oomph::HelmholtzDtNMesh< ELEMENT > Class Template Reference

`#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 ()
Compute and store the gamma integral at all integration points of the constituent elements. More...

void 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. More...

Vector< std::complex< double > > & gamma_at_gauss_point (FiniteElement *el_pt)
Gamma integral evaluated at Gauss points for specified element. More...

Vector< std::map< unsigned,
std::complex< double > > > &
d_gamma_at_gauss_point (FiniteElement *el_pt)
Derivative of Gamma integral w.r.t global unknown, evaluated at Gauss points for specified element. More...

unsigned & nfourier_terms ()
Number of Fourier terms used in the computation of the gamma integral. More...

Public Member Functions inherited from oomph::Mesh
void resize_halo_nodes ()
Helper function that resizes halo nodes to the same size as their non-halo counterparts if required. (A discrepancy can arise if a FaceElement that introduces additional unknowns are attached to a bulk element that shares a node with a haloed element. In that case the joint node between haloed and non-haloed element is resized on that processor but not on the one that holds the halo counterpart (because no FaceElement is attached to the halo element) More...

Mesh ()
Default constructor. More...

Mesh (const Vector< Mesh * > &sub_mesh_pt)
Constructor builds combined mesh from the meshes specified. Note: This simply merges the meshes' elements and nodes (ignoring duplicates; no boundary information etc. is created). More...

void merge_meshes (const Vector< Mesh * > &sub_mesh_pt)
Merge meshes. Note: This simply merges the meshes' elements and nodes (ignoring duplicates; no boundary information etc. is created). More...

virtual void setup_boundary_element_info ()
Interface for function that is used to setup the boundary information (Empty virtual function – implement this for specific Mesh classes) More...

virtual void setup_boundary_element_info (std::ostream &outfile)
Setup lookup schemes which establish whic elements are located next to mesh's boundaries. Doc in outfile (if it's open). (Empty virtual function – implement this for specific Mesh classes) More...

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)
Output boundary coordinates on boundary b – template argument specifies the bulk element type (needed to create FaceElement of appropriate type on mesh boundary). More...

virtual void scale_mesh (const double &factor)
Scale all nodal coordinates by given factor. Virtual so it can be overloaded in SolidMesh class where it also re-assigns the Lagrangian coordinates. More...

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

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

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

void flush_element_and_node_storage ()
Flush storage for elements and nodes by emptying the vectors that store the pointers to them. This is useful if a particular mesh is only built to generate a small part of a bigger mesh. Once the elements and nodes have been created, they are typically copied into the new mesh and the auxiliary mesh can be deleted. However, if we simply call the destructor of the auxiliary mesh, it will also wipe out the nodes and elements, because it still "thinks" it's in charge of these... More...

void flush_element_storage ()
Flush storage for elements (only) by emptying the vectors that store the pointers to them. This is useful if a particular mesh is only built to generate a small part of a bigger mesh. Once the elements and nodes have been created, they are typically copied into the new mesh and the auxiliary mesh can be deleted. However, if we simply call the destructor of the auxiliary mesh, it will also wipe out the nodes and elements, because it still "thinks" it's in charge of these... More...

void flush_node_storage ()
Flush storage for nodes (only) by emptying the vectors that store the pointers to them. More...

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

Nodenode_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...

GeneralisedElementelement_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...

FiniteElementfinite_element_pt (const unsigned &e) const
Upcast (downcast?) to FiniteElement (needed to access FiniteElement member functions). More...

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

Nodeboundary_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)
Remove all information about nodes stored on the b-th boundary of the mesh. More...

void remove_boundary_node (const unsigned &b, Node *const &node_pt)

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...

Add a (pointer to a) node to the mesh. More...

