#include <helmholtz_bc_elements.h>

Inheritance diagram for oomph::HelmholtzDtNMesh< ELEMENT >:

Public Member Functions
	HelmholtzDtNMesh (const double &outer_radius, const unsigned &nfourier_terms)

void	setup_gamma ()
	of the mesh's constituent elements More...

void	compute_fourier_components (Vector< std::complex< double >> &a_coeff_pos, Vector< std::complex< double >> &a_coeff_neg)

Vector< std::complex< double > > &	gamma_at_gauss_point (FiniteElement *el_pt)

Vector< std::map< unsigned, std::complex< double > > > &	d_gamma_at_gauss_point (FiniteElement *el_pt)

double &	outer_radius ()
	The outer radius. More...

unsigned &	nfourier_terms ()

Public Member Functions inherited from oomph::Mesh
	Mesh ()
	Default constructor. More...

	Mesh (const Vector< Mesh * > &sub_mesh_pt)

void	merge_meshes (const Vector< Mesh * > &sub_mesh_pt)

virtual void	setup_boundary_element_info ()

virtual void	setup_boundary_element_info (std::ostream &outfile)

virtual void	reset_boundary_element_info (Vector< unsigned > &ntmp_boundary_elements, Vector< Vector< unsigned >> &ntmp_boundary_elements_in_region, Vector< FiniteElement * > &deleted_elements)
	Virtual function to perform the reset boundary elements info rutines. More...

template<class BULK_ELEMENT >
void	doc_boundary_coordinates (const unsigned &b, std::ofstream &the_file)

virtual void	scale_mesh (const double &factor)

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

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

virtual	~Mesh ()
	Virtual Destructor to clean up all memory. More...

void	flush_element_and_node_storage ()

void	flush_element_storage ()

void	flush_node_storage ()

Node *&	node_pt (const unsigned long &n)
	Return pointer to global node n. More...

Node *	node_pt (const unsigned long &n) const
	Return pointer to global node n (const version) More...

GeneralisedElement *&	element_pt (const unsigned long &e)
	Return pointer to element e. More...

GeneralisedElement *	element_pt (const unsigned long &e) const
	Return pointer to element e (const version) More...

const Vector< GeneralisedElement * > &	element_pt () const
	Return reference to the Vector of elements. More...

Vector< GeneralisedElement * > &	element_pt ()
	Return reference to the Vector of elements. More...

FiniteElement *	finite_element_pt (const unsigned &e) const

Node *&	boundary_node_pt (const unsigned &b, const unsigned &n)
	Return pointer to node n on boundary b. More...

Node *	boundary_node_pt (const unsigned &b, const unsigned &n) const
	Return pointer to node n on boundary b. More...

void	set_nboundary (const unsigned &nbound)
	Set the number of boundaries in the mesh. More...

void	remove_boundary_nodes ()
	Clear all pointers to boundary nodes. More...

void	remove_boundary_nodes (const unsigned &b)

void	remove_boundary_node (const unsigned &b, Node *const &node_pt)
	Remove a node from the boundary b. More...

void	add_boundary_node (const unsigned &b, Node *const &node_pt)
	Add a (pointer to) a node to the b-th boundary. More...

void	copy_boundary_node_data_from_nodes ()

bool	boundary_coordinate_exists (const unsigned &i) const
	Indicate whether the i-th boundary has an intrinsic coordinate. More...

unsigned long	nelement () const
	Return number of elements in the mesh. More...

unsigned long	nnode () const
	Return number of nodes in the mesh. More...

unsigned	ndof_types () const
	Return number of dof types in mesh. More...

unsigned	elemental_dimension () const
	Return number of elemental dimension in mesh. More...

unsigned	nodal_dimension () const
	Return number of nodal dimension in mesh. More...

void	add_node_pt (Node *const &node_pt)
	Add a (pointer to a) node to the mesh. More...

void	add_element_pt (GeneralisedElement *const &element_pt)
	Add a (pointer to) an element to the mesh. More...

virtual void	node_update (const bool &update_all_solid_nodes=false)

virtual void	reorder_nodes (const bool &use_old_ordering=true)

virtual void	get_node_reordering (Vector< Node * > &reordering, const bool &use_old_ordering=true) const

template<class BULK_ELEMENT , template< class > class FACE_ELEMENT>
void	build_face_mesh (const unsigned &b, Mesh *const &face_mesh_pt)

unsigned	self_test ()
	Self-test: Check elements and nodes. Return 0 for OK. More...

void	max_and_min_element_size (double &max_size, double &min_size)

double	total_size ()

void	check_inverted_elements (bool &mesh_has_inverted_elements, std::ofstream &inverted_element_file)

void	check_inverted_elements (bool &mesh_has_inverted_elements)

unsigned	check_for_repeated_nodes (const double &epsilon=1.0e-12)

Vector< Node * >	prune_dead_nodes ()

unsigned	nboundary () const
	Return number of boundaries. More...

unsigned long	nboundary_node (const unsigned &ibound) const
	Return number of nodes on a particular boundary. More...

FiniteElement *	boundary_element_pt (const unsigned &b, const unsigned &e) const
	Return pointer to e-th finite element on boundary b. More...

Node *	get_some_non_boundary_node () const

unsigned	nboundary_element (const unsigned &b) const
	Return number of finite elements that are adjacent to boundary b. More...

int	face_index_at_boundary (const unsigned &b, const unsigned &e) const

virtual void	dump (std::ofstream &dump_file, const bool &use_old_ordering=true) const
	Dump the data in the mesh into a file for restart. More...

void	dump (const std::string &dump_file_name, const bool &use_old_ordering=true) const
	Dump the data in the mesh into a file for restart. More...

virtual void	read (std::ifstream &restart_file)
	Read solution from restart file. More...

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const

void	output_fct_paraview (std::ofstream &file_out, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const

void	output_fct_paraview (std::ofstream &file_out, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

void	output (std::ostream &outfile)
	Output for all elements. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output at f(n_plot) points in each element. More...

void	output (FILE *file_pt)
	Output for all elements (C-style output) More...

void	output (FILE *file_pt, const unsigned &nplot)
	Output at f(n_plot) points in each element (C-style output) More...

void	output (const std::string &output_filename)
	Output for all elements. More...

void	output (const std::string &output_filename, const unsigned &n_plot)
	Output at f(n_plot) points in each element. More...

void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt)
	Output a given Vector function at f(n_plot) points in each element. More...

void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt)

void	output_boundaries (std::ostream &outfile)
	Output the nodes on the boundaries (into separate tecplot zones) More...

void	output_boundaries (const std::string &output_filename)

void	assign_initial_values_impulsive ()
	Assign initial values for an impulsive start. More...

void	shift_time_values ()

void	calculate_predictions ()

void	set_nodal_and_elemental_time_stepper (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

virtual void	set_mesh_level_time_stepper (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

void	set_consistent_pinned_values_for_continuation (ContinuationStorageScheme *const &continuation_stepper_pt)
	Set consistent values for pinned data in continuation. More...

bool	does_pointer_correspond_to_mesh_data (double *const &parameter_pt)
	Does the double pointer correspond to any mesh data. More...

void	set_nodal_time_stepper (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
	Set the timestepper associated with the nodal data in the mesh. More...

void	set_elemental_internal_time_stepper (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

virtual void	compute_norm (double &norm)

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Returns the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)

bool	is_mesh_distributed () const
	Boolean to indicate if Mesh has been distributed. More...

OomphCommunicator *	communicator_pt () const

void	delete_all_external_storage ()
	Wipe the storage for all externally-based elements. More...

Private Attributes
double	Outer_radius
	Outer radius. More...

unsigned	Nfourier_terms
	Nbr of Fourier terms used in the Gamma computation. More...

std::map< FiniteElement *, Vector< std::complex< double > > >	Gamma_at_gauss_point

std::map< FiniteElement *, Vector< std::map< unsigned, std::complex< double > > > >	D_Gamma_at_gauss_point

Additional Inherited Members
Public Types inherited from oomph::Mesh
typedef void(FiniteElement::*	SteadyExactSolutionFctPt) (const Vector< double > &x, Vector< double > &soln)

typedef void(FiniteElement::*	UnsteadyExactSolutionFctPt) (const double &time, const Vector< double > &x, Vector< double > &soln)

Static Public Attributes inherited from oomph::Mesh
static Steady< 0 >	Default_TimeStepper
	The Steady Timestepper. More...

static bool	Suppress_warning_about_empty_mesh_level_time_stepper_function
	Static boolean flag to control warning about mesh level timesteppers. More...

