#include <biharmonic_problem.h>

Inheritance diagram for oomph::BiharmonicProblem< DIM >:

Public Types
typedef void(*	DirichletBCFctPt) (const double &s, double &u)

typedef void(*	BiharmonicSourceFctPt) (const Vector< double > &x, double &f)
	Definition of the Source Function. More...

Public Types inherited from oomph::Problem
typedef void(*	SpatialErrorEstimatorFctPt) (Mesh *&mesh_pt, Vector< double > &elemental_error)
	Function pointer for spatial error estimator. More...

typedef void(*	SpatialErrorEstimatorWithDocFctPt) (Mesh *&mesh_pt, Vector< double > &elemental_error, DocInfo &doc_info)
	Function pointer for spatial error estimator with doc. More...

Public Member Functions
	BiharmonicProblem ()
	Constructor. More...

virtual	~BiharmonicProblem ()
	Destructor. Delete the meshes. More...

void	actions_before_newton_solve ()
	actions before solve, performs self test More...

void	actions_after_newton_solve ()
	action after solve More...

void	doc_solution (DocInfo &doc_info, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt=0)

Mesh *	bulk_element_mesh_pt ()
	Access function to the bulk element mesh pt. More...

Public Member Functions inherited from oomph::Problem
virtual void	debug_hook_fct (const unsigned &i)

void	set_analytic_dparameter (double *const &parameter_pt)

void	unset_analytic_dparameter (double *const &parameter_pt)

bool	is_dparameter_calculated_analytically (double *const &parameter_pt)

void	set_analytic_hessian_products ()

void	unset_analytic_hessian_products ()

bool	are_hessian_products_calculated_analytically ()

void	set_pinned_values_to_zero ()

bool	distributed () const

virtual void	actions_before_adapt ()

virtual void	actions_after_adapt ()
	Actions that are to be performed after a mesh adaptation. More...

OomphCommunicator *	communicator_pt ()
	access function to the oomph-lib communicator More...

const OomphCommunicator *	communicator_pt () const
	access function to the oomph-lib communicator, const version More...

	Problem ()

	Problem (const Problem &dummy)=delete
	Broken copy constructor. More...

void	operator= (const Problem &)=delete
	Broken assignment operator. More...

virtual	~Problem ()
	Virtual destructor to clean up memory. More...

Mesh *&	mesh_pt ()
	Return a pointer to the global mesh. More...

Mesh *const &	mesh_pt () const
	Return a pointer to the global mesh (const version) More...

Mesh *&	mesh_pt (const unsigned &imesh)

Mesh *const &	mesh_pt (const unsigned &imesh) const
	Return a pointer to the i-th submesh (const version) More...

unsigned	nsub_mesh () const
	Return number of submeshes. More...

unsigned	add_sub_mesh (Mesh *const &mesh_pt)

void	flush_sub_meshes ()

void	build_global_mesh ()

void	rebuild_global_mesh ()

LinearSolver *&	linear_solver_pt ()
	Return a pointer to the linear solver object. More...

LinearSolver *const &	linear_solver_pt () const
	Return a pointer to the linear solver object (const version) More...

LinearSolver *&	mass_matrix_solver_for_explicit_timestepper_pt ()

LinearSolver *	mass_matrix_solver_for_explicit_timestepper_pt () const

EigenSolver *&	eigen_solver_pt ()
	Return a pointer to the eigen solver object. More...

EigenSolver *const &	eigen_solver_pt () const
	Return a pointer to the eigen solver object (const version) More...

Time *&	time_pt ()
	Return a pointer to the global time object. More...

Time *	time_pt () const
	Return a pointer to the global time object (const version). More...

double &	time ()
	Return the current value of continuous time. More...

double	time () const
	Return the current value of continuous time (const version) More...

TimeStepper *&	time_stepper_pt ()

const TimeStepper *	time_stepper_pt () const

TimeStepper *&	time_stepper_pt (const unsigned &i)
	Return a pointer to the i-th timestepper. More...

ExplicitTimeStepper *&	explicit_time_stepper_pt ()
	Return a pointer to the explicit timestepper. More...

unsigned long	set_timestepper_for_all_data (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data=false)

virtual void	shift_time_values ()
	Shift all values along to prepare for next timestep. More...

AssemblyHandler *&	assembly_handler_pt ()
	Return a pointer to the assembly handler object. More...

AssemblyHandler *const &	assembly_handler_pt () const
	Return a pointer to the assembly handler object (const version) More...

double &	minimum_dt ()
	Access function to min timestep in adaptive timestepping. More...

double &	maximum_dt ()
	Access function to max timestep in adaptive timestepping. More...

unsigned &	max_newton_iterations ()
	Access function to max Newton iterations before giving up. More...

void	problem_is_nonlinear (const bool &prob_lin)
	Access function to Problem_is_nonlinear. More...

double &	max_residuals ()

bool &	time_adaptive_newton_crash_on_solve_fail ()
	Access function for Time_adaptive_newton_crash_on_solve_fail. More...

double &	newton_solver_tolerance ()

void	add_time_stepper_pt (TimeStepper *const &time_stepper_pt)

void	set_explicit_time_stepper_pt (ExplicitTimeStepper *const &explicit_time_stepper_pt)

void	initialise_dt (const double &dt)

void	initialise_dt (const Vector< double > &dt)

Data *&	global_data_pt (const unsigned &i)
	Return a pointer to the the i-th global data object. More...

void	add_global_data (Data *const &global_data_pt)

void	flush_global_data ()

LinearAlgebraDistribution *const &	dof_distribution_pt () const
	Return the pointer to the dof distribution (read-only) More...

