Problem class. More...

Inheritance diagram for PMLFourierDecomposedHelmholtzProblem< ELEMENT >:

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

	~PMLFourierDecomposedHelmholtzProblem ()
	Destructor (empty) More...

void	actions_before_newton_solve ()
	Update the problem specs before solve (empty) More...

void	actions_after_newton_solve ()
	Update the problem after solve (empty) More...

void	doc_solution (DocInfo &doc_info)
	Doc the solution: doc_info contains labels/output directory etc. More...

void	create_pml_meshes ()
	Create PML meshes. More...

void	create_power_monitor_mesh ()
	Create mesh of face elements that monitor the radiated power. More...

void	complete_problem_setup ()

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 ()

Private Member Functions
void	create_flux_elements_on_inner_boundary ()
	Create flux elements on inner boundary. More...

void	delete_face_elements (Mesh *const &boundary_mesh_pt)
	Delete boundary face elements and wipe the surface mesh. More...

void	apply_zero_dirichlet_boundary_conditions ()

Private Attributes
Mesh *	Power_monitor_mesh_pt
	Pointer to mesh that stores the power monitor elements. More...

TriangleMesh< ELEMENT > *	Bulk_mesh_pt
	Pointer to the "bulk" mesh. More...

Mesh *	Helmholtz_inner_boundary_mesh_pt
	Mesh of FaceElements that apply the flux bc on the inner boundary. More...

Mesh *	PML_right_mesh_pt
	Pointer to the right PML mesh. More...

Mesh *	PML_top_mesh_pt
	Pointer to the top PML mesh. More...

Mesh *	PML_bottom_mesh_pt
	Pointer to the bottom PML mesh. More...

Mesh *	PML_top_right_mesh_pt
	Pointer to the top right corner PML mesh. More...

Mesh *	PML_bottom_right_mesh_pt
	Pointer to the bottom right corner PML mesh. More...

ofstream	Trace_file
	Trace file. More...

Additional Inherited Members
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 Attributes inherited from oomph::Problem
bool	Shut_up_in_newton_solve

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 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 ()

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<class ELEMENT>
class PMLFourierDecomposedHelmholtzProblem< ELEMENT >

Problem class.

////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////

Constructor & Destructor Documentation

◆ PMLFourierDecomposedHelmholtzProblem()

template<class ELEMENT >

PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PMLFourierDecomposedHelmholtzProblem

Constructor.

Constructor for Pml Fourier-decomposed Helmholtz problem.

Setup "bulk" mesh

 {
   string trace_file_location = ProblemParameters::Directory + "/trace.dat";
  
  // Open trace file
  Trace_file.open(trace_file_location.c_str());
  
  
  // Create the circle that represents the inner boundary
  double x_c=0.0;
  double y_c=0.0;
  double r_min=1.0;
  double r_max=3.0;
  Circle* inner_circle_pt=new Circle(x_c,y_c,r_min);
  
  
  // Edges/boundary segments making up outer boundary
  //-------------------------------------------------
  Vector<TriangleMeshCurveSection*> outer_boundary_line_pt(6);
  
  // All poly boundaries are defined by two vertices
  Vector<Vector<double> > boundary_vertices(2);
  
  
  // Bottom straight boundary on symmetry line
  //------------------------------------------
  boundary_vertices[0].resize(2);
  boundary_vertices[0][0]=0.0;
  boundary_vertices[0][1]=-r_min;
  boundary_vertices[1].resize(2);
  boundary_vertices[1][0]=0.0;
  boundary_vertices[1][1]=-r_max;
  
  unsigned boundary_id=0;
  outer_boundary_line_pt[0]=
   new TriangleMeshPolyLine(boundary_vertices,boundary_id);
  
  
  // Bottom boundary of bulk mesh
  //-----------------------------
  boundary_vertices[0][0]=0.0;
  boundary_vertices[0][1]=-r_max;
  boundary_vertices[1][0]=r_max;;
  boundary_vertices[1][1]=-r_max;
  
  boundary_id=1;
  outer_boundary_line_pt[1]=
   new TriangleMeshPolyLine(boundary_vertices,boundary_id);
  
  
  // Right boundary of bulk mesh
  //----------------------------
  boundary_vertices[0][0]=r_max;
  boundary_vertices[0][1]=-r_max;
  boundary_vertices[1][0]=r_max;;
  boundary_vertices[1][1]=r_max;
  
  boundary_id=2;
  outer_boundary_line_pt[2]=
   new TriangleMeshPolyLine(boundary_vertices,boundary_id);
  
