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Block elimination strategy for solving a block upper-triangular system. More...
#include <LOCA_BorderedSolver_UpperTriangularBlockElimination.H>
Protected Attributes | |
| Teuchos::RCP< LOCA::GlobalData > | globalData |
| Global data object. | |
Block elimination strategy for solving a block upper-triangular system.
This class solves the extended system of equations
![\[ \begin{bmatrix} op(J) & A \\ 0 & op(C) \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix} \]](form_367.png)
via block elimination:
![\[ \begin{aligned} Y &= op(C)^{-1}G \\ X &= op(J)^{-1}(F - A Y) \end{aligned} \]](form_368.png)
where 
represents either the identity operation or the transpose. 
must be nonzero, while 
, 
or 
may be zero. The solve for the non-transposed system is implemented by the solve() method, while the solve for the transposed system is implemented by the solveTranspose() method.
| LOCA::BorderedSolver::UpperTriangularBlockElimination::UpperTriangularBlockElimination | ( | const Teuchos::RCP< LOCA::GlobalData > & | global_data | ) |
Constructor.
| global_data | [in] Global data object |
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::UpperTriangularBlockElimination::solve | ( | Teuchos::ParameterList & | params, |
| const LOCA::BorderedSolver::AbstractOperator & | op, | ||
| const NOX::Abstract::MultiVector * | A, | ||
| const NOX::Abstract::MultiVector::DenseMatrix & | C, | ||
| const NOX::Abstract::MultiVector * | F, | ||
| const NOX::Abstract::MultiVector::DenseMatrix * | G, | ||
| NOX::Abstract::MultiVector & | X, | ||
| NOX::Abstract::MultiVector::DenseMatrix & | Y | ||
| ) | const |
Solves the extended system as described above.
Either A, F, or G may be zero by passing NULL.
References LOCA::BorderedSolver::AbstractOperator::applyInverse(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::assign(), NOX::Abstract::MultiVector::clone(), Teuchos::Copy, NOX::DeepCopy, NOX::Abstract::Group::Failed, Teuchos::LAPACK< OrdinalType, ScalarType >::GETRF(), Teuchos::LAPACK< OrdinalType, ScalarType >::GETRS(), NOX::Abstract::MultiVector::init(), Teuchos::NO_TRANS, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::numCols(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::numRows(), NOX::Abstract::Group::Ok, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::putScalar(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::stride(), NOX::Abstract::MultiVector::update(), and Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::values().
Referenced by LOCA::BorderedSolver::Bordering::applyInverse(), LOCA::BorderedSolver::EpetraAugmented::applyInverse(), LOCA::BorderedSolver::TpetraHouseholder::applyInverse(), and LOCA::BorderedSolver::EpetraHouseholder::applyInverse().
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::UpperTriangularBlockElimination::solveTranspose | ( | Teuchos::ParameterList & | params, |
| const LOCA::BorderedSolver::AbstractOperator & | op, | ||
| const NOX::Abstract::MultiVector * | A, | ||
| const NOX::Abstract::MultiVector::DenseMatrix & | C, | ||
| const NOX::Abstract::MultiVector * | F, | ||
| const NOX::Abstract::MultiVector::DenseMatrix * | G, | ||
| NOX::Abstract::MultiVector & | X, | ||
| NOX::Abstract::MultiVector::DenseMatrix & | Y | ||
| ) | const |
Solves the extended system using the tranpose of J and C as described above.
Either A, F, or G may be zero by passing NULL.
References LOCA::BorderedSolver::AbstractOperator::applyInverseTranspose(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::assign(), NOX::Abstract::MultiVector::clone(), Teuchos::Copy, NOX::DeepCopy, NOX::Abstract::Group::Failed, Teuchos::LAPACK< OrdinalType, ScalarType >::GETRF(), Teuchos::LAPACK< OrdinalType, ScalarType >::GETRS(), NOX::Abstract::MultiVector::init(), Teuchos::NO_TRANS, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::numCols(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::numRows(), NOX::Abstract::Group::Ok, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::putScalar(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::stride(), NOX::Abstract::MultiVector::update(), and Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::values().
Referenced by LOCA::BorderedSolver::Bordering::applyInverseTranspose(), LOCA::BorderedSolver::TpetraHouseholder::applyInverseTranspose(), and LOCA::BorderedSolver::EpetraHouseholder::applyInverseTranspose().
1.8.5