A class that is used to assemble the augmented system that defines a pitchfork (symmetry-breaking) 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 pitchfork bifurcation may be specified by the augmented system of size . More...

#include <assembly_handler.h>

Inheritance diagram for oomph::PitchForkHandler:

Public Member Functions
	PitchForkHandler (Problem const &problem_pt, AssemblyHandler const &assembly_handler_pt, double *const &parameter_pt, const DoubleVector &symmetry_vector)
	Constructor, initialise the systems.

	~PitchForkHandler ()
	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 pitchfork bifurcation by returning 2.

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.

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

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

void	solve_block_system ()
	Set to solve the block 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	~AssemblyHandler ()
	Empty virtual destructor.

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 Member Functions
unsigned	global_eqn_number (const unsigned &i)
	Function that is used to return map the global equations using the simplistic numbering scheme into the actual distributed scheme.

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.

Problem *	Problem_pt
	Pointer to the problem.

AssemblyHandler *	Assembly_handler_pt
	Pointer to the underlying (original) assembly handler.

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

LinearAlgebraDistribution *	Dof_distribution_pt
	Store the original dof distribution.

LinearAlgebraDistribution *	Augmented_dof_distribution_pt
	The augmented distribution.

double	Sigma
	A slack variable used to specify the amount of antisymmetry in the solution.

DoubleVectorWithHaloEntries	Y
	Storage for the null vector.

DoubleVectorWithHaloEntries	Psi
	A constant vector that is specifies the symmetry being broken.

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

DoubleVectorWithHaloEntries	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. This should really be an integer, but its double so that the distribution can be used.

Vector< unsigned >	Global_eqn_number
	A vector that is used to map the global equations to their actual location in a distributed problem.

double *	Parameter_pt
	Storage for the pointer to the parameter.

unsigned	Nelement

bool	Distributed
	Boolean to indicate whether the problem is distributed.

Friends
class	BlockPitchForkLinearSolver

class	AugmentedBlockPitchForkLinearSolver

Detailed Description

A class that is used to assemble the augmented system that defines a pitchfork (symmetry-breaking) 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 pitchfork bifurcation may be specified by the augmented system of size .

$R(u,\lambda) + \sigma \psi = 0,$

$Jy = 0,$

$\langle u, \phi \rangle = 0,$

$\phi \cdot y = 1.$

In the abovem is the usual Jacobian matrix, and $\phi$ is a constant vector that is chosen to ensure that the null vector, , is not trivial. Here $\sigma$ is a slack variable that is used to enforce the constraint $\langle u, \phi \rangle = 0$ — the inner product of the solution with the chosen symmetry vector is zero. At the bifurcation $\sigma$ should be very close to zero. Note that this formulation means that any odd symmetry in the problem must be about zero. Moreover, we use the dot product of two vectors to calculate the inner product, rather than an integral over the domain and so the mesh must be symmetric in the appropriate directions.

Definition at line 772 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 779 of file assembly_handler.h.

Constructor & Destructor Documentation

◆ PitchForkHandler()

oomph::PitchForkHandler::PitchForkHandler	(	Problem *const &	problem_pt,
		AssemblyHandler *const &	assembly_handler_pt,
		double *const &	parameter_pt,
		const DoubleVector &	symmetry_vector
	)

Constructor, initialise the systems.

Constructor: Initialise the PitchForkHandler by setting intial guesses for Sigma, Y, specifying C and Psi and calculating count.

Definition at line 2677 of file assembly_handler.cc.

