A class that is used to assemble the augmented system that defines a Hopf bifurcation. The "standard" problem must be a function of a global parameter $\lambda$ and a solution is $R(u,\lambda) = 0$ , where are the unknowns in the problem. A Hopf bifurcation may be specified by the augmented system of size . More...

#include <assembly_handler.h>

Inheritance diagram for oomph::HopfHandler:

Public Member Functions
	HopfHandler (Problem const &problem_pt, double const &parameter_pt)
	Constructor.

	HopfHandler (Problem const &problem_pt, double const &paramter_pt, const double &omega, const DoubleVector &phi, const DoubleVector &psi)
	Constructor with initial guesses for the frequency and null vectors, such as might be provided by an eigensolver.

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

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

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

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

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

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.

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.

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.

int	bifurcation_type () const
	Indicate that we are tracking a Hopf bifurcation by returning 3.

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

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

const double &	omega () const
	Return the frequency of the bifurcation.

void	solve_standard_system ()
	Set to solve the standard system.

void	solve_complex_system ()
	Set to solve the complex system.

void	solve_full_system ()
	Solve non-block system.

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

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.

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

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.

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.

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.

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.

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

virtual	~AssemblyHandler ()
	Empty virtual destructor.

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), and complex system (2), where the matrix is a combination of the jacobian and mass matrices.

Problem *	Problem_pt
	Pointer to the problem.

double *	Parameter_pt
	Pointer to the parameter.

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

double	Omega
	The critical frequency of the bifurcation.

Vector< double >	Phi
	The real part of the null vector.

Vector< double >	Psi
	The imaginary part of the null vector.

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

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.

Friends
class	BlockHopfLinearSolver

Detailed Description

A class that is used to assemble the augmented system that defines a Hopf bifurcation. The "standard" problem must be a function of a global parameter $\lambda$ and a solution is $R(u,\lambda) = 0$ , where are the unknowns in the problem. A Hopf bifurcation may be specified by the augmented system of size .

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

$J\phi + \omega M \psi = 0,$

$J\psi - \omega M \phi = 0,$

$c \cdot \phi = 1.$

$c \cdot \psi = 0.$

In the above is the usual Jacobian matrix, and is the mass matrix that multiplies the time derivative terms. $\phi + i\psi$ is the (complex) null vector of the complex matrix $J - i\omega M$ , where $\omega$ is the critical frequency. is a constant vector that is used to ensure that the null vector is non-trivial.

Definition at line 1049 of file assembly_handler.h.

Constructor & Destructor Documentation

◆ HopfHandler() [1/2]

oomph::HopfHandler::HopfHandler	(	Problem *const &	problem_pt,
		double *const &	parameter_pt
	)

Constructor.

Constructor: Initialise the hopf handler, by setting initial guesses for Phi, Psi and calculating Count. If the system changes, a new handler must be constructed.

Definition at line 4435 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), C, 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(), Omega, Phi, Problem_pt, Psi, oomph::LinearSolver::resolve(), oomph::LinearSolver::solve(), and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

◆ HopfHandler() [2/2]

oomph::HopfHandler::HopfHandler	(	Problem *const &	problem_pt,
		double *const &	paramter_pt,
		const double &	omega,
		const DoubleVector &	phi,
		const DoubleVector &	psi
	)

Constructor with initial guesses for the frequency and null vectors, such as might be provided by an eigensolver.

Constructor: Initialise the hopf handler, by setting initial guesses for Phi, Psi, Omega and calculating Count. If the system changes, a new handler must be constructed.

Definition at line 4569 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), C, 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(), Omega, Phi, Problem_pt, Psi, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

◆ ~HopfHandler()

oomph::HopfHandler::~HopfHandler ( )

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 4640 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(), Ndof, Problem_pt, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

Member Function Documentation

◆ bifurcation_parameter_pt()

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

inlinevirtual

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

Reimplemented from oomph::AssemblyHandler.

Definition at line 1150 of file assembly_handler.h.

References Parameter_pt.

◆ bifurcation_type()

int oomph::HopfHandler::bifurcation_type ( ) const

inlinevirtual

Indicate that we are tracking a Hopf bifurcation by returning 3.

Reimplemented from oomph::AssemblyHandler.

Definition at line 1143 of file assembly_handler.h.

◆ eqn_number()

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

virtual

Get the global equation number of the local unknown.

Reimplemented from oomph::AssemblyHandler.

Definition at line 4693 of file assembly_handler.cc.

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

Referenced by get_jacobian().

◆ get_djacobian_dparameter()

void oomph::HopfHandler::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 4991 of file assembly_handler.cc.

◆ get_dresiduals_dparameter()

void oomph::HopfHandler::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.

Get the derivatives of the augmented residuals with respect to a parameter.

Reimplemented from oomph::AssemblyHandler.

Definition at line 4937 of file assembly_handler.cc.

References oomph::GeneralisedElement::eqn_number(), oomph::GeneralisedElement::get_djacobian_and_dmass_matrix_dparameter(), i, oomph::GeneralisedElement::ndof(), Omega, Phi, Psi, and Solve_which_system.

◆ get_eigenfunction()

void oomph::HopfHandler::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 5034 of file assembly_handler.cc.

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

◆ get_hessian_vector_products()

void oomph::HopfHandler::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 5012 of file assembly_handler.cc.

◆ get_jacobian()

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

virtual

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

Reimplemented from oomph::AssemblyHandler.

