Komplex_LinearProblem: A class for forming an equivalent real formulation of a complex valued problem. More...

#include <Komplex_LinearProblem.h>

Collaboration diagram for Komplex_LinearProblem:

Public Member Functions

	Komplex_LinearProblem (double c0r, double c0i, const Epetra_RowMatrix &A0, double c1r, double c1i, const Epetra_RowMatrix &A1, const Epetra_MultiVector &Xr, const Epetra_MultiVector &Xi, const Epetra_MultiVector &Br, const Epetra_MultiVector &Bi)
	Komplex_LinearProblem constructor. More...

virtual	~Komplex_LinearProblem ()
	Komplex_LinearProblem Destructor.


int	UpdateValues (double c0r, double c0i, const Epetra_RowMatrix &A0, double c1r, double c1i, const Epetra_RowMatrix &A1, const Epetra_MultiVector &Xr, const Epetra_MultiVector &Xi, const Epetra_MultiVector &Br, const Epetra_MultiVector &Bi)
	Update the values of the equivalent real valued system. More...


int	ExtractSolution (Epetra_MultiVector &Xr, Epetra_MultiVector &Xi)
	Extrac a solution for the original complex-valued problem using the solution of the Komplex problem. More...


Epetra_LinearProblem *	KomplexProblem () const
	Returns pointer to the Epetra_LinearProblem object that defines the Komplex formulation. More...

Protected Member Functions
int	ProcessValues (double c0r, double c0i, const Epetra_RowMatrix &A0, double c1r, double c1i, const Epetra_RowMatrix &A1, const Epetra_MultiVector &Xr, const Epetra_MultiVector &Xi, const Epetra_MultiVector &Br, const Epetra_MultiVector &Bi, bool firstTime)

int	TestMaps (const Epetra_RowMatrix &A0, const Epetra_RowMatrix &A1, const Epetra_MultiVector &Xr, const Epetra_MultiVector &Xi, const Epetra_MultiVector &Br, const Epetra_MultiVector &Bi)

int	ConstructKomplexMaps (const Epetra_Map &A0DomainMap, const Epetra_Map &A0RangeMap, const Epetra_Map &A0RowMap)

int	MakeKomplexMap (const Epetra_Map &Map, Teuchos::RCP< Epetra_Map > &KMap)

int	InitMatrixAccess (const Epetra_RowMatrix &A0, const Epetra_RowMatrix &A1)

int	GetRow (int Row, const Epetra_RowMatrix &A0, const Epetra_RowMatrix &A1, int &NumIndices0, double &Values0, int &Indices0, int &NumIndices1, double &Values1, int &Indices1)

int	PutRow (int Row, int &NumIndices, double Values, int Indices, bool firstTime)

Protected Attributes
Teuchos::RCP < Epetra_LinearProblem >	KomplexProblem_

Teuchos::RCP< Epetra_CrsMatrix >	KomplexMatrix_

Teuchos::RCP< Epetra_MultiVector >	KomplexRHS_

Teuchos::RCP< Epetra_MultiVector >	KomplexLHS_

Teuchos::RCP< Epetra_Map >	KomplexMatrixRowMap_

Teuchos::RCP< Epetra_Map >	KomplexMatrixColMap_

Teuchos::RCP< Epetra_Map >	KomplexMatrixDomainMap_

Teuchos::RCP< Epetra_Map >	KomplexMatrixRangeMap_

const Epetra_CrsMatrix *	CrsA0_

const Epetra_CrsMatrix *	CrsA1_

bool	A0A1AreCrs_

std::vector< int >	Indices0_

std::vector< double >	Values0_

int	MaxNumMyEntries0_

std::vector< int >	Indices1_

std::vector< double >	Values1_

int	MaxNumMyEntries1_

std::vector< int >	IndicesK_

std::vector< double >	ValuesK_

int	MaxNumMyEntriesK_

Detailed Description

Komplex_LinearProblem: A class for forming an equivalent real formulation of a complex valued problem.

The Komplex_LinearProblem class takes a complex linear problem, separated into real and imaginary parts,
and forms an equivalent real valued system of twice the dimension.  The resulting system can then be
solved with any Trilinos solver that understands Epetra objects.

