unstructured_two_d_helmholtz.cc

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//LIC// ====================================================================
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//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
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//LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
//LIC// 
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//LIC//====================================================================
// Driver for a specific 2D Helmholtz problem with
// perfectly matched layer treatment for the exterior boundaries
 
#include<fenv.h>
 
#include "math.h"
#include <complex>
 
// Generic routines
#include "generic.h"
 
// The pml Helmholtz equations
#include "pml_helmholtz.h"
 
// The meshes needed in the PML constructions
#include "meshes/triangle_mesh.h"
#include "meshes/rectangular_quadmesh.h"
 
using namespace oomph;
using namespace std;
 
/////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////
 
//===== start_of_namespace=============================================
/// Namespace for the Helmholtz problem parameters
//=====================================================================
namespace GlobalParameters
{
 
 /// Wavenumber (also known as k), k=omega/c
 double Wavenumber = sqrt(50.0);
 
 /// Square of the wavenumber (also known as k^2)
 double K_squared = Wavenumber * Wavenumber;
 
} // end of namespace
 
 
/////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////
 
//========= start_of_problem_class=====================================
/// Problem class to demonstrate use of perfectly matched layers
/// for Helmholtz problems.
//=====================================================================
template<class ELEMENT>
class PMLProblem : public Problem
{
 
public:
 
 /// Constructor
 PMLProblem();
 
 /// Destructor (empty)
 ~PMLProblem(){}
 
 /// Update the problem specs before solve (empty)
 void actions_before_newton_solve(){}
 
 /// Update the problem specs after solve (empty)
 void actions_after_newton_solve(){}
 
 /// Doc the solution. DocInfo object stores flags/labels for where the
 /// output gets written to
 void doc_solution(DocInfo& doc_info);
 
 /// Create PML meshes
 void create_pml_meshes();
 
 // Apply boundary conditions
 void apply_boundary_conditions();
 
#ifdef ADAPTIVE
 
 /// Actions before adapt: Wipe the PML meshes
 void actions_before_adapt();
 
 /// Actions after adapt: Rebuild the PML meshes
 void actions_after_adapt();
 
#endif
 
 
#ifdef ADAPTIVE
 
private:
 
 /// Pointer to the refineable "bulk" mesh
 RefineableTriangleMesh<ELEMENT>* Bulk_mesh_pt;
 
#else
 
private:
 
 /// Pointer to the "bulk" mesh
 TriangleMesh<ELEMENT>* Bulk_mesh_pt;
 
#endif
 
 
 /// Pointer to the right PML mesh
 Mesh* PML_right_mesh_pt;
 
 /// Pointer to the top PML mesh
 Mesh* PML_top_mesh_pt;
 
 /// Pointer to the left PML mesh
 Mesh* PML_left_mesh_pt;
 
 /// Pointer to the bottom PML mesh
 Mesh* PML_bottom_mesh_pt;
 
 /// Pointer to the top right corner PML mesh
 Mesh* PML_top_right_mesh_pt;
 
 /// Pointer to the top left corner PML mesh
 Mesh* PML_top_left_mesh_pt;
 
 /// Pointer to the bottom right corner PML mesh
 Mesh* PML_bottom_right_mesh_pt;
 
 /// Pointer to the bottom left corner PML mesh
 Mesh* PML_bottom_left_mesh_pt;
 
 /// Trace file
 ofstream Trace_file;
 
}; // end of problem class
 
 
 
//=======start_of_constructor=============================================
/// Constructor for Helmholtz problem
//========================================================================
template<class ELEMENT>
PMLProblem<ELEMENT>::PMLProblem()
{
 
 // Open trace file
 Trace_file.open("RESLT/trace.dat");
 
 // Create circle representing inner boundary
 double a=0.2;
 double x_c=0.0;
 double y_c=0.0;
 Circle* inner_circle_pt=new Circle(x_c,y_c,a);
 
 // Outer boundary
 //---------------
 TriangleMeshClosedCurve* outer_boundary_pt=0;
 
 unsigned n_segments = 20;
 Vector<TriangleMeshCurveSection*> outer_boundary_line_pt(4);
 
 // Each polyline only has three vertices, provide storage for their
 // coordinates
 Vector<Vector<double> > vertex_coord(2);
 for(unsigned i=0;i<2;i++)
  {
   vertex_coord[i].resize(2);
  }
 
 // First polyline
 vertex_coord[0][0]=-2.0;
 vertex_coord[0][1]=-2.0;
 vertex_coord[1][0]=-2.0;
 vertex_coord[1][1]=2.0;
 
 // Build the 1st boundary polyline
 unsigned boundary_id=2;
 outer_boundary_line_pt[0] = new TriangleMeshPolyLine(vertex_coord,
                                                      boundary_id);
 
