A class that is used to assemble the augmented system that defines a fold (saddle-node) or limit point. The "standard" problem must be a function of a global paramter $\lambda$ , and a solution is $R(u,\lambda) = 0$ , where are the unknowns in the problem. A limit point is formally specified by the augmented system of size . More...

#include <assembly_handler.h>

Inheritance diagram for oomph::FoldHandler:

Public Member Functions
	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. More...

	FoldHandler (Problem const &problem_pt, double const &parameter_pt, const DoubleVector &eigenvector)
	Constructor in which initial eigenvector can be passed. More...

	FoldHandler (Problem const &problem_pt, double const &parameter_pt, const DoubleVector &eigenvector, const DoubleVector &normalisation)
	Constructor in which initial eigenvector and normalisation can be passed. More...

	~FoldHandler ()
	Destructor, return the problem to its original state before the augmented system was added. More...

unsigned	ndof (GeneralisedElement *const &elem_pt)
	Get the number of elemental degrees of freedom. More...

unsigned long	eqn_number (GeneralisedElement *const &elem_pt, const unsigned &ieqn_local)
	Get the global equation number of the local unknown. More...

void	get_residuals (GeneralisedElement *const &elem_pt, Vector< double > &residuals)
	Get the residuals. More...

void	get_jacobian (GeneralisedElement *const &elem_pt, Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the elemental Jacobian matrix "d equation / d variable". More...

void	get_dresiduals_dparameter (GeneralisedElement const &elem_pt, double const &parameter_pt, Vector< double > &dres_dparam)
	Overload the derivatives of the residuals with respect to a parameter to apply to the augmented system. More...

void	get_djacobian_dparameter (GeneralisedElement const &elem_pt, double const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Overload the derivative of the residuals and jacobian with respect to a parameter so that it breaks. More...

void	get_hessian_vector_products (GeneralisedElement *const &elem_pt, Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Overload the hessian vector product function so that it breaks. More...

int	bifurcation_type () const
	Indicate that we are tracking a fold bifurcation by returning 1. More...

double *	bifurcation_parameter_pt () const
	Return a pointer to the bifurcation parameter in bifurcation tracking problems. More...

void	get_eigenfunction (Vector< DoubleVector > &eigenfunction)
	Return the eigenfunction(s) associated with the bifurcation that has been detected in bifurcation tracking problems. More...

void	solve_augmented_block_system ()
	Set to solve the augmented block system. More...

void	solve_block_system ()
	Set to solve the block system. More...

void	solve_full_system ()
	Solve non-block system. More...

Public Member Functions inherited from oomph::AssemblyHandler
	AssemblyHandler ()
	Empty constructor. More...

virtual void	dof_vector (GeneralisedElement *const &elem_pt, const unsigned &t, Vector< double > &dof)
	Return vector of dofs at time level t in the element elem_pt. More...

virtual void	dof_pt_vector (GeneralisedElement const &elem_pt, Vector< double > &dof_pt)
	Return vector of pointers to dofs in the element elem_pt. More...

virtual double &	local_problem_dof (Problem *const &problem_pt, const unsigned &t, const unsigned &i)
	Return the t-th level of storage associated with the i-th (local) dof stored in the problem. More...

virtual void	get_all_vectors_and_matrices (GeneralisedElement *const &elem_pt, Vector< Vector< double >> &vec, Vector< DenseMatrix< double >> &matrix)
	Calculate all desired vectors and matrices provided by the element elem_pt. More...

virtual void	get_inner_products (GeneralisedElement *const &elem_pt, Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Compute the inner products of the given vector of pairs of history values over the element. More...

virtual void	get_inner_product_vectors (GeneralisedElement *const &elem_pt, Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Compute the vectors that when taken as a dot product with other history values give the inner product over the element. More...

virtual void	synchronise ()
	Function that is used to perform any synchronisation required during the solution. More...

virtual	~AssemblyHandler ()
	Empty virtual destructor. More...

Private Types
enum	{ Full_augmented , Block_J , Block_augmented_J }
	A little private enum to determine whether we are solving the block system or not. More...

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. More...

Problem *	Problem_pt
	Pointer to the problem. More...

unsigned	Ndof
	Store the number of degrees of freedom in the non-augmented problem. More...

Vector< double >	Phi
	A constant vector used to ensure that the null vector is not trivial. More...

Vector< double >	Y
	Storage for the null vector. More...

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. More...

double *	Parameter_pt
	Storage for the pointer to the parameter. More...