Add a (pointer to) an element to the mesh. More...

virtual void node_update (const bool &update_all_solid_nodes=false)
Update nodal positions in response to changes in the domain shape. Uses the FiniteElement::get_x(...) function for FiniteElements and doesn't do anything for other element types. If a MacroElement pointer has been set for a FiniteElement, the MacroElement representation is used to update the nodal positions; if not get_x(...) uses the FE interpolation and thus leaves the nodal positions unchanged. Virtual, so it can be overloaded by specific meshes, such as AlgebraicMeshes or SpineMeshes. Generally, this function updates the position of all nodes in response to changes in the boundary position. However, we ignore all SolidNodes since their position is computed as part of the solution – unless the bool flag is set to true. Such calls are typically made when the initial mesh is created and/or after a mesh has been refined repeatedly before the start of the computation. More...

virtual void reorder_nodes (const bool &use_old_ordering=true)
Re-order nodes in the order in which they appear in elements – can be overloaded for more efficient re-ordering. More...

virtual void get_node_reordering (Vector< Node * > &reordering, const bool &use_old_ordering=true) const
Get a reordering of the nodes in the order in which they appear in elements – can be overloaded for more efficient re-ordering. More...

template<class BULK_ELEMENT , template< class > class FACE_ELEMENT>
void build_face_mesh (const unsigned &b, Mesh *const &face_mesh_pt)
Constuct a Mesh of FACE_ELEMENTs along the b-th boundary of the mesh (which contains elements of type BULK_ELEMENT) More...

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)
Determine max and min area for all FiniteElements in the mesh (non-FiniteElements are ignored) More...

double total_size ()
Determine the sum of all "sizes" of the FiniteElements in the mesh (non-FiniteElements are ignored). This gives the length/area/volume occupied by the mesh. More...

void check_inverted_elements (bool &mesh_has_inverted_elements, std::ofstream &inverted_element_file)
Check for inverted elements and report outcome in boolean variable. This visits all elements at their integration points and checks if the Jacobian of the mapping between local and global coordinates is positive – using the same test that would be carried out (but only in PARANOID mode) during the assembly of the elements' Jacobian matrices. Inverted elements are output in inverted_element_file (if the stream is open). More...

void check_inverted_elements (bool &mesh_has_inverted_elements)
Check for inverted elements and report outcome. More...

unsigned check_for_repeated_nodes (const double &epsilon=1.0e-12)
Check for repeated nodes within a given spatial tolerance. Return (0/1) for (pass/fail). More...

Vector< Node * > prune_dead_nodes ()
Prune nodes. Nodes that have been marked as obsolete are removed from the mesh (and its boundary-node scheme). Returns vector of pointers to deleted nodes. More...

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...

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

Nodeget_some_non_boundary_node () const
Find a node not on any boundary in mesh_pt (useful for pinning a single node in a purely Neumann problem so that it is fully determined). More...

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
For the e-th finite element on boundary b, return int to indicate the face_index of the face adjacent to the boundary. This is consistent with input required during the generation of FaceElements. More...

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...

Read solution from restart file. More...

void output_paraview (std::ofstream &file_out, const unsigned &nplot) const
Output in paraview format into specified file. Breaks up each element into sub-elements for plotting purposes. We assume that all elements are of the same type (fct will break break (in paranoid mode) if paraview output fcts of the elements are inconsistent). More...

void output_fct_paraview (std::ofstream &file_out, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
Output in paraview format into specified file. Breaks up each element into sub-elements for plotting purposes. We assume that all elements are of the same type (fct will break break (in paranoid mode) if paraview output fcts of the elements are inconsistent). More...

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)
Output a given time-dep. Vector function at f(n_plot) points in each element. More...

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)

virtual void output_boundary_coordinates (const unsigned &b, std::ostream &outfile)

void output_boundary_coordinates (const unsigned &b, const std::string &output_filename)

void output_boundaries_coordinates (std::ostream &outfile)

void output_boundaries_coordinates (const std::string &output_filename)

void assign_initial_values_impulsive ()

void shift_time_values ()
Shift time-dependent data along for next timestep: Deal with nodal Data/positions and the element's internal Data. More...

void calculate_predictions ()
Calculate predictions for all Data and positions associated with the mesh, usually used in adaptive time-stepping. More...

void set_nodal_and_elemental_time_stepper (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
Set the timestepper associated with all nodal and elemental data stored in the mesh. More...

virtual void set_mesh_level_time_stepper (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
Function that can be used to set any additional timestepper data stored at the Mesh (as opposed to nodal and elemental) levels. This is virtual so that it can be overloaded in the appropriate Meshes. Examples include the SpineMeshes and adaptive triangle and tet meshes. More...