 // Second boundary polyline
 vertex_coord[0][0]=-2.0;
 vertex_coord[0][1]=2.0;
 vertex_coord[1][0]=2.0;
 vertex_coord[1][1]=2.0;
 
 // Build the 2nd boundary polyline
 boundary_id=3;
 outer_boundary_line_pt[1] = new TriangleMeshPolyLine(vertex_coord,
                                                      boundary_id);
 
 // Third boundary polyline
 vertex_coord[0][0]=2.0;
 vertex_coord[0][1]=2.0;
 vertex_coord[1][0]=2.0;
 vertex_coord[1][1]=-2.0;
 
 // Build the 3rd boundary polyline
 boundary_id=4;
 outer_boundary_line_pt[2] = new TriangleMeshPolyLine(vertex_coord,
                                                      boundary_id);
 
 // Fourth boundary polyline
 vertex_coord[0][0]=2.0;
 vertex_coord[0][1]=-2.0;
 vertex_coord[1][0]=-2.0;
 vertex_coord[1][1]=-2.0;
 
 // Build the 4th boundary polyline
 boundary_id=5;
 outer_boundary_line_pt[3] = new TriangleMeshPolyLine(vertex_coord,
                                                      boundary_id);
 
 // Create the triangle mesh polygon for outer boundary
 outer_boundary_pt = new TriangleMeshPolygon(outer_boundary_line_pt);
 
 // Inner circular boundary
 //------------------------
 Vector<TriangleMeshCurveSection*> inner_boundary_line_pt(2);
 
 // The intrinsic coordinates for the beginning and end of the curve
 double s_start = 0.0;
 double s_end   = MathematicalConstants::Pi;
 boundary_id = 0;
 inner_boundary_line_pt[0]=
  new TriangleMeshCurviLine(inner_circle_pt,
                            s_start,
                            s_end,
                            n_segments,
                            boundary_id);
 
 // The intrinsic coordinates for the beginning and end of the curve
 s_start = MathematicalConstants::Pi;
 s_end   = 2.0*MathematicalConstants::Pi;
 boundary_id = 1;
 inner_boundary_line_pt[1]=
  new TriangleMeshCurviLine(inner_circle_pt,
                            s_start,
                            s_end,
                            n_segments,
                            boundary_id);
 
 
 // Combine to hole
 //----------------
 Vector<TriangleMeshClosedCurve*> hole_pt(1);
 Vector<double> hole_coords(2);
 hole_coords[0]=0.0;
 hole_coords[1]=0.0;
 hole_pt[0]=new TriangleMeshClosedCurve(inner_boundary_line_pt,
                                        hole_coords);
 
 
 // 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 the closed curve using the TriangleMeshParameters object
 triangle_mesh_parameters.internal_closed_curve_pt() = hole_pt;
 
 // Target element size in bulk mesh
 triangle_mesh_parameters.element_area() = 0.1;
 
#ifdef ADAPTIVE
 
 // Build adaptive "bulk" mesh
 Bulk_mesh_pt=new RefineableTriangleMesh<ELEMENT>(triangle_mesh_parameters);
 
 // 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;
 
#else
 
 // Build "bulk" mesh
 Bulk_mesh_pt=new TriangleMesh<ELEMENT>(triangle_mesh_parameters);
 
#endif
 
 // Create the main triangular mesh
 add_sub_mesh(Bulk_mesh_pt);
 
 // Create PML meshes and add them to the global mesh
 create_pml_meshes();
 
 // Build the entire mesh from its submeshes
 build_global_mesh();
 
 // Let's have a look where the boundaries are
 this->mesh_pt()->output("global_mesh.dat");
 this->mesh_pt()->output_boundaries("global_mesh_boundary.dat");
 
 // Complete the build of all elements so they are fully functional
 unsigned n_element = this->mesh_pt()->nelement();
 for(unsigned e=0;e<n_element;e++)
  {
   // Upcast from GeneralisedElement to Helmholtz bulk element
   PMLHelmholtzEquations<2> *el_pt =
    dynamic_cast<PMLHelmholtzEquations<2>*>(mesh_pt()->element_pt(e));
 
   //Set the k_squared double pointer
   el_pt->k_squared_pt() = &GlobalParameters::K_squared;
  }
 
 // Apply boundary conditions
 apply_boundary_conditions();
 
 // Setup equation numbering scheme
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl;
 