Protected Member Functions inherited from oomph::Mesh
unsigned long	assign_global_eqn_numbers (Vector< double * > &Dof_pt)
	Assign (global) equation numbers to the nodes. More...

void	describe_dofs (std::ostream &out, const std::string &current_string) const

void	describe_local_dofs (std::ostream &out, const std::string &current_string) const

void	assign_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign local equation numbers in all elements. More...

void	convert_to_boundary_node (Node &node_pt, const Vector< FiniteElement > &finite_element_pt)

void	convert_to_boundary_node (Node *&node_pt)

Protected Attributes inherited from oomph::Mesh
Vector< Vector< Node * > >	Boundary_node_pt

bool	Lookup_for_elements_next_boundary_is_setup

Vector< Vector< FiniteElement * > >	Boundary_element_pt

Vector< Vector< int > >	Face_index_at_boundary

Vector< Node * >	Node_pt
	Vector of pointers to nodes. More...

Vector< GeneralisedElement * >	Element_pt
	Vector of pointers to generalised elements. More...

std::vector< bool >	Boundary_coordinate_exists

Detailed Description

template<class ELEMENT>
class oomph::HelmholtzDtNMesh< ELEMENT >

/////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////// ================================================================= Mesh for DtN boundary condition elements – provides functionality to apply Sommerfeld radiation condtion

via DtN BC

Constructor & Destructor Documentation

◆ HelmholtzDtNMesh()

template<class ELEMENT >

oomph::HelmholtzDtNMesh< ELEMENT >::HelmholtzDtNMesh	(	const double &	outer_radius,
		const unsigned &	nfourier_terms
	)

inline

Constructor: Specify radius of outer boundary and number of Fourier terms used in the computation of the gamma integral

       : Outer_radius(outer_radius), Nfourier_terms(nfourier_terms)
     {
     }

Member Function Documentation

◆ compute_fourier_components()

template<class ELEMENT >

void oomph::HelmholtzDtNMesh< ELEMENT >::compute_fourier_components	(	Vector< std::complex< double >> &	a_coeff_pos,
		Vector< std::complex< double >> &	a_coeff_neg
	)

Compute Fourier components of the solution – length of vector indicates number of terms to be computed.

////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// ================================================================ Compute Fourier components of the solution – length of

vector indicates number of terms to be computed.

   {
 #ifdef PARANOID
     if (a_coeff_pos.size() != a_coeff_neg.size())
     {
       std::ostringstream error_stream;
       error_stream << "a_coeff_pos and a_coeff_neg must have "
                    << "the same size. \n";
       throw OomphLibError(
         error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }
 #endif
  
     // Initialise
     unsigned n = a_coeff_pos.size();
     Vector<std::complex<double>> el_a_coeff_pos(n);
     Vector<std::complex<double>> el_a_coeff_neg(n);
     for (unsigned i = 0; i < n; i++)
     {
       a_coeff_pos[i] = std::complex<double>(0.0, 0.0);
       a_coeff_neg[i] = std::complex<double>(0.0, 0.0);
     }
  
     // Loop over elements e
     unsigned nel = this->nelement();
     for (unsigned e = 0; e < nel; e++)
     {
       // Get a pointer to element
       HelmholtzBCElementBase<ELEMENT>* el_pt =
         dynamic_cast<HelmholtzBCElementBase<ELEMENT>*>(this->element_pt(e));
  
       // Compute contribution
       el_pt->compute_contribution_to_fourier_components(el_a_coeff_pos,
                                                         el_a_coeff_neg);
  
       // Add to coefficients
       for (unsigned i = 0; i < n; i++)
       {
         a_coeff_pos[i] += el_a_coeff_pos[i];
         a_coeff_neg[i] += el_a_coeff_neg[i];
       }
     }
   }

References oomph::HelmholtzBCElementBase< ELEMENT >::compute_contribution_to_fourier_components(), e(), i, n, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ d_gamma_at_gauss_point()

template<class ELEMENT >

Vector<std::map<unsigned, std::complex<double> > >& oomph::HelmholtzDtNMesh< ELEMENT >::d_gamma_at_gauss_point ( FiniteElement * el_pt )

inline

Derivative of Gamma integral w.r.t global unknown, evaluated at Gauss points for specified element

     {
       return D_Gamma_at_gauss_point[el_pt];
     }

References oomph::HelmholtzDtNMesh< ELEMENT >::D_Gamma_at_gauss_point.

◆ gamma_at_gauss_point()

template<class ELEMENT >

Vector<std::complex<double> >& oomph::HelmholtzDtNMesh< ELEMENT >::gamma_at_gauss_point ( FiniteElement * el_pt )

inline

Gamma integral evaluated at Gauss points for specified element

     {
       return Gamma_at_gauss_point[el_pt];
     }

References oomph::HelmholtzDtNMesh< ELEMENT >::Gamma_at_gauss_point.

