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Bordered system solver strategy based on bordering. More...
#include <LOCA_BorderedSolver_Bordering.H>
Protected Attributes | |
| Teuchos::RCP< LOCA::GlobalData > | globalData |
| Global data object. | |
|
Teuchos::RCP < Teuchos::ParameterList > | solverParams |
| Solver parameters. | |
|
Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > | op |
| Pointer to operator. | |
|
Teuchos::RCP< const NOX::Abstract::MultiVector > | A |
| Pointer to A block. | |
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Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface > | B |
| Pointer to B block. | |
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Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > | C |
| Pointer to C block. | |
| bool | isZeroA |
| flag indicating whether A block is zero | |
| bool | isZeroB |
| flag indicating whether B block is zero | |
| bool | isZeroC |
| flag indicating whether C block is zero | |
| bool | isZeroF |
| flag indicating whether F block is zero | |
| bool | isZeroG |
| flag indicating whether G block is zero | |
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. |
|
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().
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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().
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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().
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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.
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virtual |
Intialize solver for a solve.
This should be called after setMatrixBlocks(), but before applyInverse().
Implements LOCA::BorderedSolver::AbstractStrategy.
References NOX::Abstract::Group::Ok.
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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.
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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.
1.8.5
Public Member Functions inherited from