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Moore-Spence Hopf solver strategy based on "Salinger" bordering. This is the classic 5-solve Hopf bordering method. More...
#include <LOCA_Hopf_MooreSpence_SalingerBordering.H>
Protected Member Functions | |
| NOX::Abstract::Group::ReturnType | solveContiguous (Teuchos::ParameterList ¶ms, const NOX::Abstract::MultiVector &input_x, const NOX::Abstract::MultiVector &input_y, const NOX::Abstract::MultiVector &input_z, const NOX::Abstract::MultiVector::DenseMatrix &input_w, const NOX::Abstract::MultiVector::DenseMatrix &input_p, NOX::Abstract::MultiVector &result_x, NOX::Abstract::MultiVector &result_y, NOX::Abstract::MultiVector &result_z, NOX::Abstract::MultiVector::DenseMatrix &result_w, NOX::Abstract::MultiVector::DenseMatrix &result_p) const |
| Solves equations with contiguous arguments. | |
Protected Attributes | |
| Teuchos::RCP< LOCA::GlobalData > | globalData |
| Global data object. | |
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Teuchos::RCP < Teuchos::ParameterList > | solverParams |
| Solver parameters. | |
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Teuchos::RCP < LOCA::Hopf::MooreSpence::AbstractGroup > | group |
| Underlying group. | |
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Teuchos::RCP < LOCA::Hopf::MooreSpence::ExtendedGroup > | hopfGroup |
| Hopf group. | |
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Teuchos::RCP< const NOX::Abstract::Vector > | yVector |
| Real component of eigenvector. | |
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Teuchos::RCP< const NOX::Abstract::Vector > | zVector |
| Imaginary component of eigenvector. | |
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Teuchos::RCP< const NOX::Abstract::Vector > | CeRealVector |
| Jy-wBz vector. | |
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Teuchos::RCP< const NOX::Abstract::Vector > | CeImagVector |
| Jz+wBy vector. | |
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Teuchos::RCP< const NOX::Abstract::Vector > | dfdp |
| df/dp vector | |
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Teuchos::RCP< const NOX::Abstract::Vector > | dCedpReal |
| d(Jy-wBz)/dp vector | |
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Teuchos::RCP< const NOX::Abstract::Vector > | dCedpImag |
| d(Jz+wBy)/dp vector | |
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Teuchos::RCP< const NOX::Abstract::Vector > | ByVector |
| By vector. | |
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Teuchos::RCP< const NOX::Abstract::Vector > | minusBzVector |
| -Bz vector | |
| double | w |
| Frequency w. | |
Moore-Spence Hopf solver strategy based on "Salinger" bordering. This is the classic 5-solve Hopf bordering method.
This class solves the Moore-Spence Hopf Newton equations:
![\[ \begin{bmatrix} J & 0 & 0 & 0 & f_p \\ (Jy-wBz)_x & J & -wB & -Bz & (Jy-wBz)_p \\ (Jz+wBy)_x & wB & J & By & (Jz+wBy)_p \\ 0 & \phi^T & 0 & 0 & 0 \\ 0 & 0 & \phi^T & 0 & 0 \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ \omega \\ \lambda \end{bmatrix} = \begin{bmatrix} F \\ G \\ H \\ u \\ v \end{bmatrix}. \]](form_482.png)
via the following block elimination scheme:
![\[ \begin{split} J [A \; b] &= [F \; f_p] \\ \begin{bmatrix} J & -wB \\ wB & J \end{bmatrix} \begin{bmatrix} C & e & g \\ D & f & h \end{bmatrix} &= \begin{bmatrix} G - (Jy-wBz)_x A & (Jy-wBz)_p - (Jy-wBz)_x b & -Bz \\ H - (Jz+wBy)_x A & (Jz+wBy)_p - (Jy-wBz)_x b & By \end{bmatrix} \\ \lambda &= \frac{(\phi^T h)(\phi^T C-u)-(\phi^T g)(\phi^T D-v)} {(\phi^T h)(\phi^T e)-(\phi^T g)(\phi^T f)} \\ \omega &= \frac{\phi^T D - v - (\phi^T f)\lambda}{\phi^T h} \\ X &= A - b \lambda \\ \begin{bmatrix} Y \\ Z \end{bmatrix} &= \begin{bmatrix} C \\ D \end{bmatrix} - \begin{bmatrix} e \\ f \end{bmatrix}\lambda - \begin{bmatrix} g \\ h \end{bmatrix}\omega \end{split} \]](form_483.png)
| LOCA::Hopf::MooreSpence::SalingerBordering::SalingerBordering | ( | 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 |
Set blocks in extended linear system.
| group | [in] Underlying group representing J |
| hopfGroup | [in] Hopf group representing the Hopf equations. |
| yVector | [in] Vector representing y |
| zVector | [in] Vector representing z |
| CeRealVector | [in] Vector representing Jy-wBz |
| CeImagVector | [in] Vector representing Jz+wBy |
| dfdp | [in] Vector representing df/dp |
| dCedpReal | [in] Vector representing d(Jy-wBz)/dp |
| dCedpImag | [in] Vector representing d(Jz+wBy)/dp |
| ByVector | [in] Vector representing By |
| mBzVector | [in] Vector representing -Bz |
| w | [in] Bifurcation frequency w |
Implements LOCA::Hopf::MooreSpence::SolverStrategy.
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virtual |
Solves the extended system as defined above.
The params argument is the linear solver parameters.
Implements LOCA::Hopf::MooreSpence::SolverStrategy.
References NOX::Abstract::MultiVector::clone(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getBifParams(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getFrequencies(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getImagEigenMultiVec(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getRealEigenMultiVec(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getXMultiVec(), NOX::Abstract::MultiVector::init(), LOCA::Extended::MultiVector::numVectors(), NOX::Abstract::MultiVector::setBlock(), and NOX::Abstract::MultiVector::subView().
1.8.5
Public Member Functions inherited from