KOMPLEX solves a complex-valued linear system Ax = b by solving an equivalent real-valued system of twice the dimension. Specifically, writing in terms of real and imaginary parts, we have

$(A_r + i*A_i)*(x_r + i*x_i) = (b_r + i*b_i)$

or by separating into real and imaginary equations we have

$\left( \begin{array}{rr} A_r & -A_i\\ A_i & A_r \end{array} \right) \left( \begin{array}{r} x_r\\ x_i \end{array} \right) = \left( \begin{array}{r} b_r\\ b_i \end{array} \right)$

which is a real-valued system of twice the size. If we find xr and xi, we can form the solution to the original system as x = xr +i*xi.

KOMPLEX accepts the user linear system as two real-valued matrices with no assumption about the structure of the matrices, except that they have compatible RowMap, DomainMap and RangeMap distributions. Each matrix is multiplied by user-supplied complex constants.

Although formally the system is a 2-by-2 block system, we actually apply the interleaving at the matrix entry level such that the real part of the first complex equation is followed by the imaginary part of the first complex equation, and so on. This approach is documented in:

David Day and Michael A. Heroux. Solving complex-valued linear systems via equivalent real formulations. SIAM J. Sci. Comput., 23(2):480–498, 2001.

Constructor & Destructor Documentation

Komplex_LinearProblem::Komplex_LinearProblem	(	double	c0r,
		double	c0i,
		const Epetra_RowMatrix &	A0,
		double	c1r,
		double	c1i,
		const Epetra_RowMatrix &	A1,
		const Epetra_MultiVector &	Xr,
		const Epetra_MultiVector &	Xi,
		const Epetra_MultiVector &	Br,
		const Epetra_MultiVector &	Bi
	)

Komplex_LinearProblem constructor.

Constructs the Komplex operator from the user definition of the complex-valued matrix C = (c0r+i*c0i)*A0 +(c1r+i*c1i)*A1. Using this general expression for the complex matrix allows easy formulation of a variety of common complex problems.

Parameters

c0r	(In) The real part of the complex coefficient multiplying A0.
c0i	(In) The imag part of the complex coefficient multiplying A0.
A0	(In) An Epetra_RowMatrix that is one of the matrices used to define the true complex operator.
c1r	(In) The real part of the complex coefficient multiplying A1.
c1i	(In) The imag part of the complex coefficient multiplying A1.
A1	(In) An Epetra_RowMatrix that is the second of the matrices used to define the true complex operator.
Xr	(In) The real part of the complex valued LHS.
Xi	(In) The imag part of the complex valued LHS.
Br	(In) The real part of the complex valued RHS.
Bi	(In) The imag part of the complex valued RHS.

References Epetra_CrsMatrix::FillComplete(), Teuchos::RCP< T >::get(), Teuchos::rcp(), and TEUCHOS_TEST_FOR_EXCEPT.

Member Function Documentation

int Komplex_LinearProblem::ExtractSolution	(	Epetra_MultiVector &	Xr,
		Epetra_MultiVector &	Xi
	)

Extrac a solution for the original complex-valued problem using the solution of the Komplex problem.

After solving the komplex linear system, this method can be called to extract the solution of the original problem, assuming the solution for the komplex system is valid.

Parameters

Xr	(Out) An existing Epetra_MultiVector. On exit it will contain the real part of the complex valued solution.
Xi	(Out) An existing Epetra_MultiVector. On exit it will contain the imag part of the complex valued solution.

Epetra_LinearProblem* Komplex_LinearProblem::KomplexProblem ( ) const

inline

Returns pointer to the Epetra_LinearProblem object that defines the Komplex formulation.

The pointer returned from this method will contain the address of a fully-constructed Epetra_LinearProblem instance that can be used with any Trilinos preconditioner or solver.

References Teuchos::RCP< T >::get().

int Komplex_LinearProblem::UpdateValues	(	double	c0r,
		double	c0i,
		const Epetra_RowMatrix &	A0,
		double	c1r,
		double	c1i,
		const Epetra_RowMatrix &	A1,
		const Epetra_MultiVector &	Xr,
		const Epetra_MultiVector &	Xi,
		const Epetra_MultiVector &	Br,
		const Epetra_MultiVector &	Bi
	)

Update the values of the equivalent real valued system.

This method allows the values of an existing Komplex_LinearProblem object to be updated. Note that the update that there is no change to the pattern of the matrices.

Returns: Error code, set to 0 if no error.

References Epetra_CrsMatrix::PutScalar(), and TEUCHOS_TEST_FOR_EXCEPT.

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

Komplex_LinearProblem.h
Komplex_LinearProblem.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation