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. More...

	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. More...

	~HopfHandler ()
	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 Hopf bifurcation by returning 3. 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...

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

void	solve_standard_system ()
	Set to solve the standard system. More...

void	solve_complex_system ()
	Set to solve the complex 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 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. More...

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

double *	Parameter_pt
	Pointer to the parameter. More...

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

double	Omega
	The critical frequency of the bifurcation. More...

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

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

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

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(), oomph::BlockHopfLinearSolver::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::BlackBoxFDNewtonSolver::FD_step, 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.

Referenced by oomph::BlockHopfLinearSolver::solve(), and oomph::BlockHopfLinearSolver::solve_for_two_rhs().

◆ 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.

Referenced by oomph::BlockHopfLinearSolver::solve(), and oomph::BlockHopfLinearSolver::solve_for_two_rhs().

◆ 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.

Referenced by oomph::BlockHopfLinearSolver::solve(), and oomph::BlockHopfLinearSolver::solve_for_two_rhs().

Friends And Related Function 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(), oomph::BlockHopfLinearSolver::solve(), and oomph::BlockHopfLinearSolver::solve_for_two_rhs().

◆ 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(), 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(), 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(), omega(), oomph::BlockHopfLinearSolver::solve(), oomph::BlockHopfLinearSolver::solve_for_two_rhs(), 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(), oomph::BlockHopfLinearSolver::solve(), solve_complex_system(), oomph::BlockHopfLinearSolver::solve_for_two_rhs(), 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(), 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(), oomph::BlockHopfLinearSolver::solve(), oomph::BlockHopfLinearSolver::solve_for_two_rhs(), 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 Function Documentation

◆ BlockHopfLinearSolver

Member Data Documentation

◆ C

◆ Count

◆ Ndof

◆ Omega

◆ Parameter_pt

◆ Phi

◆ Problem_pt

◆ Psi

◆ Solve_which_system