unsigned long	ndof () const
	Return the number of dofs. More...

unsigned	ntime_stepper () const
	Return the number of time steppers. More...

unsigned	nglobal_data () const
	Return the number of global data values. More...

unsigned	self_test ()
	Self-test: Check meshes and global data. Return 0 for OK. More...

void	enable_store_local_dof_pt_in_elements ()

void	disable_store_local_dof_pt_in_elements ()

unsigned long	assign_eqn_numbers (const bool &assign_local_eqn_numbers=true)

void	describe_dofs (std::ostream &out= *(oomph_info.stream_pt())) const

void	enable_discontinuous_formulation ()

void	disable_discontinuous_formulation ()

void	get_dofs (DoubleVector &dofs) const

void	get_dofs (const unsigned &t, DoubleVector &dofs) const
	Return vector of the t'th history value of all dofs. More...

void	set_dofs (const DoubleVector &dofs)
	Set the values of the dofs. More...

void	set_dofs (const unsigned &t, DoubleVector &dofs)
	Set the history values of the dofs. More...

void	set_dofs (const unsigned &t, Vector< double * > &dof_pt)

void	add_to_dofs (const double &lambda, const DoubleVector &increment_dofs)
	Add lambda x incremenet_dofs[l] to the l-th dof. More...

double *	global_dof_pt (const unsigned &i)

double &	dof (const unsigned &i)
	i-th dof in the problem More...

double	dof (const unsigned &i) const
	i-th dof in the problem (const version) More...

double *&	dof_pt (const unsigned &i)
	Pointer to i-th dof in the problem. More...

double *	dof_pt (const unsigned &i) const
	Pointer to i-th dof in the problem (const version) More...

virtual void	get_inverse_mass_matrix_times_residuals (DoubleVector &Mres)

virtual void	get_dvaluesdt (DoubleVector &f)

virtual void	get_residuals (DoubleVector &residuals)
	Get the total residuals Vector for the problem. More...

virtual void	get_jacobian (DoubleVector &residuals, DenseDoubleMatrix &jacobian)

virtual void	get_jacobian (DoubleVector &residuals, CRDoubleMatrix &jacobian)

virtual void	get_jacobian (DoubleVector &residuals, CCDoubleMatrix &jacobian)

virtual void	get_jacobian (DoubleVector &residuals, SumOfMatrices &jacobian)

void	get_fd_jacobian (DoubleVector &residuals, DenseMatrix< double > &jacobian)
	Get the full Jacobian by finite differencing. More...

void	get_derivative_wrt_global_parameter (double *const &parameter_pt, DoubleVector &result)

void	get_hessian_vector_products (DoubleVectorWithHaloEntries const &Y, Vector< DoubleVectorWithHaloEntries > const &C, Vector< DoubleVectorWithHaloEntries > &product)

void	solve_eigenproblem (const unsigned &n_eval, Vector< std::complex< double >> &eigenvalue, Vector< DoubleVector > &eigenvector, const bool &steady=true)
	Solve the eigenproblem. More...

void	solve_eigenproblem (const unsigned &n_eval, Vector< std::complex< double >> &eigenvalue, const bool &steady=true)

virtual void	get_eigenproblem_matrices (CRDoubleMatrix &mass_matrix, CRDoubleMatrix &main_matrix, const double &shift=0.0)

void	assign_eigenvector_to_dofs (DoubleVector &eigenvector)
	Assign the eigenvector passed to the function to the dofs. More...

void	add_eigenvector_to_dofs (const double &epsilon, const DoubleVector &eigenvector)

void	store_current_dof_values ()
	Store the current values of the degrees of freedom. More...

void	restore_dof_values ()
	Restore the stored values of the degrees of freedom. More...

void	enable_jacobian_reuse ()

void	disable_jacobian_reuse ()
	Disable recycling of Jacobian in Newton iteration. More...

bool	jacobian_reuse_is_enabled ()
	Is recycling of Jacobian in Newton iteration enabled? More...

bool &	use_predictor_values_as_initial_guess ()

void	newton_solve ()
	Use Newton method to solve the problem. More...

void	enable_globally_convergent_newton_method ()
	enable globally convergent Newton method More...

void	disable_globally_convergent_newton_method ()
	disable globally convergent Newton method More...

void	newton_solve (unsigned const &max_adapt)

void	steady_newton_solve (unsigned const &max_adapt=0)

void	copy (Problem *orig_problem_pt)

virtual Problem *	make_copy ()

virtual void	read (std::ifstream &restart_file, bool &unsteady_restart)

virtual void	read (std::ifstream &restart_file)

virtual void	dump (std::ofstream &dump_file) const

void	dump (const std::string &dump_file_name) const

void	delete_all_external_storage ()

virtual void	symmetrise_eigenfunction_for_adaptive_pitchfork_tracking ()

double *	bifurcation_parameter_pt () const

void	get_bifurcation_eigenfunction (Vector< DoubleVector > &eigenfunction)

void	activate_fold_tracking (double *const &parameter_pt, const bool &block_solve=true)

void	activate_bifurcation_tracking (double *const &parameter_pt, const DoubleVector &eigenvector, const bool &block_solve=true)

void	activate_bifurcation_tracking (double *const &parameter_pt, const DoubleVector &eigenvector, const DoubleVector &normalisation, const bool &block_solve=true)

void	activate_pitchfork_tracking (double *const &parameter_pt, const DoubleVector &symmetry_vector, const bool &block_solve=true)

void	activate_hopf_tracking (double *const &parameter_pt, const bool &block_solve=true)

void	activate_hopf_tracking (double *const &parameter_pt, const double &omega, const DoubleVector &null_real, const DoubleVector &null_imag, const bool &block_solve=true)

void	deactivate_bifurcation_tracking ()

void	reset_assembly_handler_to_default ()
	Reset the system to the standard non-augemented state. More...