Friends
class	AugmentedBlockFoldLinearSolver

Detailed Description

A class that is used to assemble the augmented system that defines a fold (saddle-node) or limit point. The "standard" problem must be a function of a global paramter $\lambda$ , and a solution is $R(u,\lambda) = 0$ , where are the unknowns in the problem. A limit point is formally specified by the augmented system of size .

$R(u,\lambda) = 0,$

$Jy = 0,$

$\phi\cdot y = 1.$

In the above is the usual Jacobian matrix, , and $\phi$ is a constant vector that is chosen to ensure that the null vector, , is not trivial.

Definition at line 472 of file assembly_handler.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

private

A little private enum to determine whether we are solving the block system or not.

Enumerator
Full_augmented
Block_J
Block_augmented_J

Definition at line 478 of file assembly_handler.h.

Constructor & Destructor Documentation

◆ FoldHandler() [1/3]

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 864 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), Count, oomph::LinearSolver::disable_resolve(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, e, oomph::Mesh::element_pt(), oomph::LinearSolver::enable_resolve(), oomph::GeneralisedElement::eqn_number(), oomph::Problem::get_derivative_wrt_global_parameter(), oomph::LinearSolver::is_resolve_enabled(), oomph::Problem::linear_solver_pt(), oomph::Problem::mesh_pt(), Ndof, oomph::GeneralisedElement::ndof(), oomph::Problem::ndof(), oomph::Mesh::nelement(), Phi, Problem_pt, oomph::LinearSolver::resolve(), oomph::LinearSolver::solve(), oomph::Problem::Sparse_assemble_with_arrays_previous_allocation, and Y.

◆ FoldHandler() [2/3]

oomph::FoldHandler::FoldHandler	(	Problem *const &	problem_pt,
		double *const &	parameter_pt,
		const DoubleVector &	eigenvector
	)

Constructor in which initial eigenvector can be passed.

Constructor in which the eigenvector is passed as an initial guess.

Definition at line 970 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), Count, oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, e, oomph::Mesh::element_pt(), oomph::GeneralisedElement::eqn_number(), oomph::Problem::mesh_pt(), Ndof, oomph::GeneralisedElement::ndof(), oomph::Problem::ndof(), oomph::Mesh::nelement(), Phi, Problem_pt, oomph::Problem::Sparse_assemble_with_arrays_previous_allocation, and Y.

◆ FoldHandler() [3/3]

oomph::FoldHandler::FoldHandler	(	Problem *const &	problem_pt,
		double *const &	parameter_pt,
		const DoubleVector &	eigenvector,
		const DoubleVector &	normalisation
	)

Constructor in which initial eigenvector and normalisation can be passed.

Constructor in which the eigenvector and normalisation vector are passed as an initial guess.

Definition at line 1036 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), Count, oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, e, oomph::Mesh::element_pt(), oomph::GeneralisedElement::eqn_number(), oomph::Problem::mesh_pt(), Ndof, oomph::GeneralisedElement::ndof(), oomph::Problem::ndof(), oomph::Mesh::nelement(), Phi, Problem_pt, oomph::Problem::Sparse_assemble_with_arrays_previous_allocation, and Y.

◆ ~FoldHandler()

oomph::FoldHandler::~FoldHandler ( )

Destructor, return the problem to its original state before the augmented system was added.

Destructor return the problem to its original (non-augmented) state.

Definition at line 1573 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, oomph::Problem::linear_solver_pt(), oomph::AugmentedBlockFoldLinearSolver::linear_solver_pt(), Ndof, Problem_pt, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

Member Function Documentation

◆ bifurcation_parameter_pt()

double* oomph::FoldHandler::bifurcation_parameter_pt ( ) const

inlinevirtual

Return a pointer to the bifurcation parameter in bifurcation tracking problems.

Reimplemented from oomph::AssemblyHandler.

Definition at line 584 of file assembly_handler.h.

References Parameter_pt.

◆ bifurcation_type()

int oomph::FoldHandler::bifurcation_type ( ) const

inlinevirtual

Indicate that we are tracking a fold bifurcation by returning 1.

Reimplemented from oomph::AssemblyHandler.

Definition at line 577 of file assembly_handler.h.

◆ eqn_number()

unsigned long oomph::FoldHandler::eqn_number	(	GeneralisedElement *const &	elem_pt,
		const unsigned &	ieqn_local
	)

virtual

Get the global equation number of the local unknown.

Return the global equation number associated with local equation number ieqn_local. We choose to number the unknowns according to the augmented system.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1138 of file assembly_handler.cc.

References oomph::GeneralisedElement::eqn_number(), Ndof, and oomph::GeneralisedElement::ndof().

Referenced by get_jacobian(), oomph::AugmentedBlockFoldLinearSolver::resolve(), and oomph::AugmentedBlockFoldLinearSolver::solve().