  
  // Top boundary of bulk mesh
  //--------------------------
  boundary_vertices[0][0]=r_max;
  boundary_vertices[0][1]=r_max;
  boundary_vertices[1][0]=0.0;
  boundary_vertices[1][1]=r_max;
  
  boundary_id=3;
  outer_boundary_line_pt[3]=
   new TriangleMeshPolyLine(boundary_vertices,boundary_id);
  
 // Top straight boundary on symmetry line
  //---------------------------------------
  boundary_vertices[0][0]=0.0;
  boundary_vertices[0][1]=r_max;
  boundary_vertices[1][0]=0.0;
  boundary_vertices[1][1]=r_min;
  
  boundary_id=4;
  outer_boundary_line_pt[4]=
   new TriangleMeshPolyLine(boundary_vertices,boundary_id);
  
  
  // Inner circular boundary:
  //-------------------------
  
  // Number of segments used for representing the curvilinear boundary
  unsigned n_segments = 20;
  
  // The intrinsic coordinates for the beginning and end of the curve
  double s_start =  0.5*MathematicalConstants::Pi;
  double s_end   =  -0.5*MathematicalConstants::Pi;
  
  boundary_id = 5;
  outer_boundary_line_pt[5]=
   new TriangleMeshCurviLine(inner_circle_pt,
                             s_start,
                             s_end,
                             n_segments,
                             boundary_id);
  
  
  // Create closed curve that defines outer boundary
  //------------------------------------------------
  TriangleMeshClosedCurve *outer_boundary_pt =
   new TriangleMeshClosedCurve(outer_boundary_line_pt);
  
  
  // Use the TriangleMeshParameters object for helping on the manage of the
  // TriangleMesh parameters. The only parameter that needs to take is the
  // outer boundary.
  TriangleMeshParameters triangle_mesh_parameters(outer_boundary_pt);
  
  
  // Specify maximum element area
  double element_area = ProblemParameters::Element_area;
  triangle_mesh_parameters.element_area() = element_area;
  
 #ifdef ADAPTIVE
  
  // Build "bulk" mesh
  Bulk_mesh_pt=new RefineableTriangleMesh<ELEMENT>(triangle_mesh_parameters);
  
  // Add the bulk mesh to the problem
  add_sub_mesh(Bulk_mesh_pt);
  
  // Initialise mesh as geom object
  Mesh_as_geom_obj_pt=0;
  
  // Create/set error estimator
  Bulk_mesh_pt->spatial_error_estimator_pt()=new Z2ErrorEstimator;
  
  // Choose error tolerances to force some uniform refinement
  Bulk_mesh_pt->min_permitted_error()=0.00004;
  Bulk_mesh_pt->max_permitted_error()=0.0001;
  
  // Reduce wavenumber to make effect of singularity more prominent
  ProblemParameters::K_squared = 0.1*0.1;
  
 #else
  
  // Create the bulk mesh
  Bulk_mesh_pt= new TriangleMesh<ELEMENT>(triangle_mesh_parameters);
  
  // Add the bulk mesh to the problem
  add_sub_mesh(Bulk_mesh_pt);
  
   // Create flux elements on inner boundary
  Helmholtz_inner_boundary_mesh_pt=new Mesh;
  create_flux_elements_on_inner_boundary();
  
  // ...and add the mesh to the problem
  add_sub_mesh(Helmholtz_inner_boundary_mesh_pt);
  
 #endif
  
  
  // Attach the power monitor elements
  Power_monitor_mesh_pt=new Mesh;
  create_power_monitor_mesh();
  
  // Create the pml meshes
  create_pml_meshes();
  
  // Build the Problem's global mesh from its various sub-meshes
  build_global_mesh();
  
  // Complete the build of all elements
  complete_problem_setup();
  
  // Setup equation numbering scheme
  cout <<"Number of equations: " << assign_eqn_numbers() << std::endl;
  
 } // end of constructor

References ProblemParameters::Directory, ProblemParameters::Element_area, oomph::TriangleMeshParameters::element_area(), ProblemParameters::K_squared, oomph::MathematicalConstants::Pi, BiharmonicTestFunctions2::r_max, BiharmonicTestFunctions2::r_min, and oomph::Problem_Parameter::Trace_file.