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)
Set the timestepper associated with the internal data stored within elements in the meah. More...

virtual void compute_norm (double &norm)
Compute norm of solution by summing contributions of compute_norm(...) for all constituent elements in the mesh. What that norm means depends on what's defined in the element's function; may need to take the square root afterwards if the elements compute the square of the L2 norm, say. More...

virtual void compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
Plot error when compared against a given exact solution. Also returns the norm of the error and that of the exact solution. More...

virtual void compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
Plot error when compared against a given time-depdendent exact solution. Also returns the norm of the error and that of the exact solution. More...

virtual void compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
Plot error when compared against a given time-depdendent exact solution. Also returns the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
Plot error when compared against a given time-depdendent exact solution. Also returns the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

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

OomphCommunicatorcommunicator_pt () const

void set_communicator_pt (OomphCommunicator *comm_pt)

void set_keep_all_elements_as_halos ()
Call this function to keep all the elements as halo elements. More...

void unset_keep_all_elements_as_halos ()
Calll this function to unset the flag that keeps all elements in the mesh as halo elements. More...

virtual void distribute (OomphCommunicator *comm_pt, const Vector< unsigned > &element_domain, Vector< GeneralisedElement * > &deleted_element_pt, DocInfo &doc_info, const bool &report_stats, const bool &overrule_keep_as_halo_element_status)
Distribute the problem and doc; make this virtual to allow overloading for particular meshes where further work is required. Add to vector of pointers to deleted elements. More...

void distribute (OomphCommunicator *comm_pt, const Vector< unsigned > &element_domain, Vector< GeneralisedElement * > &deleted_element_pt, const bool &report_stats=false)
Distribute the problem Add to vector of pointers to deleted elements. More...

void prune_halo_elements_and_nodes (Vector< GeneralisedElement * > &deleted_element_pt, const bool &report_stats=false)
(Irreversibly) prune halo(ed) elements and nodes, usually after another round of refinement, to get rid of excessively wide halo layers. Note that the current mesh will be now regarded as the base mesh and no unrefinement relative to it will be possible once this function has been called. More...

void prune_halo_elements_and_nodes (Vector< GeneralisedElement * > &deleted_element_pt, DocInfo &doc_info, const bool &report_stats)
(Irreversibly) prune halo(ed) elements and nodes, usually after another round of refinement, to get rid of excessively wide halo layers. Note that the current mesh will be now regarded as the base mesh and no unrefinement relative to it will be possible once this function has been called. More...

void get_efficiency_of_mesh_distribution (double &av_efficiency, double &max_efficiency, double &min_efficiency)
Get efficiency of mesh distribution: In an ideal distribution without halo overhead, each processor would only hold its own elements. Efficieny per processor = (number of non-halo elements)/ (total number of elements). More...

void doc_mesh_distribution (DocInfo &doc_info)
Doc the mesh distribution, to be processed with tecplot macros. More...

void check_halo_schemes (DocInfo &doc_info, double &max_permitted_error_for_halo_check)
Check halo and shared schemes on the mesh. More...

virtual void classify_halo_and_haloed_nodes (DocInfo &doc_info, const bool &report_stats)
Classify the halo and haloed nodes in the mesh. Virtual so it can be overloaded to perform additional functionality (such as synchronising hanging nodes) in refineable meshes, say. More...

virtual void classify_halo_and_haloed_nodes (const bool &report_stats=false)

void synchronise_shared_nodes (const bool &report_stats)
Synchronise shared node lookup schemes to cater for the the case where: (1) a certain node on the current processor is halo with proc p (i.e. its non-halo counterpart lives on processor p) (2) that node is also exists (also as a halo) on another processor (q, say) where its non-halo counter part is also known to be on processor p. However, without calling this function the current processor does not necessarily know that it shares a node with processor q. This information can be required, e.g. when synchronising hanging node schemes over all processors. More...

void get_all_halo_data (std::map< unsigned, double * > &map_of_halo_data)
Get all the halo data stored in the mesh and add pointers to the data to the map, indexed by global equation number. More...

Vector< GeneralisedElement * > halo_element_pt (const unsigned &p)
Return vector of halo elements in this Mesh whose non-halo counterpart is held on processor p. More...