◆ get_djacobian_dparameter()

void oomph::FoldHandler::get_djacobian_dparameter	(	GeneralisedElement *const &	elem_pt,
		double *const &	parameter_pt,
		Vector< double > &	dres_dparam,
		DenseMatrix< double > &	djac_dparam
	)

virtual

Overload the derivative of the residuals and jacobian with respect to a parameter so that it breaks.

Overload the derivative of the residuals and jacobian with respect to a parameter so that it breaks because it should not be required.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1512 of file assembly_handler.cc.

◆ get_dresiduals_dparameter()

void oomph::FoldHandler::get_dresiduals_dparameter	(	GeneralisedElement *const &	elem_pt,
		double *const &	parameter_pt,
		Vector< double > &	dres_dparam
	)

virtual

Overload the derivatives of the residuals with respect to a parameter to apply to the augmented system.

Formulate the derivatives of the augmented system with respect to a parameter.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1442 of file assembly_handler.cc.

References Block_augmented_J, Block_J, oomph::GeneralisedElement::eqn_number(), Full_augmented, oomph::GeneralisedElement::get_djacobian_dparameter(), oomph::GeneralisedElement::get_dresiduals_dparameter(), i, oomph::GeneralisedElement::ndof(), Solve_which_system, and Y.

◆ get_eigenfunction()

void oomph::FoldHandler::get_eigenfunction ( Vector< DoubleVector > & eigenfunction )

virtual

Return the eigenfunction(s) associated with the bifurcation that has been detected in bifurcation tracking problems.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1555 of file assembly_handler.cc.

References oomph::Problem::communicator_pt(), Ndof, Problem_pt, and Y.

◆ get_hessian_vector_products()

void oomph::FoldHandler::get_hessian_vector_products	(	GeneralisedElement *const &	elem_pt,
		Vector< double > const &	Y,
		DenseMatrix< double > const &	C,
		DenseMatrix< double > &	product
	)

virtual

Overload the hessian vector product function so that it breaks.

Overload the hessian vector product function so that it breaks because it should not be required.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1533 of file assembly_handler.cc.

◆ get_jacobian()

void oomph::FoldHandler::get_jacobian	(	GeneralisedElement *const &	elem_pt,
		Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

virtual

Calculate the elemental Jacobian matrix "d equation / d variable".

Calculate the elemental Jacobian matrix "d equation / d variable" for the augmented system.

ALICE

Reimplemented from oomph::AssemblyHandler.

Definition at line 1244 of file assembly_handler.cc.

References oomph::Problem::actions_after_change_in_bifurcation_parameter(), oomph::Problem::actions_before_newton_convergence_check(), Block_augmented_J, Block_J, Count, oomph::Problem::Dof_pt, oomph::GeneralisedElement::eqn_number(), eqn_number(), oomph::BlackBoxFDNewtonSolver::FD_step, Full_augmented, oomph::GeneralisedElement::get_jacobian(), get_residuals(), Ndof, oomph::GeneralisedElement::ndof(), ndof(), Phi, Problem_pt, Solve_which_system, and Y.

Referenced by oomph::AugmentedBlockFoldLinearSolver::resolve(), and oomph::AugmentedBlockFoldLinearSolver::solve().

◆ get_residuals()

void oomph::FoldHandler::get_residuals	(	GeneralisedElement *const &	elem_pt,
		Vector< double > &	residuals
	)

virtual

Get the residuals.

Formulate the augmented system.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1171 of file assembly_handler.cc.

References Block_augmented_J, Block_J, Count, oomph::GeneralisedElement::eqn_number(), Full_augmented, oomph::GeneralisedElement::get_jacobian(), oomph::GeneralisedElement::get_residuals(), i, oomph::Problem::mesh_pt(), oomph::GeneralisedElement::ndof(), oomph::Mesh::nelement(), Phi, Problem_pt, Solve_which_system, and Y.

Referenced by get_jacobian().

◆ ndof()

unsigned oomph::FoldHandler::ndof ( GeneralisedElement *const & elem_pt )

virtual

Get the number of elemental degrees of freedom.

The number of unknowns is 2n+1.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1105 of file assembly_handler.cc.

References Block_augmented_J, Block_J, Full_augmented, oomph::GeneralisedElement::ndof(), and Solve_which_system.

Referenced by get_jacobian(), oomph::AugmentedBlockFoldLinearSolver::resolve(), and oomph::AugmentedBlockFoldLinearSolver::solve().

◆ solve_augmented_block_system()

void oomph::FoldHandler::solve_augmented_block_system ( )

Set to solve the augmented block system.