◆ ~PMLFourierDecomposedHelmholtzProblem()

template<class ELEMENT >

PMLFourierDecomposedHelmholtzProblem< ELEMENT >::~PMLFourierDecomposedHelmholtzProblem ( )

inline

Destructor (empty)

438 {}

Member Function Documentation

◆ actions_after_newton_solve()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::actions_after_newton_solve ( )

inlinevirtual

Update the problem after solve (empty)

Reimplemented from oomph::Problem.

444 {}

◆ actions_before_newton_solve()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::actions_before_newton_solve ( )

inlinevirtual

Update the problem specs before solve (empty)

Reimplemented from oomph::Problem.

441 {}

◆ apply_zero_dirichlet_boundary_conditions()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::apply_zero_dirichlet_boundary_conditions

private

 {
  // Apply zero dirichlet conditions on the bottom straight boundary
  // and the top straight boundary located on the symmetry line.
  
  // Bottom straight boundary on symmetry line:
  {
   //Boundary id
   unsigned b=0;
  
   // How many nodes are there?
   unsigned n_node=Bulk_mesh_pt->nboundary_node(b);
   for (unsigned n=0;n<n_node;n++)
    {
     // Get the node
     Node* nod_pt=Bulk_mesh_pt->boundary_node_pt(b,n);
  
     // Pin the node
     nod_pt->pin(0);
     nod_pt->pin(1);
  
     // Set the node's value
     nod_pt->set_value(0, 0.0);
     nod_pt->set_value(1, 0.0);
    }
  }
  
 // Top straight boundary on symmetry line:
  {
   //Boundary id
   unsigned b=4;
  
   // How many nodes are there?
   unsigned n_node=Bulk_mesh_pt->nboundary_node(b);
   for (unsigned n=0;n<n_node;n++)
    {
     // Get the node
     Node* nod_pt=Bulk_mesh_pt->boundary_node_pt(b,n);
  
     // Pin the node
     nod_pt->pin(0);
     nod_pt->pin(1);
  
     // Set the node's value
     nod_pt->set_value(0, 0.0);
     nod_pt->set_value(1, 0.0);
    }
  }
  
  
 } // end of apply_zero_dirichlet_boundary_conditions

References b, n, oomph::Data::pin(), and oomph::Data::set_value().

◆ complete_problem_setup()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::complete_problem_setup

 {
  // Complete the build of all elements so they are fully functional
  unsigned n_element = this->mesh_pt()->nelement();
  for(unsigned i=0;i<n_element;i++)
   {
    // Upcast from GeneralsedElement to the present element
    PMLFourierDecomposedHelmholtzEquations *el_pt = dynamic_cast<
     PMLFourierDecomposedHelmholtzEquations*>(
      mesh_pt()->element_pt(i));
  
    if (!(el_pt==0))
     {
      //Set the frequency pointer
      el_pt->k_squared_pt()=&ProblemParameters::K_squared;
  
      // Set pointer to Fourier wave number
      el_pt->pml_fourier_wavenumber_pt()=&ProblemParameters::N_fourier;
     }
   }
  
  // If the Fourier wavenumber is odd, then apply zero dirichlet boundary
  // conditions on the two straight boundaries on the symmetry line.
  if (ProblemParameters::N_fourier % 2 == 1)
   {
    cout
     << "Zero Dirichlet boundary condition has been applied on symmetry line\n";
    cout << "due to an odd Fourier wavenumber\n" << std::endl;
    apply_zero_dirichlet_boundary_conditions();
   }
  
 } // end of complete_problem_setup

References i, ProblemParameters::K_squared, oomph::PMLFourierDecomposedHelmholtzEquations::k_squared_pt(), ProblemParameters::N_fourier, and oomph::PMLFourierDecomposedHelmholtzEquations::pml_fourier_wavenumber_pt().

◆ create_flux_elements_on_inner_boundary()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::create_flux_elements_on_inner_boundary

private

Create flux elements on inner boundary.

