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Bordered system solver strategy based on bordering. More...
#include <LOCA_BorderedSolver_Bordering.H>
Bordered system solver strategy based on bordering.
This class solves the extended system of equations
![\[ \begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix} \]](form_337.png)
via bordering (block elimination):
![\[ \begin{aligned} X_1 &= J^{-1} F \\ X_2 &= J^{-1} A \\ Y &= (C-B^T X_2)^{-1}(G-B^T X_1) \\ X &= X_1 - X_2 Y \end{aligned} \]](form_352.png)
It takes advantage of any of the matrix blocks being zero and concatenates 
and 
into a contiguous multivector to compute 
and 
in one block solve.
To solve the transpose of the system, a similar bordering algorithm is implemented. Note however that for the transpose, the constraint object representing 
must implement the LOCA::MultiContinuation::ConstraintInterfaceMVDX since appears on the right-hand-side of a linear system.
| LOCA::BorderedSolver::Bordering::Bordering | ( | const Teuchos::RCP< LOCA::GlobalData > & | global_data, |
| const Teuchos::RCP< LOCA::Parameter::SublistParser > & | topParams, | ||
| const Teuchos::RCP< Teuchos::ParameterList > & | solverParams | ||
| ) |
Constructor.
| global_data | [in] Global data object |
| topParams | [in] Parsed top-level parameter list |
| solverParams | [in] Bordered solver parameters. Currently none are referenced. |
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::apply | ( | const NOX::Abstract::MultiVector & | X, |
| const NOX::Abstract::MultiVector::DenseMatrix & | Y, | ||
| NOX::Abstract::MultiVector & | U, | ||
| NOX::Abstract::MultiVector::DenseMatrix & | V | ||
| ) | const [virtual] |
Computed extended matrix-multivector product.
Computes
![\[ \begin{bmatrix} U \\ V \end{bmatrix} = \begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} J*X + A*Y \\ B^T*X + C*Y \end{bmatrix}. \]](form_355.png)
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::Group::Failed, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::multiply(), Teuchos::NO_TRANS, and NOX::Abstract::MultiVector::update().
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::applyInverse | ( | Teuchos::ParameterList & | params, |
| const NOX::Abstract::MultiVector * | F, | ||
| const NOX::Abstract::MultiVector::DenseMatrix * | G, | ||
| NOX::Abstract::MultiVector & | X, | ||
| NOX::Abstract::MultiVector::DenseMatrix & | Y | ||
| ) | const [virtual] |
Solves the extended system as defined above using bordering.
The params argument is the linear solver parameters. If isZeroF or isZeroG is true, than the corresponding F or G pointers may be NULL.
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::MultiVector::clone(), Teuchos::ParameterList::get(), Teuchos::RCP< T >::get(), NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::MultiVector::setBlock(), LOCA::BorderedSolver::UpperTriangularBlockElimination::solve(), LOCA::BorderedSolver::LowerTriangularBlockElimination::solve(), and NOX::Abstract::MultiVector::subView().
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::applyInverseTranspose | ( | Teuchos::ParameterList & | params, |
| const NOX::Abstract::MultiVector * | F, | ||
| const NOX::Abstract::MultiVector::DenseMatrix * | G, | ||
| NOX::Abstract::MultiVector & | X, | ||
| NOX::Abstract::MultiVector::DenseMatrix & | Y | ||
| ) | const [virtual] |
Solves the transpose of the extended system as defined above using bordering.
The params argument is the linear solver parameters. If isZeroF or isZeroG is true, than the corresponding F or G pointers may be NULL. Note that for the transpose solve B must be of type LOCA::MultiContinuation::ConstraintInterfaceMVDX.
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::MultiVector::clone(), Teuchos::RCP< T >::get(), Teuchos::ParameterList::get(), LOCA::MultiContinuation::ConstraintInterfaceMVDX::getDX(), NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::MultiVector::setBlock(), LOCA::BorderedSolver::UpperTriangularBlockElimination::solveTranspose(), LOCA::BorderedSolver::LowerTriangularBlockElimination::solveTranspose(), and NOX::Abstract::MultiVector::subView().
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::applyTranspose | ( | const NOX::Abstract::MultiVector & | X, |
| const NOX::Abstract::MultiVector::DenseMatrix & | Y, | ||
| NOX::Abstract::MultiVector & | U, | ||
| NOX::Abstract::MultiVector::DenseMatrix & | V | ||
| ) | const [virtual] |
Computed extended matrix transpose-multivector product.
Computes
![\[ \begin{bmatrix} U \\ V \end{bmatrix} = \begin{bmatrix} J^T & B \\ A^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} J^T*X + B*Y \\ A^T*X + C^T*Y \end{bmatrix}. \]](form_356.png)
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::Group::Failed, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::multiply(), NOX::Abstract::MultiVector::multiply(), Teuchos::NO_TRANS, and Teuchos::TRANS.
Intialize solver for a solve.
This should be called after setMatrixBlocks(), but before applyInverse().
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::Group::Ok.
| NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::initForTransposeSolve | ( | ) | [virtual] |
Intialize solver for a transpose solve.
This should be called after setMatrixBlocks(), but before applyInverseTranspose().
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::Group::Ok.
| void LOCA::BorderedSolver::Bordering::setMatrixBlocks | ( | const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > & | op, |
| const Teuchos::RCP< const NOX::Abstract::MultiVector > & | blockA, | ||
| const Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface > & | blockB, | ||
| const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > & | blockC | ||
| ) | [virtual] |
Set blocks.
The blockA or blockC pointer may be null if either is zero. Whether block B is zero will be determined by querying blockB via ConstraintInterface::isConstraintDerivativesXZero.
Implements LOCA::BorderedSolver::AbstractStrategy.
1.7.6.1
