

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

Inits the grid in the middle of the whole domain with one single heat.

alpha reference to the coefficients vector heat the value of the heat in the middle of the domain Inits the grid in the middle the domain with an smooth heat distribution that the normal distribution formula

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::HeatEquationSolverWithStretching::initScreen ( )

Inits the grid with a constant heat.

alpha reference to the coefficients vector constHeat the temperature of the constant heat Inits the screen object

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

◆ printGrid()

void sgpp::pde::HeatEquationSolverWithStretching::printGrid	(	sgpp::base::DataVector &	alpha,
		size_t	PointesPerDimension,
		std::string	tfilename
	)		const

virtual

This is some kind of debug functionality.

It writes a file, that can be used with gnuplot the print the grid.

Is only implemented for 1D and 2D grids!

Parameters

alpha	the coefficients of the Sparse Gird's basis functions
PointesPerDimension	the distance between evaluation points
tfilename	absolute path to file into which the grid's evaluation is written

Reimplemented from sgpp::pde::PDESolver.

References sgpp::pde::PDESolver::myGrid, and sgpp::base::GridPrinterForStretching::printGrid().

◆ printGridDomain()

void sgpp::pde::HeatEquationSolverWithStretching::printGridDomain	(	sgpp::base::DataVector &	alpha,
		size_t	PointesPerDimension,
		sgpp::base::BoundingBox &	GridArea,
		std::string	tfilename
	)		const

virtual

This function is a placeholder, is not used.

Reimplemented from sgpp::pde::PDESolver.

◆ printGridDomainStretching()

void sgpp::pde::HeatEquationSolverWithStretching::printGridDomainStretching	(	sgpp::base::DataVector &	alpha,
		size_t	PointesPerDimension,
		sgpp::base::Stretching &	GridArea,
		std::string	tfilename
	)		const

This is some kind of debug functionality.

It writes a file, that can be used with gnuplot the print the grid.

Is only implemented for 2D grids!

Parameters

alpha	the coefficients of the Sparse Gird's basis functions
PointesPerDimension	the distance between evaluation points
GridArea	the area in which the function should be plotted
tfilename	absolute path to file into which the grid's evaluation is written

References sgpp::pde::PDESolver::myGrid, and sgpp::base::GridPrinterForStretching::printGridDomainStretching().

◆ printSparseGrid()

void sgpp::pde::HeatEquationSolverWithStretching::printSparseGrid	(	sgpp::base::DataVector &	alpha,
		std::string	tfilename,
		bool	bSurplus
	)		const

virtual

Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus.

This function is available for all dimensions

Parameters

alpha	the coefficients of the grid's ansatzfunctions
tfilename	absoulte path to the file the grid is written into
bSurplus	specifies whether the surplus (true) or the node basis value (false) is written

Reimplemented from sgpp::pde::PDESolver.

References sgpp::pde::PDESolver::myGrid, and sgpp::base::GridPrinterForStretching::printSparseGrid().

◆ printSparseGridExpTransform()

void sgpp::pde::HeatEquationSolverWithStretching::printSparseGridExpTransform	(	sgpp::base::DataVector &	alpha,
		std::string	tfilename,
		bool	bSurplus
	)		const

virtual

Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus.

This function is available for all dimensions.

The coordinates of the grid points are pushed the exp function. So log transformed grids can be plotted in cartesion coordinates.

Parameters

alpha	the coefficients of the grid's ansatzfunctions
tfilename	absoulte path to the file the grid is written into
bSurplus	specifies whether the surplus (true) or the node basis value (false) is written

Reimplemented from sgpp::pde::PDESolver.

References sgpp::pde::PDESolver::myGrid, and sgpp::base::GridPrinterForStretching::printSparseGridExpTransform().

◆ setHeatCoefficient()

void sgpp::pde::HeatEquationSolverWithStretching::setHeatCoefficient ( double a )

This method sets the heat coefficient of the regarded material.

Parameters

a	the heat coefficient

◆ solveCrankNicolson()

void sgpp::pde::HeatEquationSolverWithStretching::solveCrankNicolson	(	size_t	numTimesteps,
		double	timestepsize,
		size_t	maxCGIterations,
		double	epsilonCG,
		sgpp::base::DataVector &	alpha,
		size_t	NumImEul = `0`
	)

virtual

Call this routine to use the Crank Nicolson algorithm to solve the parabolic PDE.