◆ nfourier_terms()

template<class ELEMENT >

unsigned& oomph::HelmholtzDtNMesh< ELEMENT >::nfourier_terms ( )

inline

Number of Fourier terms used in the computation of the gamma integral

     {
       return Nfourier_terms;
     }

References oomph::HelmholtzDtNMesh< ELEMENT >::Nfourier_terms.

◆ outer_radius()

template<class ELEMENT >

double& oomph::HelmholtzDtNMesh< ELEMENT >::outer_radius ( )

inline

The outer radius.

     {
       return Outer_radius;
     }

References oomph::HelmholtzDtNMesh< ELEMENT >::Outer_radius.

◆ setup_gamma()

template<class ELEMENT >

void oomph::HelmholtzDtNMesh< ELEMENT >::setup_gamma

of the mesh's constituent elements

Compute and store the gamma integral at all integration points of the constituent elements.

================================================================ Compute and store the gamma integral and derivates

   {
 #ifdef PARANOID
     {
       // Loop over elements e
       unsigned nel = this->nelement();
       for (unsigned e = 0; e < nel; e++)
       {
         FiniteElement* fe_pt = finite_element_pt(e);
         unsigned nnod = fe_pt->nnode();
         for (unsigned j = 0; j < nnod; j++)
         {
           Node* nod_pt = fe_pt->node_pt(j);
  
           // Extract nodal coordinates from node:
           Vector<double> x(2);
           x[0] = nod_pt->x(0);
           x[1] = nod_pt->x(1);
  
           // Evaluate the radial distance
           double r = sqrt(x[0] * x[0] + x[1] * x[1]);
  
           // Check
           if (Outer_radius == 0.0)
           {
             throw OomphLibError("Outer radius for DtN BC must not be zero!",
                                 OOMPH_CURRENT_FUNCTION,
                                 OOMPH_EXCEPTION_LOCATION);
           }
  
           if (std::fabs((r - this->Outer_radius) / Outer_radius) >
               ToleranceForHelmholtzOuterBoundary::Tol)
           {
             std::ostringstream error_stream;
             error_stream << "Node at " << x[0] << " " << x[1] << " has radius "
                          << r << " which does not "
                          << " agree with \nspecified outer radius "
                          << this->Outer_radius << " within relative tolerance "
                          << ToleranceForHelmholtzOuterBoundary::Tol
                          << ".\nYou can adjust the tolerance via\n"
                          << "ToleranceForHelmholtzOuterBoundary::Tol\n"
                          << "or recompile without PARANOID.\n";
             throw OomphLibError(error_stream.str(),
                                 OOMPH_CURRENT_FUNCTION,
                                 OOMPH_EXCEPTION_LOCATION);
           }
         }
       }
     }
 #endif
  
  
     // Get Helmholtz parameter from bulk element
     HelmholtzDtNBoundaryElement<ELEMENT>* el_pt =
       dynamic_cast<HelmholtzDtNBoundaryElement<ELEMENT>*>(this->element_pt(0));
     double k =
       sqrt(dynamic_cast<ELEMENT*>(el_pt->bulk_element_pt())->k_squared());
  
     // Precompute factors in sum
     Vector<std::complex<double>> h_a(Nfourier_terms), hp_a(Nfourier_terms),
       q(Nfourier_terms);
     Hankel_functions_for_helmholtz_problem::Hankel_first(
       Nfourier_terms, Outer_radius * k, h_a, hp_a);
     for (unsigned i = 0; i < Nfourier_terms; i++)
     {
       q[i] = (k / (2.0 * MathematicalConstants::Pi)) * (hp_a[i] / h_a[i]);
     }
  
     // first loop over elements e
     unsigned nel = this->nelement();
     for (unsigned e = 0; e < nel; e++)
     {
       // Get a pointer to element
       HelmholtzDtNBoundaryElement<ELEMENT>* el_pt =
         dynamic_cast<HelmholtzDtNBoundaryElement<ELEMENT>*>(
           this->element_pt(e));
  
       // Set the value of n_intpt
       const unsigned n_intpt = el_pt->integral_pt()->nweight();
  
       // initialise gamma integral and its derivatives
       Vector<std::complex<double>> gamma_vector(n_intpt,
                                                 std::complex<double>(0.0, 0.0));
       Vector<std::map<unsigned, std::complex<double>>> d_gamma_vector(n_intpt);
  