Set to solve the augmented-by-one block system.

Definition at line 1600 of file assembly_handler.cc.

References Block_augmented_J, Block_J, oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, Ndof, Parameter_pt, Problem_pt, Solve_which_system, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

Referenced by oomph::AugmentedBlockFoldLinearSolver::resolve(), and oomph::AugmentedBlockFoldLinearSolver::solve().

◆ solve_block_system()

void oomph::FoldHandler::solve_block_system ( )

Set to solve the block system.

Set to solve the block system. The boolean flag specifies whether the block decomposition should use exactly the same jacobian.

Definition at line 1629 of file assembly_handler.cc.

References Block_J, oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, Ndof, Problem_pt, Solve_which_system, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

◆ solve_full_system()

void oomph::FoldHandler::solve_full_system ( )

Solve non-block system.

Set to Solve non-block system.

Definition at line 1649 of file assembly_handler.cc.

References Block_J, oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, Full_augmented, Ndof, Parameter_pt, Problem_pt, Solve_which_system, oomph::Problem::Sparse_assemble_with_arrays_previous_allocation, and Y.

Referenced by oomph::AugmentedBlockFoldLinearSolver::resolve(), and oomph::AugmentedBlockFoldLinearSolver::solve().

Friends And Related Function Documentation

◆ AugmentedBlockFoldLinearSolver

friend class AugmentedBlockFoldLinearSolver

friend

Definition at line 474 of file assembly_handler.h.

Member Data Documentation

◆ Count

Vector<int> oomph::FoldHandler::Count

private

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.

Definition at line 509 of file assembly_handler.h.

Referenced by FoldHandler(), get_jacobian(), and get_residuals().

◆ Ndof

unsigned oomph::FoldHandler::Ndof

private

Store the number of degrees of freedom in the non-augmented problem.

Definition at line 497 of file assembly_handler.h.

Referenced by eqn_number(), FoldHandler(), get_eigenfunction(), get_jacobian(), solve_augmented_block_system(), solve_block_system(), solve_full_system(), and ~FoldHandler().

◆ Parameter_pt

double* oomph::FoldHandler::Parameter_pt

private

Storage for the pointer to the parameter.

Definition at line 512 of file assembly_handler.h.

Referenced by bifurcation_parameter_pt(), solve_augmented_block_system(), and solve_full_system().

◆ Phi

Vector<double> oomph::FoldHandler::Phi

private

A constant vector used to ensure that the null vector is not trivial.

Definition at line 501 of file assembly_handler.h.

Referenced by FoldHandler(), get_jacobian(), and get_residuals().

◆ Problem_pt

Problem* oomph::FoldHandler::Problem_pt

private

Pointer to the problem.

Definition at line 493 of file assembly_handler.h.

Referenced by FoldHandler(), get_eigenfunction(), get_jacobian(), get_residuals(), solve_augmented_block_system(), solve_block_system(), solve_full_system(), and ~FoldHandler().

◆ Solve_which_system

unsigned oomph::FoldHandler::Solve_which_system

private

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.

Definition at line 490 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_jacobian(), get_residuals(), ndof(), solve_augmented_block_system(), solve_block_system(), and solve_full_system().

◆ Y

Vector<double> oomph::FoldHandler::Y

private

Storage for the null vector.

Definition at line 504 of file assembly_handler.h.

Referenced by FoldHandler(), get_dresiduals_dparameter(), get_eigenfunction(), get_jacobian(), get_residuals(), oomph::AugmentedBlockFoldLinearSolver::resolve(), oomph::AugmentedBlockFoldLinearSolver::solve(), and solve_full_system().

The documentation for this class was generated from the following files:

Public Member Functions

Private Types

Private Attributes

Friends

Detailed Description

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ FoldHandler() [1/3]

◆ FoldHandler() [2/3]

◆ FoldHandler() [3/3]

◆ ~FoldHandler()

Member Function Documentation

◆ bifurcation_parameter_pt()

◆ bifurcation_type()

◆ eqn_number()

◆ get_djacobian_dparameter()

◆ get_dresiduals_dparameter()

◆ get_eigenfunction()

◆ get_hessian_vector_products()

◆ get_jacobian()

◆ get_residuals()

◆ ndof()

◆ solve_augmented_block_system()

◆ solve_block_system()

◆ solve_full_system()

Friends And Related Function Documentation

◆ AugmentedBlockFoldLinearSolver

Member Data Documentation

◆ Count

◆ Ndof

◆ Parameter_pt

◆ Phi

◆ Problem_pt

◆ Solve_which_system

◆ Y