References Assembly_handler_pt, Augmented_dof_distribution_pt, oomph::DoubleVector::build(), oomph::DoubleVectorWithHaloEntries::build_halo_scheme(), C, oomph::Problem::communicator_pt(), Count, Distributed, oomph::Problem::distributed(), Dof_distribution_pt, oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, e, oomph::Mesh::element_pt(), oomph::AssemblyHandler::eqn_number(), oomph::LinearAlgebraDistribution::first_row(), Global_eqn_number, oomph::DoubleVectorWithHaloEntries::global_value(), oomph::Problem::Halo_scheme_pt, oomph::GeneralisedElement::is_halo(), oomph::Problem::mesh_pt(), Ndof, oomph::Problem::ndof(), oomph::AssemblyHandler::ndof(), Nelement, oomph::Mesh::nelement(), oomph::LinearAlgebraDistribution::nrow_local(), Problem_pt, Psi, oomph::Problem::setup_dof_halo_scheme(), Sigma, oomph::Problem::Sparse_assemble_with_arrays_previous_allocation, oomph::DoubleVectorWithHaloEntries::sum_all_halo_and_haloed_values(), and Y.

◆ ~PitchForkHandler()

oomph::PitchForkHandler::~PitchForkHandler ( )

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 2897 of file assembly_handler.cc.

References Dof_distribution_pt, oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, oomph::Problem::linear_solver_pt(), oomph::LinearAlgebraDistribution::nrow_local(), Problem_pt, and oomph::Problem::Sparse_assemble_with_arrays_previous_allocation.

Member Function Documentation

◆ bifurcation_parameter_pt()

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

inlinevirtual

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

Reimplemented from oomph::AssemblyHandler.

Definition at line 924 of file assembly_handler.h.

References Parameter_pt.

◆ bifurcation_type()

int oomph::PitchForkHandler::bifurcation_type ( ) const

inlinevirtual

Indicate that we are tracking a pitchfork bifurcation by returning 2.

Reimplemented from oomph::AssemblyHandler.

Definition at line 917 of file assembly_handler.h.

◆ eqn_number()

unsigned long oomph::PitchForkHandler::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 2974 of file assembly_handler.cc.

References Block_augmented_J, Block_J, Distributed, oomph::GeneralisedElement::eqn_number(), Full_augmented, global_eqn_number(), Ndof, oomph::GeneralisedElement::ndof(), and Solve_which_system.

◆ get_djacobian_dparameter()

void oomph::PitchForkHandler::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 3394 of file assembly_handler.cc.

◆ get_dresiduals_dparameter()

void oomph::PitchForkHandler::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 residuals with respect to a parameter.

Reimplemented from oomph::AssemblyHandler.

Definition at line 3316 of file assembly_handler.cc.

References oomph::Problem::actions_before_newton_convergence_check(), Block_augmented_J, Block_J, oomph::GeneralisedElement::eqn_number(), Full_augmented, oomph::GeneralisedElement::get_djacobian_dparameter(), oomph::GeneralisedElement::get_dresiduals_dparameter(), oomph::DoubleVectorWithHaloEntries::global_value(), i, oomph::GeneralisedElement::ndof(), Problem_pt, Solve_which_system, and Y.

◆ get_eigenfunction()

void oomph::PitchForkHandler::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 3430 of file assembly_handler.cc.

References Dof_distribution_pt, and Y.

◆ get_hessian_vector_products()

void oomph::PitchForkHandler::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 calls the underlying element's hessian function.

Reimplemented from oomph::AssemblyHandler.

Definition at line 3416 of file assembly_handler.cc.

References C, oomph::GeneralisedElement::get_hessian_vector_products(), and Y.

◆ get_jacobian()

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

virtual

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

ALICE:

ALICE

Reimplemented from oomph::AssemblyHandler.

Definition at line 3137 of file assembly_handler.cc.

References oomph::Problem::actions_after_change_in_bifurcation_parameter(), oomph::Problem::actions_before_newton_convergence_check(), Assembly_handler_pt, Block_augmented_J, Block_J, C, Count, oomph::GeneralisedElement::eqn_number(), oomph::AssemblyHandler::eqn_number(), Full_augmented, oomph::GeneralisedElement::get_jacobian(), get_residuals(), oomph::Problem::global_dof_pt(), oomph::DoubleVectorWithHaloEntries::global_value(), i, oomph::GeneralisedElement::ndof(), ndof(), Parameter_pt, Problem_pt, Psi, Sigma, and Solve_which_system.

