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Protected Member Functions | Protected Attributes
Komplex_LinearProblem Class Reference

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:
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List of all members.

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.
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.
int ExtractSolution (Epetra_MultiVector &Xr, Epetra_MultiVector &Xi)
 Extrac a solution for the original complex-valued problem using the solution of the Komplex problem.
Epetra_LinearProblemKomplexProblem () const
 Returns pointer to the Epetra_LinearProblem object that defines the Komplex formulation.

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_CrsMatrixKomplexMatrix_
Teuchos::RCP< Epetra_MultiVectorKomplexRHS_
Teuchos::RCP< Epetra_MultiVectorKomplexLHS_
Teuchos::RCP< Epetra_MapKomplexMatrixRowMap_
Teuchos::RCP< Epetra_MapKomplexMatrixColMap_
Teuchos::RCP< Epetra_MapKomplexMatrixDomainMap_
Teuchos::RCP< Epetra_MapKomplexMatrixRangeMap_
const Epetra_CrsMatrixCrsA0_
const Epetra_CrsMatrixCrsA1_
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 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.

References Epetra_MultiVector::MyLength(), and Epetra_MultiVector::NumVectors().

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 TEUCHOS_TEST_FOR_EXCEPT.


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