Vector< GeneralisedElement * > haloed_element_pt (const unsigned &p)
Return vector of haloed elements in this Mesh whose haloing counterpart is held on processor p. More...

unsigned nnon_halo_element ()
Total number of non-halo elements in this mesh (Costly call computes result on the fly) More...

unsigned nroot_halo_element ()
Total number of root halo elements in this Mesh. More...

unsigned nroot_halo_element (const unsigned &p)
Number of root halo elements in this Mesh whose non-halo counterpart is held on processor p. More...

Vector< GeneralisedElement * > root_halo_element_pt (const unsigned &p)
Vector of pointers to root halo elements in this Mesh whose non-halo counterpart is held on processor p. More...

GeneralisedElement *& root_halo_element_pt (const unsigned &p, const unsigned &e)
Access fct to the e-th root halo element in this Mesh whose non-halo counterpart is held on processor p. More...

void add_root_halo_element_pt (const unsigned &p, GeneralisedElement *&el_pt)
Add root halo element whose non-halo counterpart is held on processor p to this Mesh. More...

unsigned nhalo_node ()
Total number of halo nodes in this Mesh. More...

unsigned nhalo_node (const unsigned &p)
Number of halo nodes in this Mesh whose non-halo counterpart is held on processor p. More...

void add_halo_node_pt (const unsigned &p, Node *&nod_pt)
Add halo node whose non-halo counterpart is held on processor p to the storage scheme for halo nodes. More...

Nodehalo_node_pt (const unsigned &p, const unsigned &j)
Access fct to the j-th halo node in this Mesh whose non-halo counterpart is held on processor p. More...

unsigned nroot_haloed_element ()
Total number of root haloed elements in this Mesh. More...

unsigned nroot_haloed_element (const unsigned &p)
Number of root haloed elements in this Mesh whose non-halo counterpart is held on processor p. More...

Vector< GeneralisedElement * > root_haloed_element_pt (const unsigned &p)
Vector of pointers to root haloed elements in this Mesh whose non-halo counterpart is held on processor p. More...

GeneralisedElement *& root_haloed_element_pt (const unsigned &p, const unsigned &e)
Access fct to the e-th root haloed element in this Mesh whose non-halo counterpart is held on processor p. More...

void add_root_haloed_element_pt (const unsigned &p, GeneralisedElement *&el_pt)
Add root haloed element whose non-halo counterpart is held on processor p to the storage scheme for haloed elements. Note: This does not add the element to the storage scheme for elements as it's understood to naturally live on this processor anyway! More...

unsigned nhaloed_node ()
Total number of haloed nodes in this Mesh. More...

unsigned nhaloed_node (const unsigned &p)
Number of haloed nodes in this Mesh whose haloed counterpart is held on processor p. More...

Nodehaloed_node_pt (const unsigned &p, const unsigned &j)
Access fct to the j-th haloed node in this Mesh whose halo counterpart is held on processor p. More...

void add_haloed_node_pt (const unsigned &p, Node *&nod_pt)
Add haloed node whose halo counterpart is held on processor p to the storage scheme for haloed nodes. More...

void disable_resizing_of_halo_nodes ()
Function to suppress resizing of halo nodes – optmisation but call it at your own risk! More...

void enable_resizing_of_halo_nodes ()
Function to (re-)enable resizing of halo nodes – this returns things to the default behaviour. More...

void disable_output_of_halo_elements ()
Function to disable halo element output. More...

void enable_output_of_halo_elements ()
Function to enable halo element output. More...

unsigned nshared_node ()
Total number of shared nodes in this Mesh. More...

void doc_shared_nodes ()
Doc shared nodes. More...

unsigned nshared_node (const unsigned &p)
Number of shared nodes in this Mesh who have a counterpart on processor p. More...