double	arc_length_step_solve (double *const &parameter_pt, const double &ds, const unsigned &max_adapt=0)

double	arc_length_step_solve (Data *const &data_pt, const unsigned &data_index, const double &ds, const unsigned &max_adapt=0)

void	reset_arc_length_parameters ()

int &	sign_of_jacobian ()

void	explicit_timestep (const double &dt, const bool &shift_values=true)
	Take an explicit timestep of size dt. More...

void	unsteady_newton_solve (const double &dt)

void	unsteady_newton_solve (const double &dt, const bool &shift_values)

void	unsteady_newton_solve (const double &dt, const unsigned &max_adapt, const bool &first, const bool &shift=true)

double	doubly_adaptive_unsteady_newton_solve (const double &dt, const double &epsilon, const unsigned &max_adapt, const bool &first, const bool &shift=true)

double	doubly_adaptive_unsteady_newton_solve (const double &dt, const double &epsilon, const unsigned &max_adapt, const unsigned &suppress_resolve_after_spatial_adapt_flag, const bool &first, const bool &shift=true)

double	adaptive_unsteady_newton_solve (const double &dt_desired, const double &epsilon)

double	adaptive_unsteady_newton_solve (const double &dt_desired, const double &epsilon, const bool &shift_values)

void	assign_initial_values_impulsive ()

void	assign_initial_values_impulsive (const double &dt)

void	calculate_predictions ()
	Calculate predictions. More...

void	enable_mass_matrix_reuse ()

void	disable_mass_matrix_reuse ()

bool	mass_matrix_reuse_is_enabled ()
	Return whether the mass matrix is being reused. More...

void	refine_uniformly (const Vector< unsigned > &nrefine_for_mesh)

void	refine_uniformly (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh)

void	refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	refine_uniformly (DocInfo &doc_info)

void	refine_uniformly_and_prune (DocInfo &doc_info)

void	refine_uniformly ()

void	refine_uniformly (const unsigned &i_mesh, DocInfo &doc_info)
	Do uniform refinement for submesh i_mesh with documentation. More...

void	refine_uniformly (const unsigned &i_mesh)
	Do uniform refinement for submesh i_mesh without documentation. More...

void	p_refine_uniformly (const Vector< unsigned > &nrefine_for_mesh)

void	p_refine_uniformly (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	p_refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh)

void	p_refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	p_refine_uniformly (DocInfo &doc_info)

void	p_refine_uniformly_and_prune (DocInfo &doc_info)

void	p_refine_uniformly ()

void	p_refine_uniformly (const unsigned &i_mesh, DocInfo &doc_info)
	Do uniform p-refinement for submesh i_mesh with documentation. More...

void	p_refine_uniformly (const unsigned &i_mesh)
	Do uniform p-refinement for submesh i_mesh without documentation. More...

void	refine_selected_elements (const Vector< unsigned > &elements_to_be_refined)

void	refine_selected_elements (const Vector< RefineableElement * > &elements_to_be_refined_pt)

void	refine_selected_elements (const unsigned &i_mesh, const Vector< unsigned > &elements_to_be_refined)

void	refine_selected_elements (const unsigned &i_mesh, const Vector< RefineableElement * > &elements_to_be_refined_pt)

void	refine_selected_elements (const Vector< Vector< unsigned >> &elements_to_be_refined)

void	refine_selected_elements (const Vector< Vector< RefineableElement * >> &elements_to_be_refined_pt)

void	p_refine_selected_elements (const Vector< unsigned > &elements_to_be_refined)

void	p_refine_selected_elements (const Vector< PRefineableElement * > &elements_to_be_refined_pt)

void	p_refine_selected_elements (const unsigned &i_mesh, const Vector< unsigned > &elements_to_be_refined)

void	p_refine_selected_elements (const unsigned &i_mesh, const Vector< PRefineableElement * > &elements_to_be_refined_pt)

void	p_refine_selected_elements (const Vector< Vector< unsigned >> &elements_to_be_refined)

void	p_refine_selected_elements (const Vector< Vector< PRefineableElement * >> &elements_to_be_refined_pt)

unsigned	unrefine_uniformly ()

unsigned	unrefine_uniformly (const unsigned &i_mesh)

void	p_unrefine_uniformly (DocInfo &doc_info)

void	p_unrefine_uniformly (const unsigned &i_mesh, DocInfo &doc_info)
	Do uniform p-unrefinement for submesh i_mesh without documentation. More...

void	adapt (unsigned &n_refined, unsigned &n_unrefined)

void	adapt ()

void	p_adapt (unsigned &n_refined, unsigned &n_unrefined)

void	p_adapt ()

void	adapt_based_on_error_estimates (unsigned &n_refined, unsigned &n_unrefined, Vector< Vector< double >> &elemental_error)

void	adapt_based_on_error_estimates (Vector< Vector< double >> &elemental_error)

void	get_all_error_estimates (Vector< Vector< double >> &elemental_error)

void	doc_errors (DocInfo &doc_info)
	Get max and min error for all elements in submeshes. More...

void	doc_errors ()
	Get max and min error for all elements in submeshes. More...

void	enable_info_in_newton_solve ()

void	disable_info_in_newton_solve ()
	Disable the output of information when in the newton solver. More...

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

	ExplicitTimeSteppableObject (const ExplicitTimeSteppableObject &)=delete
	Broken copy constructor. More...

void	operator= (const ExplicitTimeSteppableObject &)=delete
	Broken assignment operator. More...