 {
  // Apply flux bc on inner boundary (boundary 5)
  unsigned b=5;
  
 // Loop over the bulk elements adjacent to boundary b
  unsigned n_element = Bulk_mesh_pt->nboundary_element(b);
  for(unsigned e=0;e<n_element;e++)
   {
    // Get pointer to the bulk element that is adjacent to boundary b
    ELEMENT* bulk_elem_pt = dynamic_cast<ELEMENT*>(
     Bulk_mesh_pt->boundary_element_pt(b,e));
  
    //Find the index of the face of element e along boundary b
    int face_index = Bulk_mesh_pt->face_index_at_boundary(b,e);
  
    // Build the corresponding prescribed incoming-flux element
    PMLFourierDecomposedHelmholtzFluxElement<ELEMENT>*
     flux_element_pt = new
     PMLFourierDecomposedHelmholtzFluxElement<ELEMENT>
     (bulk_elem_pt,face_index);
  
    //Add the prescribed incoming-flux element to the surface mesh
    Helmholtz_inner_boundary_mesh_pt->add_element_pt(flux_element_pt);
  
    // Set the pointer to the prescribed flux function
    flux_element_pt->flux_fct_pt() = &ProblemParameters::exact_minus_dudr;
  
   } //end of loop over bulk elements adjacent to boundary b
  
 } // end of create flux elements on inner boundary

References b, e(), ProblemParameters::exact_minus_dudr(), and oomph::PMLFourierDecomposedHelmholtzFluxElement< ELEMENT >::flux_fct_pt().

◆ create_pml_meshes()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::create_pml_meshes

Create PML meshes.

Create PML meshes and add them to the problem's sub-meshes.

 {
  // Bulk mesh bottom boundary id
  unsigned int bottom_boundary_id = 1;
  
  // Bulk mesh right boundary id
  unsigned int right_boundary_id = 2;
  
  // Bulk mesh top boundary id
  unsigned int top_boundary_id = 3;
  
  // PML width in elements for the right layer
  unsigned n_x_right_pml = ProblemParameters::Nel_pml;
  
  // PML width in elements for the top layer
  unsigned n_y_top_pml = ProblemParameters::Nel_pml;
  
  // PML width in elements for the bottom layer
  unsigned n_y_bottom_pml = ProblemParameters::Nel_pml;
  
  
  // Outer physical length of the PML layers
  // defaults to 4.0
  double width_x_right_pml  = ProblemParameters::PML_thickness;
  double width_y_top_pml    = ProblemParameters::PML_thickness;
  double width_y_bottom_pml = ProblemParameters::PML_thickness;
  
  // Build the PML meshes based on the new adapted triangular mesh
  PML_right_mesh_pt = TwoDimensionalPMLHelper::create_right_pml_mesh
   <PMLLayerElement<ELEMENT> >(Bulk_mesh_pt,
                               right_boundary_id,
                               n_x_right_pml,
                               width_x_right_pml);
  PML_top_mesh_pt   = TwoDimensionalPMLHelper::create_top_pml_mesh
   <PMLLayerElement<ELEMENT> >(Bulk_mesh_pt,
                               top_boundary_id,
                               n_y_top_pml,
                               width_y_top_pml);
  PML_bottom_mesh_pt= TwoDimensionalPMLHelper::create_bottom_pml_mesh
   <PMLLayerElement<ELEMENT> >(Bulk_mesh_pt,
                               bottom_boundary_id,
                               n_y_bottom_pml,
                               width_y_bottom_pml);
  
  // Add submeshes to the global mesh
  add_sub_mesh(PML_right_mesh_pt);
  add_sub_mesh(PML_top_mesh_pt);
  add_sub_mesh(PML_bottom_mesh_pt);
  
  // Rebuild corner PML meshes
  PML_top_right_mesh_pt    =
   TwoDimensionalPMLHelper::create_top_right_pml_mesh
   <PMLLayerElement<ELEMENT> >(PML_right_mesh_pt,
                               PML_top_mesh_pt,
                               Bulk_mesh_pt,
                               right_boundary_id);
  
  PML_bottom_right_mesh_pt =
   TwoDimensionalPMLHelper::create_bottom_right_pml_mesh
   <PMLLayerElement<ELEMENT> >(PML_right_mesh_pt,
                               PML_bottom_mesh_pt,
                               Bulk_mesh_pt,
                               right_boundary_id);
  
  // Add submeshes to the global mesh
  add_sub_mesh(PML_top_right_mesh_pt);
  add_sub_mesh(PML_bottom_right_mesh_pt);
  
 } // end of create_pml_meshes

References oomph::TwoDimensionalPMLHelper::create_bottom_pml_mesh(), oomph::TwoDimensionalPMLHelper::create_bottom_right_pml_mesh(), oomph::TwoDimensionalPMLHelper::create_right_pml_mesh(), oomph::TwoDimensionalPMLHelper::create_top_pml_mesh(), oomph::TwoDimensionalPMLHelper::create_top_right_pml_mesh(), ProblemParameters::Nel_pml, and ProblemParameters::PML_thickness.