◆ get_residuals()

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

virtual

Get the residuals.

Reimplemented from oomph::AssemblyHandler.

Definition at line 3034 of file assembly_handler.cc.

References Block_augmented_J, Block_J, C, Count, oomph::GeneralisedElement::eqn_number(), Full_augmented, oomph::GeneralisedElement::get_jacobian(), oomph::GeneralisedElement::get_residuals(), oomph::Problem::global_dof_pt(), oomph::DoubleVectorWithHaloEntries::global_value(), i, oomph::GeneralisedElement::ndof(), Nelement, Problem_pt, Psi, Sigma, Solve_which_system, and Y.

Referenced by get_jacobian().

◆ global_eqn_number()

unsigned oomph::PitchForkHandler::global_eqn_number ( const unsigned & i )

inlineprivate

Function that is used to return map the global equations using the simplistic numbering scheme into the actual distributed scheme.

Definition at line 848 of file assembly_handler.h.

References Distributed, Global_eqn_number, and i.

Referenced by eqn_number().

◆ ndof()

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

virtual

Get the number of elemental degrees of freedom.

Reimplemented from oomph::AssemblyHandler.

Definition at line 2944 of file assembly_handler.cc.

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

Referenced by get_jacobian().

◆ solve_augmented_block_system()

void oomph::PitchForkHandler::solve_augmented_block_system ( )

Set to solve the augmented block system.

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

Definition at line 3476 of file assembly_handler.cc.

References Block_augmented_J, Block_J, 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.

◆ solve_block_system()

void oomph::PitchForkHandler::solve_block_system ( )

Set to solve the block system.

Set to solve the block system. The boolean flag is used to specify whether the block decomposition should use exactly the same jacobian as the original system.

Definition at line 3512 of file assembly_handler.cc.

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

◆ solve_full_system()

void oomph::PitchForkHandler::solve_full_system ( )

Solve non-block system.

Definition at line 3535 of file assembly_handler.cc.

References Augmented_dof_distribution_pt, Block_J, oomph::Problem::communicator_pt(), Distributed, Dof_distribution_pt, oomph::Problem::Dof_distribution_pt, oomph::Problem::Dof_pt, Full_augmented, oomph::LinearAlgebraDistribution::nrow_local(), Parameter_pt, Problem_pt, Sigma, Solve_which_system, oomph::Problem::Sparse_assemble_with_arrays_previous_allocation, and Y.

◆ synchronise()

void oomph::PitchForkHandler::synchronise ( )

virtual

Function that is used to perform any synchronisation required during the solution.

Reimplemented from oomph::AssemblyHandler.

Definition at line 3448 of file assembly_handler.cc.

References oomph::Problem::communicator_pt(), Distributed, Parameter_pt, Problem_pt, Sigma, oomph::DoubleVectorWithHaloEntries::synchronise(), and Y.

Friends And Related Symbol Documentation

◆ AugmentedBlockPitchForkLinearSolver

friend class AugmentedBlockPitchForkLinearSolver

friend

Definition at line 775 of file assembly_handler.h.

◆ BlockPitchForkLinearSolver

friend class BlockPitchForkLinearSolver

friend

Definition at line 774 of file assembly_handler.h.

Member Data Documentation

◆ Assembly_handler_pt

AssemblyHandler* oomph::PitchForkHandler::Assembly_handler_pt

private

Pointer to the underlying (original) assembly handler.

Definition at line 797 of file assembly_handler.h.

Referenced by get_jacobian(), and PitchForkHandler().

◆ Augmented_dof_distribution_pt

LinearAlgebraDistribution* oomph::PitchForkHandler::Augmented_dof_distribution_pt

private

The augmented distribution.

Definition at line 807 of file assembly_handler.h.

Referenced by PitchForkHandler(), and solve_full_system().

◆ C

DoubleVectorWithHaloEntries oomph::PitchForkHandler::C

private

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

Definition at line 821 of file assembly_handler.h.