Nodeshared_node_pt (const unsigned &p, const unsigned &j)
Access fct to the j-th shared node in this Mesh who has a counterpart on processor p. More...

void get_shared_node_pt (const unsigned &p, Vector< Node * > &shared_node_pt)
Get vector of pointers to shared nodes with processor p. Required for faster search in Missing_masters_functions::add_external_haloed_node_helper() and Missing_masters_functions::add_external_haloed_master_node_helper() More...

void add_shared_node_pt (const unsigned &p, Node *&nod_pt)
Add shared node whose counterpart is held on processor p to the storage scheme for shared nodes. (NB: ensure that this routine is called twice, once for each process) More...

void get_halo_node_stats (double &av_number, unsigned &max_number, unsigned &min_number)
Get halo node stats for this distributed mesh: Average/max/min number of halo nodes over all processors. Careful: Involves MPI Broadcasts and must therefore be called on all processors! More...

void get_haloed_node_stats (double &av_number, unsigned &max_number, unsigned &min_number)
Get haloed node stats for this distributed mesh: Average/max/min number of haloed nodes over all processors. Careful: Involves MPI Broadcasts and must therefore be called on all processors! More...

void output_external_halo_elements (std::ostream &outfile, const unsigned &n_plot=5)
Output all external halo elements. More...

void output_external_halo_elements (const unsigned &p, std::ostream &outfile, const unsigned &n_plot=5)
Output all external halo elements with processor p. More...

void output_external_haloed_elements (std::ostream &outfile, const unsigned &n_plot=5)
Output all external haloed elements. More...

void output_external_haloed_elements (const unsigned &p, std::ostream &outfile, const unsigned &n_plot=5)
Output all external haloed elements with processor p. More...

unsigned nexternal_halo_element ()
Total number of external halo elements in this Mesh. More...

unsigned nexternal_halo_element (const unsigned &p)
Number of external halo elements in this Mesh whose non-halo counterpart is held on processor p. More...

GeneralisedElement *& external_halo_element_pt (const unsigned &p, const unsigned &e)
Access fct to the e-th external halo element in this Mesh whose non-halo counterpart is held on processor p. More...

void add_external_halo_element_pt (const unsigned &p, GeneralisedElement *&el_pt)
Add external halo element whose non-halo counterpart is held on processor p to this Mesh. More...

unsigned nexternal_haloed_element ()
Total number of external haloed elements in this Mesh. More...

unsigned nexternal_haloed_element (const unsigned &p)
Number of external haloed elements in this Mesh whose non-halo counterpart is held on processor p. More...

GeneralisedElement *& external_haloed_element_pt (const unsigned &p, const unsigned &e)
Access fct to the e-th external haloed element in this Mesh whose non-halo counterpart is held on processor p. More...

unsigned add_external_haloed_element_pt (const unsigned &p, GeneralisedElement *&el_pt)
Add external haloed element whose non-halo counterpart is held on processor p to the storage scheme for haloed elements. More...

unsigned nexternal_halo_node ()
Total number of external halo nodes in this Mesh. More...

void get_external_halo_node_pt (Vector< Node * > &external_halo_node_pt)
Get vector of pointers to all external halo nodes. More...

unsigned nexternal_halo_node (const unsigned &p)
Number of external halo nodes in this Mesh whose non-halo (external) counterpart is held on processor p. More...

void add_external_halo_node_pt (const unsigned &p, Node *&nod_pt)
Add external halo node whose non-halo (external) counterpart is held on processor p to the storage scheme for halo nodes. More...

Node *& external_halo_node_pt (const unsigned &p, const unsigned &j)
Access fct to the j-th external halo node in this Mesh whose non-halo external counterpart is held on processor p. More...

Vector< Node * > external_halo_node_pt (const unsigned &p)
Access fct to vector of external halo node in this Mesh whose non-halo external counterpart is held on processor p. (read only) More...

void set_external_halo_node_pt (const unsigned &p, const Vector< Node * > &external_halo_node_pt)
Set vector of external halo node in this Mesh whose non-halo external counterpart is held on processor p. More...

void null_external_halo_node (const unsigned &p, Node *nod_pt)
Null out specified external halo node (used when deleting duplicates) More...

void remove_null_pointers_from_external_halo_node_storage ()
Consolidate external halo node storage by removing nulled out pointes in external halo and haloed schemes. More...

unsigned nexternal_haloed_node ()
Total number of external haloed nodes in this Mesh. More...

unsigned nexternal_haloed_node (const unsigned &p)
Number of external haloed nodes in this Mesh whose halo (external) counterpart is held on processor p. More...

Node *& external_haloed_node_pt (const unsigned &p, const unsigned &j)
Access fct to the j-th external haloed node in this Mesh whose halo external counterpart is held on processor p. More...

unsigned add_external_haloed_node_pt (const unsigned &p, Node *&nod_pt)
Add external haloed node whose halo (external) counterpart is held on processor p to the storage scheme for haloed nodes. More...

