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Public Member Functions |
| | FoldHandler (Problem *const &problem_pt, double *const ¶meter_pt) |
| | Constructor: initialise the fold handler, by setting initial guesses for Y, Phi and calculating count. If the system changes, a new fold handler must be constructed.
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| | ~FoldHandler () |
| | Destructor return the problem to its original (non-augmented) state.
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| unsigned | ndof (GeneralisedElement *const &elem_pt) |
| | The number of unknowns is 2n+1.
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| unsigned long | eqn_number (GeneralisedElement *const &elem_pt, const unsigned &ieqn_local) |
| | Get the global equation number of the local unknown.
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| void | get_residuals (GeneralisedElement *const &elem_pt, Vector< double > &residuals) |
| | Formulate the augmented system.
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| void | get_jacobian (GeneralisedElement *const &elem_pt, Vector< double > &residuals, DenseMatrix< double > &jacobian) |
| | Calculate the elemental Jacobian matrix "d equation / d variable".
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| int | bifurcation_type () const |
| | Indicate that we are tracking a fold bifurcation by returning 1.
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| double * | bifurcation_parameter_pt () const |
| | Return a pointer to the bifurcation parameter in bifurcation tracking problems.
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| void | get_eigenfunction (Vector< DoubleVector > &eigenfunction) |
| | Return the eigenfunction(s) associated with the bifurcation that has been detected in bifurcation tracking problems.
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| void | solve_augmented_block_system () |
| | Set to solve the augmented-by-one block system.
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| void | solve_block_system () |
| | Set to solve the block system.
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| void | solve_full_system () |
| | Set to Solve non-block system.
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Private Types |
| | Full_augmented |
| | Block_J |
| | Block_augmented_J |
| enum | { Full_augmented,
Block_J,
Block_augmented_J
} |
Private Attributes |
| unsigned | Solve_which_system |
| | Integer flag to indicate which system should be assembled. There are three possibilities. The full augmented system (0), the non-augmented jacobian system (1), a system in which the jacobian is augmented by 1 row and column to ensure that it is non-singular (2). See the enum above.
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| Problem * | Problem_pt |
| | Pointer to the problem.
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| unsigned | Ndof |
| | Store the number of degrees of freedom in the non-augmented problem.
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| Vector< double > | Phi |
| | A constant vector used to ensure that the null vector is not trivial.
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| Vector< double > | Y |
| | Storage for the null vector.
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| Vector< int > | Count |
| | A vector that is used to determine how many elements contribute to a particular equation. It is used to ensure that the global system is correctly formulated.
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| double * | Parameter_pt |
| | Storage for the pointer to the parameter.
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Friends |
| class | AugmentedBlockFoldLinearSolver |
| oomph::FoldHandler::FoldHandler |
( |
Problem *const & |
problem_pt, |
|
|
double *const & |
parameter_pt | |
|
) |
| | |
Constructor: initialise the fold handler, by setting initial guesses for Y, Phi and calculating count. If the system changes, a new fold handler must be constructed.
Constructor: Initialise the fold handler, by setting initial guesses for Y, Phi and calculating Count. If the system changes, a new handler must be constructed.
Definition at line 719 of file assembly_handler.cc.
References oomph::Problem::communicator_pt(), Count, oomph::LinearSolver::disable_resolve(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, oomph::Mesh::element_pt(), oomph::LinearSolver::enable_resolve(), oomph::Problem::get_derivative_wrt_global_parameter(), oomph::Problem::linear_solver_pt(), oomph::Problem::mesh_pt(), oomph::GeneralisedElement::ndof(), oomph::Problem::ndof(), Ndof, oomph::Mesh::nelement(), Phi, Problem_pt, oomph::LinearAlgebraDistribution::rebuild(), oomph::LinearSolver::resolve(), oomph::LinearSolver::resolve_is_enabled(), oomph::LinearSolver::solve(), and Y.
| void oomph::FoldHandler::get_eigenfunction |
( |
Vector< DoubleVector > & |
eigenfunction |
) |
[virtual] |
Calculate the elemental Jacobian matrix "d equation / d variable".
Calculate the elemental Jacobian matrix "d equation / d variable" for the augmented system
Reimplemented from oomph::AssemblyHandler.
Definition at line 956 of file assembly_handler.cc.
References oomph::Problem::actions_after_change_in_bifurcation_parameter(), Block_augmented_J, Block_J, Count, oomph::Problem::Dof_pt, eqn_number(), oomph::GeneralisedElement::eqn_number(), oomph::BlackBoxFDNewtonSolver::FD_step, Full_augmented, oomph::GeneralisedElement::get_jacobian(), get_residuals(), Ndof, oomph::GeneralisedElement::ndof(), ndof(), OOMPH_EXCEPTION_LOCATION, Phi, Problem_pt, Solve_which_system, and Y.
Referenced by oomph::AugmentedBlockFoldLinearSolver::resolve(), and oomph::AugmentedBlockFoldLinearSolver::solve().
, and a solution is 
, where 
are the unknowns in the problem. A limit point is formally specified by the augmented system of size 
![\[ R(u,\lambda) = 0, \]](form_24.png)
![\[ Jy = 0, \]](form_25.png)
![\[\phi\cdot y = 1. \]](form_26.png)
is the usual Jacobian matrix, 
, and 
is a constant vector that is chosen to ensure that the null vector, 
, is not trivial.