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

virtual void	actions_before_explicit_stage ()

virtual void	actions_after_explicit_stage ()

Public Attributes
Mesh *	Bulk_element_mesh_pt

Mesh *	Face_element_mesh_pt
	mesh for face elements More...

Public Attributes inherited from oomph::Problem
bool	Shut_up_in_newton_solve

Protected Member Functions
void	build_bulk_mesh (const unsigned n_x, const unsigned n_y, TopologicallyRectangularDomain *domain_pt, HermiteQuadMesh< BiharmonicElement< 2 >>::MeshSpacingFnPtr spacing_fn=0)

void	build_global_mesh_and_assign_eqn_numbers ()
	Build global mesh and assign equation numbers. More...

void	set_source_function (const BiharmonicSourceFctPt source_fct_pt)

void	set_dirichlet_boundary_condition (const unsigned &b, DirichletBCFctPt u_fn=0, DirichletBCFctPt dudn_fn=0)

void	set_neumann_boundary_condition (const unsigned &b, BiharmonicFluxElement< 2 >::FluxFctPt flux0_fct_pt, BiharmonicFluxElement< 2 >::FluxFctPt flux1_fct_pt=0)

Protected Member Functions inherited from oomph::Problem
unsigned	setup_element_count_per_dof ()

virtual void	sparse_assemble_row_or_column_compressed (Vector< int * > &column_or_row_index, Vector< int * > &row_or_column_start, Vector< double * > &value, Vector< unsigned > &nnz, Vector< double * > &residual, bool compressed_row_flag)

virtual void	actions_before_newton_convergence_check ()

virtual void	actions_before_newton_step ()

virtual void	actions_after_newton_step ()

virtual void	actions_before_implicit_timestep ()

virtual void	actions_after_implicit_timestep ()

virtual void	actions_after_implicit_timestep_and_error_estimation ()

virtual void	actions_before_explicit_timestep ()
	Actions that should be performed before each explicit time step. More...

virtual void	actions_after_explicit_timestep ()
	Actions that should be performed after each explicit time step. More...

virtual void	actions_before_read_unstructured_meshes ()

virtual void	actions_after_read_unstructured_meshes ()

virtual void	actions_after_change_in_global_parameter (double *const &parameter_pt)

virtual void	actions_after_change_in_bifurcation_parameter ()

virtual void	actions_after_parameter_increase (double *const &parameter_pt)

double &	dof_derivative (const unsigned &i)

double &	dof_current (const unsigned &i)

virtual void	set_initial_condition ()

virtual double	global_temporal_error_norm ()

unsigned	newton_solve_continuation (double *const &parameter_pt)

unsigned	newton_solve_continuation (double *const &parameter_pt, DoubleVector &z)

void	calculate_continuation_derivatives (double *const &parameter_pt)

void	calculate_continuation_derivatives (const DoubleVector &z)

void	calculate_continuation_derivatives_fd (double *const &parameter_pt)

bool	does_pointer_correspond_to_problem_data (double *const &parameter_pt)

void	set_consistent_pinned_values_for_continuation ()

Additional Inherited Members
Static Public Attributes inherited from oomph::Problem
static bool	Suppress_warning_about_actions_before_read_unstructured_meshes

Protected Types inherited from oomph::Problem
enum	Assembly_method { Perform_assembly_using_vectors_of_pairs , Perform_assembly_using_two_vectors , Perform_assembly_using_maps , Perform_assembly_using_lists , Perform_assembly_using_two_arrays }
	Enumerated flags to determine which sparse assembly method is used. More...

Protected Attributes inherited from oomph::Problem
Vector< Problem * >	Copy_of_problem_pt

std::map< double *, bool >	Calculate_dparameter_analytic

bool	Calculate_hessian_products_analytic

LinearAlgebraDistribution *	Dof_distribution_pt

Vector< double * >	Dof_pt
	Vector of pointers to dofs. More...

DoubleVectorWithHaloEntries	Element_count_per_dof

double	Relaxation_factor

double	Newton_solver_tolerance

unsigned	Max_newton_iterations
	Maximum number of Newton iterations. More...

unsigned	Nnewton_iter_taken

Vector< double >	Max_res
	Maximum residuals at start and after each newton iteration. More...

double	Max_residuals

bool	Time_adaptive_newton_crash_on_solve_fail

bool	Jacobian_reuse_is_enabled
	Is re-use of Jacobian in Newton iteration enabled? Default: false. More...

bool	Jacobian_has_been_computed

bool	Problem_is_nonlinear

bool	Pause_at_end_of_sparse_assembly

bool	Doc_time_in_distribute

unsigned	Sparse_assembly_method

unsigned	Sparse_assemble_with_arrays_initial_allocation

unsigned	Sparse_assemble_with_arrays_allocation_increment

Vector< Vector< unsigned > >	Sparse_assemble_with_arrays_previous_allocation

double	Numerical_zero_for_sparse_assembly

double	FD_step_used_in_get_hessian_vector_products

bool	Mass_matrix_reuse_is_enabled

bool	Mass_matrix_has_been_computed

bool	Discontinuous_element_formulation

double	Minimum_dt
	Minimum desired dt: if dt falls below this value, exit. More...

double	Maximum_dt
	Maximum desired dt. More...

double	DTSF_max_increase

double	DTSF_min_decrease

double	Minimum_dt_but_still_proceed

bool	Scale_arc_length
	Boolean to control whether arc-length should be scaled. More...

double	Desired_proportion_of_arc_length
	Proportion of the arc-length to taken by the parameter. More...

double	Theta_squared

int	Sign_of_jacobian
	Storage for the sign of the global Jacobian. More...

double	Continuation_direction

double	Parameter_derivative
	Storage for the derivative of the global parameter wrt arc-length. More...

double	Parameter_current
	Storage for the present value of the global parameter. More...

bool	Use_continuation_timestepper
	Boolean to control original or new storage of dof stuff. More...

unsigned	Dof_derivative_offset

unsigned	Dof_current_offset

Vector< double >	Dof_derivative
	Storage for the derivative of the problem variables wrt arc-length. More...