Vector< Node * > external_haloed_node_pt (const unsigned &p)
Access fct to vector of external haloed node in this Mesh whose halo external counterpart is held on processor p. (read only) More...

void set_external_haloed_node_pt (const unsigned &p, const Vector< Node * > &external_haloed_node_pt)
Set vector of external haloed node in this Mesh whose halo external counterpart is held on processor p. More...

std::set< int > external_halo_proc ()
Return the set of processors that hold external halo nodes. This is required to avoid having to pass a communicator into the node_update functions for Algebraic-based and MacroElement-based Meshes. More...

virtual void create_shared_boundaries (OomphCommunicator *comm_pt, const Vector< unsigned > &element_domain, const Vector< GeneralisedElement * > &backed_up_el_pt, const Vector< FiniteElement * > &backed_up_f_el_pt, std::map< Data *, std::set< unsigned > > &processors_associated_with_data, const bool &overrule_keep_as_halo_element_status)
Creates the shared boundaries, only used in unstructured meshes In this case with the "TriangleMesh" class. More...

virtual unsigned try_to_add_root_haloed_element_pt (const unsigned &p, GeneralisedElement *&el_pt)

virtual unsigned try_to_add_haloed_node_pt (const unsigned &p, Node *&nod_pt)

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

## Private Attributes

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

std::map< FiniteElement
*, Vector< std::complex
< double > > >
Gamma_at_gauss_point
Container to store the gamma integral for given Gauss point and element. More...

std::map< FiniteElement
*, Vector< std::map< unsigned,
std::complex< double > > > >
D_Gamma_at_gauss_point
Container to store the derivate of Gamma integral w.r.t global unknown evaluated at Gauss points for specified element. More...

Public Types inherited from oomph::Mesh
typedef void(FiniteElement::* SteadyExactSolutionFctPt )(const Vector< double > &x, Vector< double > &soln)
Typedef for function pointer to function that computes steady exact solution. More...

typedef void(FiniteElement::* UnsteadyExactSolutionFctPt )(const double &time, const Vector< double > &x, Vector< double > &soln)
Typedef for function pointer to function that computes unsteady exact solution. More...

Public Attributes inherited from oomph::Mesh
bool Output_halo_elements
Bool for output of halo elements. More...

Static Public Attributes inherited from oomph::Mesh
Default Steady Timestepper, to be used in default arguments to Mesh constructors. More...

Boolean used to control warning about empty mesh level timestepper function. More...

Protected Member Functions inherited from oomph::Mesh
void setup_shared_node_scheme ()
Setup shared node scheme. More...

unsigned long assign_global_eqn_numbers (Vector< double * > &Dof_pt)
Assign the global equation numbers in the Data stored at the nodes and also internal element Data. Also, build (via push_back) the Vector of pointers to the dofs (variables). More...

void describe_dofs (std::ostream &out, const std::string &current_string) const
Function to describe the dofs of the Mesh. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

void describe_local_dofs (std::ostream &out, const std::string &current_string) const
Function to describe the local dofs of the elements. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

void assign_local_eqn_numbers (const bool &store_local_dof_pt)
Assign the local equation numbers in all elements If the boolean argument is true then also store pointers to dofs. More...

void convert_to_boundary_node (Node *&node_pt, const Vector< FiniteElement * > &finite_element_pt)
A function that upgrades an ordinary node to a boundary node We shouldn't ever really use this, but it does make life that bit easier for the lazy mesh writer. The pointer to the node is replaced by a pointer to the new boundary node in all element look-up schemes and in the mesh's Node_pt vector. The new node is also addressed by node_pt on return from the function. More...

void convert_to_boundary_node (Node *&node_pt)

Protected Attributes inherited from oomph::Mesh
Vector< Vector< Node * > > Boundary_node_pt
Vector of Vector of pointers to nodes on the boundaries: Boundary_node_pt(b,n). Note that this is private to force the use of the add_boundary_node() function, which ensures that the reverse look-up schemes for the nodes are set up. More...

bool Lookup_for_elements_next_boundary_is_setup

Vector< Vector< FiniteElement * > > Boundary_element_pt
Vector of Vector of pointers to elements on the boundaries: Boundary_element_pt(b,e) More...