} // end of constructor
 
 
#ifdef ADAPTIVE
 
//=====================start_of_actions_before_adapt======================
/// Actions before adapt: Wipe the mesh of face elements
//========================================================================
template<class ELEMENT>
void PMLProblem<ELEMENT>::actions_before_adapt()
{
 // Before adapting the added PML meshes must be removed
 // as they are not refineable and are to be rebuilt from the
 // newly refined triangular mesh
 delete PML_right_mesh_pt;
 PML_right_mesh_pt=0;
 delete PML_top_mesh_pt;
 PML_top_mesh_pt=0;
 delete PML_left_mesh_pt;
 PML_left_mesh_pt=0;
 delete PML_bottom_mesh_pt;
 PML_bottom_mesh_pt=0;
 delete PML_top_right_mesh_pt;
 PML_top_right_mesh_pt=0;
 delete PML_top_left_mesh_pt;
 PML_top_left_mesh_pt=0;
 delete PML_bottom_right_mesh_pt;
 PML_bottom_right_mesh_pt=0;
 delete PML_bottom_left_mesh_pt;
 PML_bottom_left_mesh_pt=0;
 
 // Rebuild the Problem's global mesh from its various sub-meshes
 // but first flush all its submeshes
 flush_sub_meshes();
 
 // Then add the triangular mesh back
 add_sub_mesh(Bulk_mesh_pt);
 
 //  Rebuild the global mesh such that it now stores
 // the triangular mesh only
 rebuild_global_mesh();
 
}// end of actions_before_adapt
 
 
//=====================start_of_actions_after_adapt=======================
///  Actions after adapt: Rebuild the face element meshes
//========================================================================
template<class ELEMENT>
void PMLProblem<ELEMENT>::actions_after_adapt()
{
 
 // Build PML meshes  and add them to the global mesh
 create_pml_meshes();
 
 // Build the entire mesh from its submeshes
 rebuild_global_mesh();
 
 // Complete the build of all elements so they are fully functional
 
 // Loop over the entire mesh elements to set up element-specific
 // things that cannot be handled by constructor
 unsigned n_element = this->mesh_pt()->nelement();
 
 for(unsigned e=0;e<n_element;e++)
  {
   // Upcast from GeneralisedElement to PMLHelmholtz bulk element
   PMLHelmholtzEquations<2> *el_pt =
    dynamic_cast<PMLHelmholtzEquations<2>*>(mesh_pt()->element_pt(e));
 
   //Set the frequency function pointer
   el_pt->k_squared_pt() = &GlobalParameters::K_squared;
  }
 
 // Re-apply boundary conditions
 apply_boundary_conditions();
 
}// end of actions_after_adapt
 
#endif
 
//==================start_of_apply_boundary_conditions====================
/// Apply boundary conditions
//========================================================================
template<class ELEMENT>
void PMLProblem<ELEMENT>::apply_boundary_conditions()
{
 
 // Boundary conditions are set on the surface of the circle
 // as a constant nonzero Dirichlet boundary condition
 unsigned n_bound = Bulk_mesh_pt->nboundary();
 
 for(unsigned b=0;b<n_bound;b++)
  {
   unsigned n_node = Bulk_mesh_pt->nboundary_node(b);
   for (unsigned n=0;n<n_node;n++)
    {
     if ((b==0) || (b==1))
      {
       Node* nod_pt=Bulk_mesh_pt->boundary_node_pt(b,n);
       nod_pt->pin(0);
       nod_pt->pin(1);
 
       nod_pt->set_value(0,0.1);
       nod_pt->set_value(1,0.0);
      }
    }
  }
 
}// end of apply_boundary_conditions
 
 
//=====================start_of_doc=======================================
/// Doc the solution: doc_info contains labels/output directory etc.
//========================================================================
template<class ELEMENT>
void PMLProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{
 
 ofstream some_file,some_file2;
 char filename[100];
 
 // Number of plot points
 unsigned npts;
 npts=5;
 
 // Output solution
 //-----------------
 snprintf(filename, sizeof(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 coarse solution
 //-----------------------
 snprintf(filename, sizeof(filename), "%s/coarse_soln%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 unsigned npts_coarse=2;
 Bulk_mesh_pt->output(some_file,npts_coarse);
 some_file.close();
 
 
 // Output solution within pml domains
 //-----------------------------------
 snprintf(filename, sizeof(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_left_mesh_pt->output(some_file,npts);
 PML_top_right_mesh_pt->output(some_file,npts);
 PML_bottom_right_mesh_pt->output(some_file,npts);
 PML_top_left_mesh_pt->output(some_file,npts);
 PML_bottom_left_mesh_pt->output(some_file,npts);
 some_file.close();
 
 
 
 
 // Write norm of solution to trace file
 double norm=0.0;
 Bulk_mesh_pt->compute_norm(norm);
 Trace_file  << norm << std::endl;
 