◆ create_power_monitor_mesh()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::create_power_monitor_mesh

Create mesh of face elements that monitor the radiated power.

Create BC elements on outer boundary.

 {
  // Loop over outer boundaries
  for (unsigned b=1;b<4;b++)
   {
    // Loop over the bulk elements adjacent to boundary b?
    unsigned n_element = Bulk_mesh_pt->nboundary_element(b);
    for(unsigned e=0;e<n_element;e++)
     {
      // Get pointer to the bulk element that is adjacent to boundary b
      ELEMENT* bulk_elem_pt = dynamic_cast<ELEMENT*>(
       Bulk_mesh_pt->boundary_element_pt(b,e));
  
      //Find the index of the face of element e along boundary b
      int face_index = Bulk_mesh_pt->face_index_at_boundary(b,e);
  
      // Build the corresponding element
      PMLFourierDecomposedHelmholtzPowerMonitorElement<ELEMENT>*
       flux_element_pt = new
       PMLFourierDecomposedHelmholtzPowerMonitorElement<ELEMENT>
       (bulk_elem_pt,face_index);
  
      //Add the flux boundary element
      Power_monitor_mesh_pt->add_element_pt(flux_element_pt);
     }
   }
 } // end of create_power_monitor_mesh

References b, and e().

◆ delete_face_elements()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::delete_face_elements ( Mesh *const & boundary_mesh_pt )

inlineprivate

Delete boundary face elements and wipe the surface mesh.

   {
    // Loop over the surface elements
    unsigned n_element = boundary_mesh_pt->nelement();
    for(unsigned e=0;e<n_element;e++)
     {
      // Kill surface element
      delete  boundary_mesh_pt->element_pt(e);
     }
  
    // Wipe the mesh
    boundary_mesh_pt->flush_element_and_node_storage();
   }

References e(), oomph::Mesh::element_pt(), oomph::Mesh::flush_element_and_node_storage(), and oomph::Mesh::nelement().

◆ doc_solution()

template<class ELEMENT >

void PMLFourierDecomposedHelmholtzProblem< ELEMENT >::doc_solution ( DocInfo & doc_info )

Doc the solution: doc_info contains labels/output directory etc.

Doc the solution. DocInfo object stores flags/labels for where the output gets written to

 {
  
  ofstream some_file;
  char filename[100];
  
  // Number of plot points: npts x npts
  unsigned npts=5;
  
  
  // Total radiated power
  double power=0.0;
  
  // Compute/output the radiated power
  //----------------------------------
  sprintf(filename,"%s/power%i.dat",doc_info.directory().c_str(),
          doc_info.number());
  some_file.open(filename);
  
  // Accumulate contribution from elements
  unsigned nn_element=Power_monitor_mesh_pt->nelement();
  for(unsigned e=0;e<nn_element;e++)
   {
    PMLFourierDecomposedHelmholtzPowerMonitorElement<ELEMENT> *el_pt =
     dynamic_cast<PMLFourierDecomposedHelmholtzPowerMonitorElement
     <ELEMENT>*>(Power_monitor_mesh_pt->element_pt(e));
    power += el_pt->global_power_contribution(some_file);
   }
  some_file.close();
  oomph_info << "Total radiated power: " << power << std::endl;
  
  
  // Output solution within the bulk mesh
  //-------------------------------------
  sprintf(filename,"%s/soln%i.dat",doc_info.directory().c_str(),
          doc_info.number());
  some_file.open(filename);
  Bulk_mesh_pt->output(some_file,npts);
  some_file.close();
  
  // Output solution within pml domains
  //-----------------------------------
  sprintf(filename,"%s/pml_soln%i.dat",doc_info.directory().c_str(),
          doc_info.number());
  some_file.open(filename);
  PML_top_mesh_pt->output(some_file,npts);
  PML_right_mesh_pt->output(some_file,npts);
  PML_bottom_mesh_pt->output(some_file,npts);
  PML_top_right_mesh_pt->output(some_file,npts);
  PML_bottom_right_mesh_pt->output(some_file,npts);
  some_file.close();
  