Vector< Vector< int > > Face_index_at_boundary
For the e-th finite element on boundary b, this is the index of the face that lies along that boundary. More...

std::map< unsigned, Vector
< GeneralisedElement * > >
Root_halo_element_pt
Map of vectors holding the pointers to the root halo elements. More...

std::map< unsigned, Vector
< GeneralisedElement * > >
Root_haloed_element_pt
Map of vectors holding the pointers to the root haloed elements. More...

std::map< unsigned, Vector
< Node * > >
Halo_node_pt
Map of vectors holding the pointers to the halo nodes. More...

std::map< unsigned, Vector
< Node * > >
Haloed_node_pt
Map of vectors holding the pointers to the haloed nodes. More...

std::map< unsigned, Vector
< Node * > >
Shared_node_pt

OomphCommunicatorComm_pt
Pointer to communicator – set to NULL if mesh is not distributed. More...

std::map< unsigned, Vector
< GeneralisedElement * > >
External_halo_element_pt
Map of vectors holding the pointers to the external halo elements. More...

std::map< unsigned, Vector
< GeneralisedElement * > >
External_haloed_element_pt
Map of vectors holding the pointers to the external haloed elements. More...

std::map< unsigned, Vector
< Node * > >
External_halo_node_pt
Map of vectors holding the pointers to the external halo nodes. More...

std::map< unsigned, Vector
< Node * > >
External_haloed_node_pt
Map of vectors holding the pointers to the external haloed nodes. More...

bool Keep_all_elements_as_halos
bool to indicate whether to keep all elements in a mesh as halos or not More...

bool Resize_halo_nodes_not_required
Set this to true to suppress resizing of halo nodes (at your own risk!) More...

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
Vector of boolean data that indicates whether the boundary coordinates have been set for the boundary. More...

## 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

Definition at line 569 of file helmholtz_bc_elements.h.

## Constructor & Destructor Documentation

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

Definition at line 575 of file helmholtz_bc_elements.h.

## Member Function Documentation

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.

================================================================================================================================

Definition at line 1629 of file helmholtz_bc_elements.h.

template<class ELEMENT>
 Vector > >& 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.

Definition at line 599 of file helmholtz_bc_elements.h.

template<class ELEMENT>
 Vector >& oomph::HelmholtzDtNMesh< ELEMENT >::gamma_at_gauss_point ( FiniteElement * el_pt )
inline

Gamma integral evaluated at Gauss points for specified element.

Definition at line 591 of file helmholtz_bc_elements.h.

template<class ELEMENT>
 unsigned& oomph::HelmholtzDtNMesh< ELEMENT >::nfourier_terms ( )
inline

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

Definition at line 612 of file helmholtz_bc_elements.h.

template<class ELEMENT>
 double& oomph::HelmholtzDtNMesh< ELEMENT >::outer_radius ( )
inline

Definition at line 605 of file helmholtz_bc_elements.h.

template<class ELEMENT >
 void oomph::HelmholtzDtNMesh< ELEMENT >::setup_gamma ( )

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

of the mesh's constituent elements

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

Definition at line 1688 of file helmholtz_bc_elements.h.

## Member Data Documentation

template<class ELEMENT>
 std::map > > > oomph::HelmholtzDtNMesh< ELEMENT >::D_Gamma_at_gauss_point
private

Container to store the derivate of Gamma integral w.r.t global unknown evaluated at Gauss points for specified element.

Definition at line 634 of file helmholtz_bc_elements.h.

template<class ELEMENT>
 std::map > > oomph::HelmholtzDtNMesh< ELEMENT >::Gamma_at_gauss_point
private

Container to store the gamma integral for given Gauss point and element.

Definition at line 628 of file helmholtz_bc_elements.h.

template<class ELEMENT>
 unsigned oomph::HelmholtzDtNMesh< ELEMENT >::Nfourier_terms
private

Nbr of Fourier terms used in the Gamma computation.

Definition at line 623 of file helmholtz_bc_elements.h.

Referenced by oomph::HelmholtzDtNMesh< ELEMENT >::nfourier_terms().

template<class ELEMENT>