Vector< double >	Dof_current
	Storage for the present values of the variables. More...

double	Ds_current
	Storage for the current step value. More...

unsigned	Desired_newton_iterations_ds

double	Minimum_ds
	Minimum desired value of arc-length. More...

bool	Bifurcation_detection
	Boolean to control bifurcation detection via determinant of Jacobian. More...

bool	Bisect_to_find_bifurcation
	Boolean to control wheter bisection is used to located bifurcation. More...

bool	First_jacobian_sign_change
	Boolean to indicate whether a sign change has occured in the Jacobian. More...

bool	Arc_length_step_taken
	Boolean to indicate whether an arc-length step has been taken. More...

bool	Use_finite_differences_for_continuation_derivatives

OomphCommunicator *	Communicator_pt
	The communicator for this problem. More...

bool	Always_take_one_newton_step

double	Timestep_reduction_factor_after_nonconvergence

bool	Keep_temporal_error_below_tolerance

Static Protected Attributes inherited from oomph::Problem
static ContinuationStorageScheme	Continuation_time_stepper
	Storage for the single static continuation timestorage object. More...

Detailed Description

template<unsigned DIM>
class oomph::BiharmonicProblem< DIM >

Biharmonic Plate Problem Class - for problems where the load can be assumed to be acting normal to the surface of the plate and the deflections are small relative to the thickness of the plate. Developed for the topologically rectangular Hermite Element Mesh. Contains functions allowing the following boundary conditions to be applied (on a given edge):

clamped : u and du/dn imposed
simply supported : u and laplacian(u) imposed
free : laplacian(u) and dlaplacian(u)/dn imposed

Member Typedef Documentation

◆ BiharmonicSourceFctPt

template<unsigned DIM>

typedef void(* oomph::BiharmonicProblem< DIM >::BiharmonicSourceFctPt) (const Vector< double > &x, double &f)

Definition of the Source Function.

◆ DirichletBCFctPt

template<unsigned DIM>

typedef void(* oomph::BiharmonicProblem< DIM >::DirichletBCFctPt) (const double &s, double &u)

Definition of a dirichlet boundary condition function pointer. Takes the position along a boundary (s) in the macro element coordinate scheme and returns the value of the boundary condition at that point (u).

Constructor & Destructor Documentation

◆ BiharmonicProblem()

template<unsigned DIM>

oomph::BiharmonicProblem< DIM >::BiharmonicProblem ( )

inline

Constructor.

     {
       Bulk_element_mesh_pt = 0;
       Face_element_mesh_pt = 0;
     }

References oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt, and oomph::BiharmonicProblem< DIM >::Face_element_mesh_pt.

◆ ~BiharmonicProblem()

template<unsigned DIM>

virtual oomph::BiharmonicProblem< DIM >::~BiharmonicProblem ( )

inlinevirtual

Destructor. Delete the meshes.

     {
       delete Bulk_element_mesh_pt;
       delete Face_element_mesh_pt;
     };

References oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt, and oomph::BiharmonicProblem< DIM >::Face_element_mesh_pt.

Member Function Documentation

◆ actions_after_newton_solve()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::actions_after_newton_solve ( )

inlinevirtual

action after solve

Reimplemented from oomph::Problem.

109 {}

◆ actions_before_newton_solve()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::actions_before_newton_solve ( )

inlinevirtual

actions before solve, performs self test

Reimplemented from oomph::Problem.

     {
 #ifdef PARANOID
       if (0 == self_test())
       {
         oomph_info << "self test passed" << std::endl;
       }
       else
       {
         oomph_info << "self test failed" << std::endl;
       }
 #endif
     }

References oomph::oomph_info, and oomph::Problem::self_test().

◆ build_bulk_mesh()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::build_bulk_mesh	(	const unsigned	n_x,
		const unsigned	n_y,
		TopologicallyRectangularDomain *	domain_pt,
		HermiteQuadMesh< BiharmonicElement< 2 >>::MeshSpacingFnPtr	spacing_fn = `0`
	)

inlineprotected

builds the bulk mesh on a prescribed domain with a node spacing defined by spacing fn with n_x by n_y elements

     {
       if (spacing_fn == 0)
       {
         Bulk_element_mesh_pt =
           new HermiteQuadMesh<Hijacked<BiharmonicElement<2>>>(
             n_x, n_y, domain_pt);
       }
       else
       {
         Bulk_element_mesh_pt =
           new HermiteQuadMesh<Hijacked<BiharmonicElement<2>>>(
             n_x, n_y, domain_pt, spacing_fn);
       }
       //   add_sub_mesh(Bulk_element_mesh_pt);
       //   build_global_mesh();
     }

References oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt.

◆ build_global_mesh_and_assign_eqn_numbers()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::build_global_mesh_and_assign_eqn_numbers ( )

inlineprotected

Build global mesh and assign equation numbers.