  
  // Output exact solution
  //----------------------
  sprintf(filename,"%s/exact_soln%i.dat",doc_info.directory().c_str(),
          doc_info.number());
  some_file.open(filename);
  Bulk_mesh_pt->output_fct(some_file,npts,ProblemParameters::get_exact_u);
  some_file.close();
  
  
  // Doc error and return of the square of the L2 error
  //---------------------------------------------------
  double error,norm;
  sprintf(filename,"%s/error%i.dat",doc_info.directory().c_str(),
          doc_info.number());
  some_file.open(filename);
  Bulk_mesh_pt->compute_error(some_file,ProblemParameters::get_exact_u,
                              error,norm);
  some_file.close();
  
  // Doc L2 error and norm of solution
  cout << "\nNorm of error   : " << sqrt(error) << std::endl;
  cout << "Norm of solution: " << sqrt(norm) << std::endl << std::endl;
  
  sprintf(filename,"%s/int_error%i.dat",doc_info.directory().c_str(),
          doc_info.number());
  some_file.open(filename);
  // Doc L2 error and norm of solution
  some_file << "\nNorm of error   : " << sqrt(error) << std::endl;
  some_file << "Norm of solution: " << sqrt(norm) << std::endl <<std::endl;
  some_file << "Relative error: " << sqrt(error)/sqrt(norm) << std::endl;
  some_file.close();
  
  // Write norm and radiated power of solution to trace file
  Bulk_mesh_pt->compute_norm(norm);
  Trace_file  << norm << " "  << power << std::endl;
  
 } // end of doc

References oomph::DocInfo::directory(), e(), calibrate::error, MergeRestartFiles::filename, ProblemParameters::get_exact_u(), oomph::PMLFourierDecomposedHelmholtzPowerMonitorElement< ELEMENT >::global_power_contribution(), oomph::DocInfo::number(), oomph::oomph_info, sqrt(), and oomph::Problem_Parameter::Trace_file.

Member Data Documentation

◆ Bulk_mesh_pt

template<class ELEMENT >

TriangleMesh<ELEMENT>* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::Bulk_mesh_pt

private

Pointer to the "bulk" mesh.

◆ Helmholtz_inner_boundary_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::Helmholtz_inner_boundary_mesh_pt

private

Mesh of FaceElements that apply the flux bc on the inner boundary.

◆ PML_bottom_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PML_bottom_mesh_pt

private

Pointer to the bottom PML mesh.

◆ PML_bottom_right_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PML_bottom_right_mesh_pt

private

Pointer to the bottom right corner PML mesh.

◆ PML_right_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PML_right_mesh_pt

private

Pointer to the right PML mesh.

◆ PML_top_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PML_top_mesh_pt

private

Pointer to the top PML mesh.

◆ PML_top_right_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PML_top_right_mesh_pt

private

Pointer to the top right corner PML mesh.

◆ Power_monitor_mesh_pt

template<class ELEMENT >

Mesh* PMLFourierDecomposedHelmholtzProblem< ELEMENT >::Power_monitor_mesh_pt

private

Pointer to mesh that stores the power monitor elements.

◆ Trace_file

template<class ELEMENT >

ofstream PMLFourierDecomposedHelmholtzProblem< ELEMENT >::Trace_file

private

Trace file.

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

oscillating_sphere.cc

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class PMLFourierDecomposedHelmholtzProblem< ELEMENT >

Constructor & Destructor Documentation

◆ PMLFourierDecomposedHelmholtzProblem()

◆ ~PMLFourierDecomposedHelmholtzProblem()

Member Function Documentation

◆ actions_after_newton_solve()

◆ actions_before_newton_solve()

◆ apply_zero_dirichlet_boundary_conditions()

◆ complete_problem_setup()

◆ create_flux_elements_on_inner_boundary()

◆ create_pml_meshes()

◆ create_power_monitor_mesh()

◆ delete_face_elements()

◆ doc_solution()

Member Data Documentation

◆ Bulk_mesh_pt

◆ Helmholtz_inner_boundary_mesh_pt

◆ PML_bottom_mesh_pt

◆ PML_bottom_right_mesh_pt

◆ PML_right_mesh_pt

◆ PML_top_mesh_pt

◆ PML_top_right_mesh_pt

◆ Power_monitor_mesh_pt

◆ Trace_file

template<class ELEMENT>
class PMLFourierDecomposedHelmholtzProblem< ELEMENT >