SG++-Doxygen-Documentation
sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries Class Referenceabstract

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

#include <OperationEllipticPDESolverSystemFreeBoundaries.hpp>

Inheritance diagram for sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries:

## Public Member Functions

virtual sgpp::base::DataVectorgenerateRHS ()
generates the right hand side of the system More...

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

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

virtual ~OperationEllipticPDESolverSystemFreeBoundaries ()
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 applyLOperator (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)=0
applies the PDE's system matrix, on complete grid - with boundaries More...

Protected Attributes inherited from sgpp::pde::OperationEllipticPDESolverSystem
sgpp::base::GridBoundGrid
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::DataVectorrhs
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, here degrees of freedom exists on the boundaries!

$$L \vec{u} = rhs$$

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

## ◆ OperationEllipticPDESolverSystemFreeBoundaries()

 sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries::OperationEllipticPDESolverSystemFreeBoundaries ( 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

## ◆ ~OperationEllipticPDESolverSystemFreeBoundaries()

 sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries::~OperationEllipticPDESolverSystemFreeBoundaries ( )
virtual

Destructor.

## ◆ applyLOperator()

 virtual void sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries::applyLOperator ( 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

Referenced by mult().

## ◆ generateRHS()

 sgpp::base::DataVector * sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries::generateRHS ( )
virtual

generates the right hand side of the system

Returns
returns the rhs

Implements sgpp::pde::OperationEllipticPDESolverSystem.

## ◆ mult()

 void sgpp::pde::OperationEllipticPDESolverSystemFreeBoundaries::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 applyLOperator().

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