 // //Do animation of Helmholtz solution
 // //-----------------------------------
 // unsigned nstep=40;
 // for (unsigned i=0;i<nstep;i++)
 //  {
 //   snprintf(filename, sizeof(filename), "%s/helmholtz_animation%i_frame%i.dat",
 //           doc_info.directory().c_str(),
 //           doc_info.number(),i);
 //   some_file.open(filename);
 //   double phi=2.0*MathematicalConstants::Pi*double(i)/double(nstep-1);
 //   unsigned nelem=Bulk_mesh_pt->nelement();
 //   for (unsigned e=0;e<nelem;e++)
 //    {
 //     ELEMENT* el_pt=dynamic_cast<ELEMENT*>(
 //      Bulk_mesh_pt->element_pt(e));
 //     el_pt->output_real(some_file,phi,npts);
 //    }
 //   some_file.close();
 //  }
 
} // end of doc
 
//============start_of_create_pml_meshes======================================
/// Create PML meshes and add them to the problem's sub-meshes
//============================================================================
template<class ELEMENT>
void PMLProblem<ELEMENT>::create_pml_meshes()
{
 
 // Bulk mesh left boundary id
 unsigned int left_boundary_id = 2;
 
 // Bulk mesh top boundary id
 unsigned int top_boundary_id = 3;
 
 // Bulk mesh right boundary id
 unsigned int right_boundary_id = 4;
 
 // Bulk mesh bottom boundary id
 unsigned int bottom_boundary_id = 5;
 
 // PML width in elements for the right layer
 unsigned n_x_right_pml = 3;
 
 // PML width in elements for the top layer
 unsigned n_y_top_pml = 3;
 
 // PML width in elements for the left layer
 unsigned n_x_left_pml = 3;
 
 // PML width in elements for the left layer
 unsigned n_y_bottom_pml = 3;
 
 // Outer physical length of the PML layers
 // defaults to 0.2, so 10% of the size of the
 // physical domain
 double width_x_right_pml  = 0.2;
 double width_y_top_pml    = 0.2;
 double width_x_left_pml   = 0.2;
 double width_y_bottom_pml = 0.2;
 
 // 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_left_mesh_pt  =
  TwoDimensionalPMLHelper::create_left_pml_mesh
  <PMLLayerElement<ELEMENT> >
  (Bulk_mesh_pt, left_boundary_id,
   n_x_left_pml, width_x_left_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_left_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);
 
 PML_top_left_mesh_pt     =
  TwoDimensionalPMLHelper::create_top_left_pml_mesh
  <PMLLayerElement<ELEMENT> >
  (PML_left_mesh_pt, PML_top_mesh_pt,
   Bulk_mesh_pt, left_boundary_id);
 
 PML_bottom_left_mesh_pt  =
  TwoDimensionalPMLHelper::create_bottom_left_pml_mesh
  <PMLLayerElement<ELEMENT> >
  (PML_left_mesh_pt, PML_bottom_mesh_pt,
   Bulk_mesh_pt, left_boundary_id);
 
 // Add submeshes to the global mesh
 add_sub_mesh(PML_top_right_mesh_pt);
 add_sub_mesh(PML_bottom_right_mesh_pt);
 add_sub_mesh(PML_top_left_mesh_pt);
 add_sub_mesh(PML_bottom_left_mesh_pt);
 
} // end of create_pml_meshes
 
 
 
//==========start_of_main=================================================
/// Solve 2D Helmholtz problem
//========================================================================
int main(int argc, char **argv)
{
 //Set up the problem
 //------------------
 
#ifdef ADAPTIVE
 
 // Set up the problem with projectable 2D six-node elements from the
 // TPMLHelmholtzElement family.
 PMLProblem<ProjectablePMLHelmholtzElement
  <TPMLHelmholtzElement<2,3> > > problem;
 
 // Set up the problem with 2D ten-node elements from the
 // TPMLHelmholtzElement family.
 // PMLProblem<ProjectablePMLHelmholtzElement
 //  <TPMLHelmholtzElement<2,4> > > problem;
 
#else
 
 // Set up the problem with 2D six-node elements from the
 // TPMLHelmholtzElement family.
 PMLProblem<TPMLHelmholtzElement<2,3> >  problem;
 
 // Set up the problem with 2D ten-node elements from the
 // TPMLHelmholtzElement family.
 //   PMLProblem<TPMLHelmholtzElement<2,4> >  problem;
 
#endif
 
 // Create label for output
 //------------------------
 DocInfo doc_info;
 
 // Set output directory
 doc_info.set_directory("RESLT");
 
 
#ifdef ADAPTIVE
 
 // Max. number of adaptations
 unsigned max_adapt=1;
 
 // Solve the problem with the adaptive Newton's method, allowing
 // up to max_adapt mesh adaptations after every solve.
 problem.newton_solve(max_adapt);
 
#else
 
 // Solve the problem with Newton's method
 problem.newton_solve();
 
#endif
 
 //Output solution
 problem.doc_solution(doc_info);
 
} //end of main