Definition at line 4782 of file assembly_handler.cc.

References oomph::Problem::actions_after_change_in_bifurcation_parameter(), C, Count, oomph::Problem::Dof_pt, oomph::GeneralisedElement::eqn_number(), eqn_number(), oomph::GeneralisedElement::get_jacobian(), oomph::GeneralisedElement::get_jacobian_and_mass_matrix(), get_residuals(), Ndof, oomph::GeneralisedElement::ndof(), ndof(), Omega, Phi, Problem_pt, Psi, and Solve_which_system.

◆ get_residuals()

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

virtual

Get the residuals.

Reimplemented from oomph::AssemblyHandler.

Definition at line 4725 of file assembly_handler.cc.

References C, Count, oomph::GeneralisedElement::eqn_number(), oomph::GeneralisedElement::get_jacobian_and_mass_matrix(), i, oomph::Problem::mesh_pt(), oomph::GeneralisedElement::ndof(), oomph::Mesh::nelement(), Omega, Phi, Problem_pt, Psi, and Solve_which_system.

Referenced by get_jacobian().

◆ ndof()

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

virtual

Get the number of elemental degrees of freedom.

Reimplemented from oomph::AssemblyHandler.

Definition at line 4665 of file assembly_handler.cc.

References oomph::GeneralisedElement::ndof(), and Solve_which_system.

Referenced by get_jacobian().

◆ omega()

const double & oomph::HopfHandler::omega ( ) const

inline

Return the frequency of the bifurcation.

Definition at line 1160 of file assembly_handler.h.

References Omega.

◆ solve_complex_system()

void oomph::HopfHandler::solve_complex_system ( )

Set to solve the complex system.

Set to solve the complex (jacobian and mass matrix) system.

Definition at line 5071 of file assembly_handler.cc.

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

◆ solve_full_system()

void oomph::HopfHandler::solve_full_system ( )

Solve non-block system.

Set to Solve full system system.

Definition at line 5097 of file assembly_handler.cc.

References oomph::LinearAlgebraDistribution::build(), oomph::Problem::communicator_pt(), oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, Ndof, Omega, Parameter_pt, Phi, Problem_pt, Psi, Solve_which_system, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

◆ solve_standard_system()

void oomph::HopfHandler::solve_standard_system ( )

Set to solve the standard system.

Set to solve the standard (underlying jacobian) system.

Definition at line 5054 of file assembly_handler.cc.

References 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.

Friends And Related Symbol Documentation

◆ BlockHopfLinearSolver

friend class BlockHopfLinearSolver

friend

Definition at line 1051 of file assembly_handler.h.

Member Data Documentation

◆ C

Vector<double> oomph::HopfHandler::C

private

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

Definition at line 1081 of file assembly_handler.h.

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

◆ Count

Vector<int> oomph::HopfHandler::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 1086 of file assembly_handler.h.

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

◆ Ndof

unsigned oomph::HopfHandler::Ndof

private

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

Definition at line 1068 of file assembly_handler.h.

Referenced by eqn_number(), get_eigenfunction(), get_jacobian(), HopfHandler(), HopfHandler(), solve_complex_system(), solve_full_system(), solve_standard_system(), and ~HopfHandler().

◆ Omega

double oomph::HopfHandler::Omega

private

The critical frequency of the bifurcation.

Definition at line 1071 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_jacobian(), get_residuals(), HopfHandler(), HopfHandler(), omega(), and solve_full_system().

◆ Parameter_pt

double* oomph::HopfHandler::Parameter_pt

private

Pointer to the parameter.

Definition at line 1064 of file assembly_handler.h.

Referenced by bifurcation_parameter_pt(), and solve_full_system().

◆ Phi

Vector<double> oomph::HopfHandler::Phi

private

The real part of the null vector.

Definition at line 1074 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_eigenfunction(), get_jacobian(), get_residuals(), HopfHandler(), HopfHandler(), solve_complex_system(), and solve_full_system().

◆ Problem_pt

Problem* oomph::HopfHandler::Problem_pt

private

Pointer to the problem.

Definition at line 1061 of file assembly_handler.h.

Referenced by get_eigenfunction(), get_jacobian(), get_residuals(), HopfHandler(), HopfHandler(), solve_complex_system(), solve_full_system(), solve_standard_system(), and ~HopfHandler().

◆ Psi

Vector<double> oomph::HopfHandler::Psi

private

The imaginary part of the null vector.

Definition at line 1077 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_eigenfunction(), get_jacobian(), get_residuals(), HopfHandler(), HopfHandler(), and solve_full_system().

◆ Solve_which_system

unsigned oomph::HopfHandler::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), and complex system (2), where the matrix is a combination of the jacobian and mass matrices.

Definition at line 1058 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_jacobian(), get_residuals(), ndof(), solve_complex_system(), solve_full_system(), and solve_standard_system().

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

Public Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ HopfHandler() [1/2]

◆ HopfHandler() [2/2]

◆ ~HopfHandler()

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()

◆ omega()

◆ solve_complex_system()

◆ solve_full_system()

◆ solve_standard_system()

Friends And Related Symbol Documentation

◆ BlockHopfLinearSolver

Member Data Documentation

◆ C

◆ Count

◆ Ndof

◆ Omega

◆ Parameter_pt

◆ Phi

◆ Problem_pt

◆ Psi

◆ Solve_which_system