       // Loop over the integration points
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Allocate and initialise coordinate
         unsigned ndim_local = el_pt->dim();
         Vector<double> x(ndim_local + 1, 0.0);
  
         // Set the Vector to hold local coordinates
         Vector<double> s(ndim_local, 0.0);
         for (unsigned i = 0; i < ndim_local; i++)
         {
           s[i] = el_pt->integral_pt()->knot(ipt, i);
         }
  
         // Get the coordinates of the integration point
         el_pt->interpolated_x(s, x);
  
         // Polar angle
         double phi = atan2(x[1], x[0]);
  
         // Elemental contribution to gamma integral and its derivative
         std::complex<double> gamma_con_p(0.0, 0.0), gamma_con_n(0.0, 0.0);
         std::map<unsigned, std::complex<double>> d_gamma_con_p, d_gamma_con_n;
  
         // loop over the Fourier terms
         for (unsigned nn = 0; nn < Nfourier_terms; nn++)
         {
           // Second loop over the element
           // to evaluate the complete integral
           for (unsigned ee = 0; ee < nel; ee++)
           {
             HelmholtzDtNBoundaryElement<ELEMENT>* eel_pt =
               dynamic_cast<HelmholtzDtNBoundaryElement<ELEMENT>*>(
                 this->element_pt(ee));
  
             // contribution of the positive term in the sum
             eel_pt->compute_gamma_contribution(
               phi, int(nn), gamma_con_p, d_gamma_con_p);
  
             // contribution of the negative term in the sum
             eel_pt->compute_gamma_contribution(
               phi, -int(nn), gamma_con_n, d_gamma_con_n);
  
             unsigned n_node = eel_pt->nnode();
             if (nn == 0)
             {
               gamma_vector[ipt] += q[nn] * gamma_con_p;
               for (unsigned l = 0; l < n_node; l++)
               {
                 // Add the contribution of the real local data
                 int local_unknown_p_real = eel_pt->nodal_local_eqn(
                   l, eel_pt->u_index_helmholtz().real());
                 if (local_unknown_p_real >= 0)
                 {
                   int global_unknown_p_real =
                     eel_pt->eqn_number(local_unknown_p_real);
                   d_gamma_vector[ipt][global_unknown_p_real] +=
                     q[nn] * d_gamma_con_p[global_unknown_p_real];
                 }
  
                 // Add the contribution of the imag local data
                 int local_unknown_p_imag = eel_pt->nodal_local_eqn(
                   l, eel_pt->u_index_helmholtz().imag());
  
                 if (local_unknown_p_imag >= 0)
                 {
                   int global_unknown_p_imag =
                     eel_pt->eqn_number(local_unknown_p_imag);
  
                   d_gamma_vector[ipt][global_unknown_p_imag] +=
                     q[nn] * d_gamma_con_p[global_unknown_p_imag];
                 }
               } // end of loop over the node
             } // End of if
             else
             {
               gamma_vector[ipt] += q[nn] * (gamma_con_p + gamma_con_n);
               for (unsigned l = 0; l < n_node; l++)
               {
                 // Add the contribution of the real local data
                 int local_unknown_real = eel_pt->nodal_local_eqn(
                   l, eel_pt->u_index_helmholtz().real());
                 if (local_unknown_real >= 0)
                 {
                   int global_unknown_real =
                     eel_pt->eqn_number(local_unknown_real);
                   d_gamma_vector[ipt][global_unknown_real] +=
                     q[nn] * (d_gamma_con_p[global_unknown_real] +
                              d_gamma_con_n[global_unknown_real]);
                 }
                 // Add the contribution of the imag local data
                 int local_unknown_imag = eel_pt->nodal_local_eqn(
                   l, eel_pt->u_index_helmholtz().imag());
                 if (local_unknown_imag >= 0)
                 {
                   int global_unknown_imag =
                     eel_pt->eqn_number(local_unknown_imag);
                   d_gamma_vector[ipt][global_unknown_imag] +=
                     q[nn] * (d_gamma_con_p[global_unknown_imag] +
                              d_gamma_con_n[global_unknown_imag]);
                 }
               } // end of loop over the node
             } // End of else
           } // End of second loop over the elements
         } // End of loop over Fourier terms
       } // end of loop over integration point
  
       // Store it in map
       Gamma_at_gauss_point[el_pt] = gamma_vector;
       D_Gamma_at_gauss_point[el_pt] = d_gamma_vector;
  
     } // end of first loop over element
   }