#include <LOCA_Hopf_MooreSpence_SalingerBordering.H>
Inheritance diagram for LOCA::Hopf::MooreSpence::SalingerBordering:
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_451.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_452.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. |
| void LOCA::Hopf::MooreSpence::SalingerBordering::setBlocks | ( | const Teuchos::RCP< LOCA::Hopf::MooreSpence::AbstractGroup > & | group, | |
| const Teuchos::RCP< LOCA::Hopf::MooreSpence::ExtendedGroup > & | hopfGroup, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | yVector, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | zVector, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | CeRealVector, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | CeImagVector, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | dfdp, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | dCedpReal, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | dCedpImag, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | ByVector, | |||
| const Teuchos::RCP< const NOX::Abstract::Vector > & | mBzVector, | |||
| double | w | |||
| ) | [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.
| NOX::Abstract::Group::ReturnType LOCA::Hopf::MooreSpence::SalingerBordering::solve | ( | Teuchos::ParameterList & | params, | |
| const LOCA::Hopf::MooreSpence::ExtendedMultiVector & | input, | |||
| LOCA::Hopf::MooreSpence::ExtendedMultiVector & | result | |||
| ) | const [virtual] |
Solves the extended system as defined above.
The params argument is the linear solver parameters.
Implements LOCA::Hopf::MooreSpence::SolverStrategy.
1.4.7