Parameters

numTimesteps	the number of timesteps that should be executed
timestepsize	the size of the interval one timestep moves forward
maxCGIterations	the maximum of interation in the CG solver
epsilonCG	the epsilon used in the CG
alpha	the coefficients of the Sparse Gird's basis functions
NumImEul	specifies how many ImEul steps should be executed before CrNic is used, default is 0

Implements sgpp::pde::ParabolicPDESolver.

References sgpp::pde::PDESolver::bGridConstructed, sgpp::pde::PDESolver::myGrid, sgpp::solver::CrankNicolson::solve(), sgpp::solver::Euler::solve(), sgpp::base::SGppStopwatch::start(), sgpp::base::SGppStopwatch::stop(), sgpp::base::ScreenOutput::writeEmptyLines(), and sgpp::base::ScreenOutput::writeStartSolve().

◆ solveExplicitEuler()

void sgpp::pde::HeatEquationSolverWithStretching::solveExplicitEuler	(	size_t	numTimesteps,
		double	timestepsize,
		size_t	maxCGIterations,
		double	epsilonCG,
		sgpp::base::DataVector &	alpha,
		bool	verbose = `false`,
		bool	generateAnimation = `false`
	)

virtual

Call this routine to use an explicit Euler algorithm to solve the parabolic PDE.

Parameters

numTimesteps	the number of timesteps that should be executed
timestepsize	the size of the interval one timestep moves forward
maxCGIterations	the maximum of interation in the CG solver
epsilonCG	the epsilon used in the CG
alpha	the coefficients of the Sparse Gird's basis functions
verbose	enables verbose output during solving
generateAnimation	set this to true, if you want to generate a grid output in every timestep

Implements sgpp::pde::ParabolicPDESolver.

References sgpp::pde::PDESolver::bGridConstructed, sgpp::pde::PDESolver::myGrid, sgpp::solver::Euler::solve(), sgpp::base::SGppStopwatch::start(), sgpp::base::SGppStopwatch::stop(), sgpp::base::ScreenOutput::writeEmptyLines(), and sgpp::base::ScreenOutput::writeStartSolve().

◆ solveImplicitEuler()

void sgpp::pde::HeatEquationSolverWithStretching::solveImplicitEuler	(	size_t	numTimesteps,
		double	timestepsize,
		size_t	maxCGIterations,
		double	epsilonCG,
		sgpp::base::DataVector &	alpha,
		bool	verbose = `false`,
		bool	generateAnimation = `false`
	)

virtual

Call this routine to use an explicit Euler algorithm to solve the parabolic PDE.

Parameters

numTimesteps	the number of timesteps that should be executed
timestepsize	the size of the interval one timestep moves forward
maxCGIterations	the maximum of interation in the CG solver
epsilonCG	the epsilon used in the CG
alpha	the coefficients of the Sparse Gird's basis functions
verbose	enables verbose output during solving
generateAnimation	set this to true, if you want to generate a grid output in every timestep

Implements sgpp::pde::ParabolicPDESolver.

References sgpp::pde::PDESolver::bGridConstructed, sgpp::pde::PDESolver::myGrid, sgpp::solver::Euler::solve(), sgpp::base::SGppStopwatch::start(), sgpp::base::SGppStopwatch::stop(), sgpp::base::ScreenOutput::writeEmptyLines(), and sgpp::base::ScreenOutput::writeStartSolve().

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

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

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HeatEquationSolverWithStretching()

◆ ~HeatEquationSolverWithStretching()

Member Function Documentation

◆ constructGrid() [1/2]

◆ constructGrid() [2/2]

◆ initGridWithSmoothHeat()

◆ initScreen()

◆ printGrid()

◆ printGridDomain()

◆ printGridDomainStretching()

◆ printSparseGrid()

◆ printSparseGridExpTransform()

◆ setHeatCoefficient()

◆ solveCrankNicolson()

◆ solveExplicitEuler()

◆ solveImplicitEuler()