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

#include <OperationEllipticPDESolverSystemDirichlet.hpp>

Inheritance diagram for sgpp::pde::OperationEllipticPDESolverSystemDirichlet:

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	getSolutionBoundGrid (sgpp::base::DataVector &Solution, sgpp::base::DataVector &SolutionInner)
	Gets the solution for the complete grid. More...

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

	OperationEllipticPDESolverSystemDirichlet (sgpp::base::Grid &SparseGrid, sgpp::base::DataVector &rhs)
	Constructor. More...

virtual	~OperationEllipticPDESolverSystemDirichlet ()
	Destructor. More...

Public Member Functions inherited from sgpp::pde::OperationEllipticPDESolverSystem
size_t	getNumGridPointsComplete ()
	Returns the number of grid points for the complete grid. More...

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

	OperationEllipticPDESolverSystem (sgpp::base::Grid &SparseGrid, sgpp::base::DataVector &rhs)
	Constructor. More...

virtual	~OperationEllipticPDESolverSystem ()
	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...

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...

sgpp::base::DataVector *	rhs_inner
	rhs for the inner grid More...

Protected Attributes inherited from sgpp::pde::OperationEllipticPDESolverSystem
sgpp::base::Grid *	BoundGrid
	Pointer to the grid object. More...

size_t	numGridpointsComplete
	Stores number of gridpoints, complete grid. More...

size_t	numGridpointsInner
	Stores number of gridpoints, inner grid. More...

sgpp::base::DataVector *	rhs
	the right hand side of the system More...

Detailed Description

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

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

\(L \vec{u} = rhs\)

L: space discretization (L-Operator) rhs: right hand side

This class is a specialized version of OperationEllipticPDESolverSystem which exploits Dirichlet boundary conditions. Since 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.

The inner grid is constructed during the constructor call!

Constructor & Destructor Documentation

◆ OperationEllipticPDESolverSystemDirichlet()

sgpp::pde::OperationEllipticPDESolverSystemDirichlet::OperationEllipticPDESolverSystemDirichlet	(	sgpp::base::Grid &	SparseGrid,
		sgpp::base::DataVector &	rhs
	)

Constructor.

Parameters

SparseGrid	the grid, for which the system should be solved
rhs	the right hand side of the corresponding system

References alpha_inner, BoundaryUpdate, sgpp::pde::OperationEllipticPDESolverSystem::BoundGrid, sgpp::base::Grid::getSize(), sgpp::base::Grid::getStorage(), GridConverter, InnerGrid, sgpp::pde::OperationEllipticPDESolverSystem::numGridpointsInner, and rhs_inner.

◆ ~OperationEllipticPDESolverSystemDirichlet()

sgpp::pde::OperationEllipticPDESolverSystemDirichlet::~OperationEllipticPDESolverSystemDirichlet ( )

virtual

Destructor.

References alpha_inner, BoundaryUpdate, GridConverter, InnerGrid, and rhs_inner.

Member Function Documentation

◆ applyLOperatorComplete()

virtual void sgpp::pde::OperationEllipticPDESolverSystemDirichlet::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::PoissonEquationEllipticPDESolverSystemDirichlet.

Referenced by generateRHS().

◆ applyLOperatorInner()

virtual void sgpp::pde::OperationEllipticPDESolverSystemDirichlet::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::PoissonEquationEllipticPDESolverSystemDirichlet.

Referenced by mult().

◆ generateRHS()

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

virtual

generates the right hand side of the system

Returns: returns the rhs

Implements sgpp::pde::OperationEllipticPDESolverSystem.

References applyLOperatorComplete(), BoundaryUpdate, sgpp::base::DirichletGridConverter::calcInnerCoefs(), GridConverter, InnerGrid, sgpp::base::DataVector::mult(), sgpp::pde::OperationEllipticPDESolverSystem::rhs, rhs_inner, and sgpp::base::DirichletUpdateVector::setInnerPointsToZero().

Referenced by sgpp::pde::PoissonEquationSolver::solvePDE(), sgpp::pde::PoissonEquationSolver::storeInnerRHS(), and sgpp::pde::PoissonEquationSolver::storeInnerSolution().

◆ getGridCoefficientsForCG()

sgpp::base::DataVector * sgpp::pde::OperationEllipticPDESolverSystemDirichlet::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

References alpha_inner, sgpp::base::Grid::getSize(), InnerGrid, and sgpp::base::DataVector::setAll().

Referenced by sgpp::pde::PoissonEquationSolver::solvePDE(), and sgpp::pde::PoissonEquationSolver::storeInnerSolution().

◆ getSolutionBoundGrid()

void sgpp::pde::OperationEllipticPDESolverSystemDirichlet::getSolutionBoundGrid	(	sgpp::base::DataVector &	Solution,
		sgpp::base::DataVector &	SolutionInner
	)

virtual

Gets the solution for the complete grid.

Parameters

Solution	sgpp::base::DataVector that must have a dimension equal to the bound's grid dimension, the result is written to Solution
SolutionInner	Solution on the inner grid

References GridConverter, sgpp::pde::OperationEllipticPDESolverSystem::rhs, and sgpp::base::DirichletGridConverter::updateBoundaryCoefs().

Referenced by sgpp::pde::PoissonEquationSolver::solvePDE().

◆ mult()

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

virtual

Multiplicates a vector with the matrix \( L \).

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::pde::OperationEllipticPDESolverSystem.

References applyLOperatorInner().