Referenced by get_hessian_vector_products(), get_jacobian(), get_residuals(), and PitchForkHandler().

◆ Count

DoubleVectorWithHaloEntries oomph::PitchForkHandler::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. This should really be an integer, but its double so that the distribution can be used.

Definition at line 828 of file assembly_handler.h.

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

◆ Distributed

bool oomph::PitchForkHandler::Distributed

private

Boolean to indicate whether the problem is distributed.

Definition at line 842 of file assembly_handler.h.

Referenced by eqn_number(), global_eqn_number(), PitchForkHandler(), solve_full_system(), and synchronise().

◆ Dof_distribution_pt

LinearAlgebraDistribution* oomph::PitchForkHandler::Dof_distribution_pt

private

Store the original dof distribution.

Definition at line 804 of file assembly_handler.h.

Referenced by get_eigenfunction(), PitchForkHandler(), solve_block_system(), solve_full_system(), and ~PitchForkHandler().

◆ Global_eqn_number

Vector<unsigned> oomph::PitchForkHandler::Global_eqn_number

private

A vector that is used to map the global equations to their actual location in a distributed problem.

Definition at line 832 of file assembly_handler.h.

Referenced by global_eqn_number(), and PitchForkHandler().

◆ Ndof

unsigned oomph::PitchForkHandler::Ndof

private

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

Definition at line 801 of file assembly_handler.h.

Referenced by eqn_number(), PitchForkHandler(), and solve_augmented_block_system().

◆ Nelement

unsigned oomph::PitchForkHandler::Nelement

private

Definition at line 838 of file assembly_handler.h.

Referenced by get_residuals(), and PitchForkHandler().

◆ Parameter_pt

double* oomph::PitchForkHandler::Parameter_pt

private

Storage for the pointer to the parameter.

Definition at line 835 of file assembly_handler.h.

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

◆ Problem_pt

Problem* oomph::PitchForkHandler::Problem_pt

private

Pointer to the problem.

Definition at line 794 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_jacobian(), get_residuals(), PitchForkHandler(), solve_augmented_block_system(), solve_block_system(), solve_full_system(), synchronise(), and ~PitchForkHandler().

◆ Psi

DoubleVectorWithHaloEntries oomph::PitchForkHandler::Psi

private

A constant vector that is specifies the symmetry being broken.

Definition at line 817 of file assembly_handler.h.

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

◆ Sigma

double oomph::PitchForkHandler::Sigma

private

A slack variable used to specify the amount of antisymmetry in the solution.

Definition at line 811 of file assembly_handler.h.

Referenced by get_jacobian(), get_residuals(), PitchForkHandler(), solve_full_system(), and synchronise().

◆ Solve_which_system

unsigned oomph::PitchForkHandler::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 791 of file assembly_handler.h.

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

◆ Y

DoubleVectorWithHaloEntries oomph::PitchForkHandler::Y

private

Storage for the null vector.

Definition at line 814 of file assembly_handler.h.

Referenced by get_dresiduals_dparameter(), get_eigenfunction(), get_hessian_vector_products(), get_residuals(), PitchForkHandler(), solve_full_system(), and synchronise().

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

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ PitchForkHandler()

◆ ~PitchForkHandler()

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()

◆ global_eqn_number()

◆ ndof()

◆ solve_augmented_block_system()

◆ solve_block_system()

◆ solve_full_system()

◆ synchronise()

Friends And Related Symbol Documentation

◆ AugmentedBlockPitchForkLinearSolver

◆ BlockPitchForkLinearSolver

Member Data Documentation

◆ Assembly_handler_pt

◆ Augmented_dof_distribution_pt

◆ C

◆ Count

◆ Distributed

◆ Dof_distribution_pt

◆ Global_eqn_number

◆ Ndof

◆ Nelement

◆ Parameter_pt

◆ Problem_pt

◆ Psi

◆ Sigma

◆ Solve_which_system

◆ Y