LOCA::Hopf::MooreSpence::SalingerBordering Class Reference

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>

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List of all members.

Public Member Functions

 SalingerBordering (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &solverParams)
 Constructor.
virtual ~SalingerBordering ()
 Destructor.
virtual void 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)
 Set blocks in extended linear system.
virtual NOX::Abstract::Group::ReturnType solve (Teuchos::ParameterList &params, const LOCA::Hopf::MooreSpence::ExtendedMultiVector &input, LOCA::Hopf::MooreSpence::ExtendedMultiVector &result) const
 Solves the extended system as defined above.

Protected Member Functions

NOX::Abstract::Group::ReturnType solveContiguous (Teuchos::ParameterList &params, 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::GlobalDataglobalData
 Global data object.
Teuchos::RCP< Teuchos::ParameterListsolverParams
 Solver parameters.
Teuchos::RCP< LOCA::Hopf::MooreSpence::AbstractGroupgroup
 Underlying group.
Teuchos::RCP< LOCA::Hopf::MooreSpence::ExtendedGrouphopfGroup
 Hopf group.
Teuchos::RCP< const NOX::Abstract::VectoryVector
 Real component of eigenvector.
Teuchos::RCP< const NOX::Abstract::VectorzVector
 Imaginary component of eigenvector.
Teuchos::RCP< const NOX::Abstract::VectorCeRealVector
 Jy-wBz vector.
Teuchos::RCP< const NOX::Abstract::VectorCeImagVector
 Jz+wBy vector.
Teuchos::RCP< const NOX::Abstract::Vectordfdp
 df/dp vector
Teuchos::RCP< const NOX::Abstract::VectordCedpReal
 d(Jy-wBz)/dp vector
Teuchos::RCP< const NOX::Abstract::VectordCedpImag
 d(Jz+wBy)/dp vector
Teuchos::RCP< const NOX::Abstract::VectorByVector
 By vector.
Teuchos::RCP< const NOX::Abstract::VectorminusBzVector
 -Bz vector
double w
 Frequency w.

Detailed Description

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:

\[ \begin{bmatrix} J & 0 & 0 & 0 & f_p \\ (Jy-wBz)_x & J & -wB & -Bz & (Jy-wBz)_p \\ (Jz+wBy)_x & wB & J & By & (Jz+wBy)_p \\ 0 & \phi^T & 0 & 0 & 0 \\ 0 & 0 & \phi^T & 0 & 0 \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ \omega \\ \lambda \end{bmatrix} = \begin{bmatrix} F \\ G \\ H \\ u \\ v \end{bmatrix}. \]

via the following block elimination scheme:

\[ \begin{split} J [A \; b] &= [F \; f_p] \\ \begin{bmatrix} J & -wB \\ wB & J \end{bmatrix} \begin{bmatrix} C & e & g \\ D & f & h \end{bmatrix} &= \begin{bmatrix} G - (Jy-wBz)_x A & (Jy-wBz)_p - (Jy-wBz)_x b & -Bz \\ H - (Jz+wBy)_x A & (Jz+wBy)_p - (Jy-wBz)_x b & By \end{bmatrix} \\ \lambda &= \frac{(\phi^T h)(\phi^T C-u)-(\phi^T g)(\phi^T D-v)} {(\phi^T h)(\phi^T e)-(\phi^T g)(\phi^T f)} \\ \omega &= \frac{\phi^T D - v - (\phi^T f)\lambda}{\phi^T h} \\ X &= A - b \lambda \\ \begin{bmatrix} Y \\ Z \end{bmatrix} &= \begin{bmatrix} C \\ D \end{bmatrix} - \begin{bmatrix} e \\ f \end{bmatrix}\lambda - \begin{bmatrix} g \\ h \end{bmatrix}\omega \end{split} \]


Constructor & Destructor Documentation

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.

Parameters:
global_data [in] Global data object
topParams [in] Parsed top-level parameter list
solverParams [in] Bordered solver parameters. Currently none are referenced.


Member Function Documentation

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.

Parameters:
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.


The documentation for this class was generated from the following files:
Generated on Wed May 12 21:41:56 2010 for NOX by  doxygen 1.4.7