     {
       add_sub_mesh(Bulk_element_mesh_pt);
       if (Face_element_mesh_pt != 0)
       {
         add_sub_mesh(Face_element_mesh_pt);
       }
       build_global_mesh();
       assign_eqn_numbers();
     }

References oomph::Problem::add_sub_mesh(), oomph::Problem::assign_eqn_numbers(), oomph::Problem::build_global_mesh(), oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt, and oomph::BiharmonicProblem< DIM >::Face_element_mesh_pt.

◆ bulk_element_mesh_pt()

template<unsigned DIM>

Mesh* oomph::BiharmonicProblem< DIM >::bulk_element_mesh_pt ( )

inline

Access function to the bulk element mesh pt.

     {
       return Bulk_element_mesh_pt;
     }

References oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt.

◆ doc_solution()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::doc_solution	(	DocInfo &	doc_info,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt = `0`
	)

documents the solution, and if an exact solution is provided, then the error between the numerical and exact solution is presented

   {
     std::ofstream some_file;
     std::ostringstream filename;
  
     // Number of plot points: npts x npts
     unsigned npts = 5;
  
     // Output solution
     filename << doc_info.directory() << "/soln_" << doc_info.number() << ".dat";
     some_file.open(filename.str().c_str());
     Bulk_element_mesh_pt->output(some_file, npts);
     some_file.close();
  
     // if the exact solution is not provided
     if (exact_soln_pt != 0)
     {
       // Output exact solution
       filename.str("");
       filename << doc_info.directory() << "/exact_soln_" << doc_info.number()
                << ".dat";
       some_file.open(filename.str().c_str());
       Bulk_element_mesh_pt->output_fct(some_file, npts, exact_soln_pt);
       some_file.close();
  
       // Doc error and return of the square of the L2 error
       double error, norm;
       filename.str("");
       filename << doc_info.directory() << "/error_" << doc_info.number()
                << ".dat";
       some_file.open(filename.str().c_str());
       Bulk_element_mesh_pt->compute_error(
         some_file, exact_soln_pt, error, norm);
       some_file.close();
  
       // Doc L2 error and norm of solution
       oomph_info << "\nNorm of error   : " << sqrt(error) << std::endl;
       oomph_info << "Norm of solution: " << sqrt(norm) << std::endl
                  << std::endl;
     }
   }

References oomph::DocInfo::directory(), calibrate::error, MergeRestartFiles::filename, oomph::DocInfo::number(), oomph::oomph_info, and sqrt().

◆ set_dirichlet_boundary_condition()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::set_dirichlet_boundary_condition	(	const unsigned &	b,
		DirichletBCFctPt	u_fn = `0`,
		DirichletBCFctPt	dudn_fn = `0`
	)

protected

Imposes the prescribed dirichlet BCs u (u_fn) and du/dn (dudn_fn) dirichlet BCs by 'pinning'

Impose a Clamped Edge. Imposes the prescribed dirichlet BCs u and du/dn dirichlet BCs by pinning

   {
     // number of nodes on boundary b
     unsigned n_node = Bulk_element_mesh_pt->nboundary_node(b);
  
     // fixed faced index for boundary
     int face_index = Bulk_element_mesh_pt->face_index_at_boundary(b, 0);
  
     // Need to get the s_fixed_index
     unsigned s_fixed_index = 0;
     switch (face_index)
     {
       case -1:
       case 1:
         s_fixed_index = 0;
         break;
  
       case -2:
       case 2:
         s_fixed_index = 1;
         break;
  
       default:
         throw OomphLibError("Face Index not +/-1 or +/-2: Need 2D QElements",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
     }
  
     // node position along edge b in macro element boundary representation
     // [-1,1]
     Vector<double> s(1);
  
     // Set the edge sign
     int edge_sign = 0;
     switch (face_index)
     {
       case -1:
       case 2:
         edge_sign = -1;
         break;
  
       case 1:
       case -2:
         edge_sign = 1;
         break;
     }
  
     // finite difference step
     const double h = 10e-8;
  
     // node position along edge b in macro element boundary representation
     // [-1,1]
     Vector<double> m(2);
  
     // if u is prescribed then impose
     if (u_fn != 0)
     {
       // loop over nodes on boundary b
       for (unsigned n = 0; n < n_node; n++)
       {
         // find node position along edge [-1,1] in macro element representation
         Bulk_element_mesh_pt->boundary_node_pt(b, n)
           ->get_coordinates_on_boundary(b, m);
  
         // get u at node
         double u;
         (*u_fn)(m[0], u);
  
         // finite difference is used to compute dudm_t
         // u0 and u1 store values of u left/below and right/above node n
         double u_L, u_R;
  
         // if left/lower corner node
         if (n == 0)
         {
           (*u_fn)(m[0], u_L);
           (*u_fn)(m[0] + h, u_R);
         }
         // if right/upper corner node
         else if (n == n_node - 1)
         {
           (*u_fn)(m[0] - h, u_L);
           (*u_fn)(m[0], u_R);
         }
         // if other node
         else
         {
           (*u_fn)(m[0] - 0.5 * h, u_L);
           (*u_fn)(m[0] + 0.5 * h, u_R);
         }
  
         // compute dudm_t
         double dudm_t = (u_R - u_L) / h;
  
         // compute duds_t
         double duds_t = m[1] * dudm_t;
  
         // pin and set u type dof
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->pin(0);
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->set_value(0, u);
  
         // pin and set duds_t type degree of freedom
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->pin(2 - s_fixed_index);
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->set_value(
           2 - s_fixed_index, duds_t);
       }
     }
  
     // if dudn is prescribed then impose
     if (dudn_fn != 0)
     {
       // loop over nodes on boundary b
       for (unsigned n = 0; n < n_node; n++)
       {
         // vectors for dx_i/ds_n and dx_i/ds_t
         Vector<double> dxds_n(2);
         Vector<double> dxds_t(2);
         dxds_n[0] = Bulk_element_mesh_pt->boundary_node_pt(b, n)->x_gen(
           1 + s_fixed_index, 0);
         dxds_n[1] = Bulk_element_mesh_pt->boundary_node_pt(b, n)->x_gen(
           1 + s_fixed_index, 1);
         dxds_t[0] = Bulk_element_mesh_pt->boundary_node_pt(b, n)->x_gen(
           2 - s_fixed_index, 0);
         dxds_t[1] = Bulk_element_mesh_pt->boundary_node_pt(b, n)->x_gen(
           2 - s_fixed_index, 1);
  
         // vector for d2xi/ds_n ds_t
         Vector<double> d2xds_nds_t(2);
         d2xds_nds_t[0] =
           Bulk_element_mesh_pt->boundary_node_pt(b, n)->x_gen(3, 0);
         d2xds_nds_t[1] =
           Bulk_element_mesh_pt->boundary_node_pt(b, n)->x_gen(3, 1);
  
         // compute dn/ds_n
         double dnds_n =
           ((dxds_n[0] * dxds_t[1]) - (dxds_n[1] * dxds_t[0])) /
           (sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]) * edge_sign);
  
         // compute dt/ds_n
         double dtds_n = ((dxds_n[0] * dxds_t[0]) + (dxds_n[1] * dxds_t[1])) /
                         sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
         // compute dt/ds_t
         double dtds_t = sqrt(pow(dxds_t[0], 2) + pow(dxds_t[1], 2));
  
         // compute ds_n/dn
         double ds_ndn =
           -1.0 * (edge_sign * sqrt(pow(dxds_t[0], 2) + pow(dxds_t[1], 2))) /
           (dxds_t[0] * dxds_n[1] - dxds_n[0] * dxds_t[1]);
  
         // compute ds_t/dt
         double ds_tdt = 1 / sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
         // compute d2t/ds_nds_t
         double d2tds_nds_t =
           (dxds_t[0] * d2xds_nds_t[0] + dxds_t[1] * d2xds_nds_t[1]) /
           sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
         // compute d2s_t/ds_ndt
         double d2s_tds_ndt =
           (dxds_t[0] * d2xds_nds_t[0] + dxds_t[1] * d2xds_nds_t[1]) /
           pow(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1], 3.0 / 2.0);
  
         // get m_t and dm_t/ds_t for this node
         Vector<double> m_N(2);
         Bulk_element_mesh_pt->boundary_node_pt(b, n)
           ->get_coordinates_on_boundary(b, m_N);
  
         // compute d2u/dm_t2 and d/dm_t(dudn) by finite difference
         double d2udm_t2 = 0;
         double ddm_tdudn = 0;
         double u_2L, u_N, u_2R, dudn_L, dudn_R;
         // evaluate u_fn and dudn_fn for current node
         if (n == 0)
         {
           (*u_fn)(m_N[0], u_2L);
           (*u_fn)(m_N[0] + h, u_N);
           (*u_fn)(m_N[0] - 2 * h, u_2R);
           (*dudn_fn)(m_N[0], dudn_L);
           (*dudn_fn)(m_N[0] + h, dudn_R);
         }
         else if (n == n_node - 1)
         {
           (*u_fn)(m_N[0] - 2 * h, u_2L);
           (*u_fn)(m_N[0] - h, u_N);
           (*u_fn)(m_N[0], u_2R);
           (*dudn_fn)(m_N[0] - h, dudn_L);
           (*dudn_fn)(m_N[0], dudn_R);
         }
         else
         {
           (*u_fn)(m_N[0] - h, u_2L);
           u_N = Bulk_element_mesh_pt->boundary_node_pt(b, n)->value(0);
           (*u_fn)(m_N[0] + h, u_2R);
           (*dudn_fn)(m_N[0] - 0.5 * h, dudn_L);
           (*dudn_fn)(m_N[0] + 0.5 * h, dudn_R);
         }
         // compute
         d2udm_t2 = (u_2L + u_2R - 2 * u_N) / (h * h);
         ddm_tdudn = (dudn_R - dudn_L) / h;
  
         // get dudn at the node
         double dudn;
         (*dudn_fn)(m_N[0], dudn);
  
         // compute d2u/ds_t2
         double d2uds_t2 = m_N[1] * m_N[1] * d2udm_t2;
  
         // get duds_t
         double duds_t = Bulk_element_mesh_pt->boundary_node_pt(b, n)->value(
           2 - s_fixed_index);
  
         // get du/dt
         double dudt = ds_tdt * duds_t;
  
         // compute d2u/dndt
         double d2udndt = ds_tdt = dtds_t * m_N[1] * ddm_tdudn;
  
         // compute d2udt2
         double dtds_nd2udt2 =
           edge_sign * (dxds_t[0] * dxds_n[1] - dxds_n[0] * dxds_t[1]) *
           (ds_tdt *
            (d2udndt - ds_ndn * (d2s_tds_ndt * dudt + ds_tdt * d2uds_t2)));
  
         // compute dds_n(dudt)
         double dds_ndudt = dtds_nd2udt2 + dnds_n * d2udndt;
  
         // compute du/ds_n
         double duds_n = dnds_n * dudn + dtds_n * ds_tdt * duds_t;
  
         // compute d2u/ds_nds_t
         double d2uds_nds_t = d2tds_nds_t * dudt + dtds_t * dds_ndudt;
  
         // pin du/ds_n dof and set value
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->pin(1 + s_fixed_index);
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->set_value(
           1 + s_fixed_index, duds_n);
  
         // pin d2u/ds_nds_t dof and set value
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->pin(3);
         Bulk_element_mesh_pt->boundary_node_pt(b, n)->set_value(3, d2uds_nds_t);
       }
     }
   }

References b, e(), m, n, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ set_neumann_boundary_condition()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::set_neumann_boundary_condition	(	const unsigned &	b,
		BiharmonicFluxElement< 2 >::FluxFctPt	flux0_fct_pt,
		BiharmonicFluxElement< 2 >::FluxFctPt	flux1_fct_pt = `0`
	)

protected

Imposes the prescribed Neumann BCs laplacian(u) (flux0_fct_pt) and dlaplacian(u)/dn (flux1_fct_pt) with flux edge elements

Imposes a 'free' edge. Imposes the prescribed Neumann BCs laplacian(u) and dlaplacian(u)/dn with flux edge elements

   {
     // if the face element mesh pt does not exist then build it
     if (Face_element_mesh_pt == 0)
     {
       Face_element_mesh_pt = new Mesh();
     }
  
     // How many bulk elements are adjacent to boundary b?
     unsigned n_element = Bulk_element_mesh_pt->nboundary_element(b);
  
     // Loop over the bulk elements adjacent to boundary b?
     for (unsigned e = 0; e < n_element; e++)
     {
       // Get pointer to the bulk element that is adjacent to boundary b
       FiniteElement* bulk_elem_pt = dynamic_cast<FiniteElement*>(
         Bulk_element_mesh_pt->boundary_element_pt(b, e));
  
       // What is the face index along the boundary
       int face_index = Bulk_element_mesh_pt->face_index_at_boundary(b, e);
  
       // Build the corresponding prescribed-flux element
       BiharmonicFluxElement<2>* flux_element_pt =
         new BiharmonicFluxElement<2>(bulk_elem_pt, face_index, b);
  
  
       // pass the flux BC pointers to the flux elements
       flux_element_pt->flux0_fct_pt() = flux0_fct_pt;
       if (flux1_fct_pt != 0)
       {
         flux_element_pt->flux1_fct_pt() = flux1_fct_pt;
       }
  
       // Add the prescribed-flux element to the mesh
       Face_element_mesh_pt->add_element_pt(flux_element_pt);
     }
   }

References b, e(), oomph::BiharmonicFluxElement< DIM >::flux0_fct_pt(), and oomph::BiharmonicFluxElement< DIM >::flux1_fct_pt().

◆ set_source_function()

template<unsigned DIM>

void oomph::BiharmonicProblem< DIM >::set_source_function ( const BiharmonicSourceFctPt source_fct_pt )

inlineprotected

Impose a load to the surface of the plate. note : MUST be called before neumann boundary conditions are imposed, i.e. a free edge or a simply supported edge with laplacian(u) imposed

     {
       // number of elements in mesh
       unsigned n_bulk_element = Bulk_element_mesh_pt->nelement();
  
       // loop over bulk elements
       for (unsigned i = 0; i < n_bulk_element; i++)
       {
         // upcast from generalised element to specific element
         BiharmonicElement<2>* element_pt = dynamic_cast<BiharmonicElement<2>*>(
           Bulk_element_mesh_pt->element_pt(i));
  
         // set the source function pointer
         element_pt->source_fct_pt() = source_fct_pt;
       }
     }

References oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt, oomph::Mesh::element_pt(), i, oomph::Mesh::nelement(), oomph::source_fct_pt(), and oomph::BiharmonicEquations< DIM >::source_fct_pt().

Member Data Documentation

◆ Bulk_element_mesh_pt

template<unsigned DIM>

Mesh* oomph::BiharmonicProblem< DIM >::Bulk_element_mesh_pt

Mesh for BiharmonicElement<DIM> only - the block preconditioner assemble the global equation number to block number mapping from elements in this mesh only

Referenced by oomph::BiharmonicProblem< DIM >::BiharmonicProblem(), oomph::BiharmonicProblem< DIM >::build_bulk_mesh(), oomph::BiharmonicProblem< DIM >::build_global_mesh_and_assign_eqn_numbers(), oomph::BiharmonicProblem< DIM >::bulk_element_mesh_pt(), oomph::BiharmonicProblem< DIM >::set_source_function(), and oomph::BiharmonicProblem< DIM >::~BiharmonicProblem().

◆ Face_element_mesh_pt

template<unsigned DIM>

Mesh* oomph::BiharmonicProblem< DIM >::Face_element_mesh_pt

mesh for face elements

Referenced by oomph::BiharmonicProblem< DIM >::BiharmonicProblem(), oomph::BiharmonicProblem< DIM >::build_global_mesh_and_assign_eqn_numbers(), and oomph::BiharmonicProblem< DIM >::~BiharmonicProblem().

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

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Additional Inherited Members

Detailed Description

template<unsigned DIM> class oomph::BiharmonicProblem< DIM >

Member Typedef Documentation

◆ BiharmonicSourceFctPt

◆ DirichletBCFctPt

Constructor & Destructor Documentation

◆ BiharmonicProblem()

◆ ~BiharmonicProblem()

Member Function Documentation

◆ actions_after_newton_solve()

◆ actions_before_newton_solve()

◆ build_bulk_mesh()

◆ build_global_mesh_and_assign_eqn_numbers()

◆ bulk_element_mesh_pt()

◆ doc_solution()

◆ set_dirichlet_boundary_condition()

◆ set_neumann_boundary_condition()

◆ set_source_function()

Member Data Documentation

◆ Bulk_element_mesh_pt

◆ Face_element_mesh_pt

template<unsigned DIM>
class oomph::BiharmonicProblem< DIM >