mesh_from_triangle_poisson.cc

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//LIC// ====================================================================
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//LIC// 
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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
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//LIC//====================================================================
// Driver code for a simple test poisson problem using a mesh
// generated from an input file generated by the triangle mesh generator
// Triangle.

//Generic routines
#include "generic.h"

// Poisson equations
#include "poisson.h"

// The mesh
#include "meshes/triangle_mesh.h"

using namespace std;

using namespace oomph;

//====================================================================
/// Namespace for exact solution for Poisson equation with sharp step 
//====================================================================
namespace TanhSolnForPoisson
{

 /// Parameter for steepness of step
 double Alpha;

 /// Parameter for angle of step
 double Beta;

 
 /// Exact solution as a Vector
 void get_exact_u(const Vector<double>& x, Vector<double>& u)
 {
  u[0]=tanh(1.0-Alpha*(Beta*x[0]-x[1]));
 }


 /// Exact solution as a scalar
 void get_exact_u(const Vector<double>& x, double& u)
 {
  u=tanh(1.0-Alpha*(Beta*x[0]-x[1]));
 }


 /// Source function to make it an exact solution 
 void get_source(const Vector<double>& x, double& source)
 {
  source = 2.0*tanh(-1.0+Alpha*(Beta*x[0]-x[1]))*
             (1.0-pow(tanh(-1.0+Alpha*(Beta*x[0]-x[1])),2.0))*
             Alpha*Alpha*Beta*Beta+2.0*tanh(-1.0+Alpha*(Beta*x[0]-x[1]))*
            (1.0-pow(tanh(-1.0+Alpha*(Beta*x[0]-x[1])),2.0))*Alpha*Alpha;
 }

}







//====================================================================
/// Micky mouse Poisson problem.
//====================================================================

// Poisson problem
template<class ELEMENT> 
class PoissonProblem : public Problem
{

public:


 /// \short Constructor: Pass pointer to source function and names of
 /// two triangle input files
 PoissonProblem(PoissonEquations<2>::PoissonSourceFctPt source_fct_pt,
                const string& node_file_name,
                const string& element_file_name,
                const string& poly_file_name);

 /// Destructor (empty)
 ~PoissonProblem(){}

 /// Update the problem specs before solve: (Re)set boundary conditions
 void actions_before_newton_solve()
  {
   //Loop over the boundaries
   unsigned num_bound = mesh_pt()->nboundary();
   for(unsigned ibound=0;ibound<num_bound;ibound++)
    {
     // Loop over the nodes on boundary
     unsigned num_nod=mesh_pt()->nboundary_node(ibound);
     for (unsigned inod=0;inod<num_nod;inod++)
      {
       Node* nod_pt=mesh_pt()->boundary_node_pt(ibound,inod);
       double u;
       Vector<double> x(2);
       x[0]=nod_pt->x(0);
       x[1]=nod_pt->x(1);
       TanhSolnForPoisson::get_exact_u(x,u);
       nod_pt->set_value(0,u);
      }
    }
  }

 /// Update the problem specs before solve (empty)
 void actions_after_newton_solve()
  {}
 
#ifdef ADAPT
 /// Actions performed after the adaptation steps
 void actions_after_adapt();
#endif
 
#ifdef ADAPT
 /// Access function for the specific mesh
 RefineableTriangleMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<RefineableTriangleMesh<ELEMENT>*>(Problem::mesh_pt());
  }
#else
 /// Access function for the specific mesh
 TriangleMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<TriangleMesh<ELEMENT>*>(Problem::mesh_pt());
  }
#endif

  /// Doc the solution
 void doc_solution(DocInfo& doc_info);

private:

 /// Pointer to source function
 PoissonEquations<2>::PoissonSourceFctPt Source_fct_pt;
 
#ifdef ADAPT
 /// Pointer to the bulk mesh
 RefineableTriangleMesh<ELEMENT> *Bulk_mesh_pt;
 
 /// Error estimator
 Z2ErrorEstimator* error_estimator_pt;
#endif
 
};



//========================================================================
/// Constructor for Poisson problem
//========================================================================
template<class ELEMENT>
PoissonProblem<ELEMENT>::
 PoissonProblem(PoissonEquations<2>::PoissonSourceFctPt source_fct_pt,
                const string& node_file_name,
                const string& element_file_name,
                const string& poly_file_name)
        : Source_fct_pt(source_fct_pt)
{ 

 // Setup parameters for exact tanh solution

 // Steepness of step
 TanhSolnForPoisson::Alpha=1.0; 

 // Orientation of step
 TanhSolnForPoisson::Beta=1.4;

#ifdef ADAPT
 //Create mesh
 Bulk_mesh_pt = new RefineableTriangleMesh<ELEMENT>(node_file_name,
                                                    element_file_name,
                                                    poly_file_name);
 
 // Set error estimator for bulk mesh
 Z2ErrorEstimator* error_estimator_pt=new Z2ErrorEstimator;
 Bulk_mesh_pt->spatial_error_estimator_pt() = error_estimator_pt;

 // Set the problem mesh pointer to the bulk mesh
 Problem::mesh_pt() = Bulk_mesh_pt;
 
#else
 //Create mesh
  Problem::mesh_pt() = new TriangleMesh<ELEMENT>(node_file_name,
                                                 element_file_name,
                                                 poly_file_name);
#endif

 // Set the boundary conditions for this problem: All nodes are
 // free by default -- just pin the ones that have Dirichlet conditions
 // here. 
 unsigned num_bound = mesh_pt()->nboundary();
 for(unsigned ibound=0;ibound<num_bound;ibound++)
 {
   unsigned num_nod= mesh_pt()->nboundary_node(ibound);
   for (unsigned inod=0;inod<num_nod;inod++)
   {
     mesh_pt()->boundary_node_pt(ibound,inod)->pin(0);
   }
 }

 // Complete the build of all elements so they are fully functional

 //Find number of elements in mesh
 unsigned n_element = mesh_pt()->nelement();

 // Loop over the elements to set up element-specific 
 // things that cannot be handled by constructor
 for(unsigned i=0;i<n_element;i++)
  {
   // Upcast from GeneralElement to the present element
   ELEMENT* el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(i));

   //Set the source function pointer
   el_pt->source_fct_pt() = Source_fct_pt;
  }

 // Setup equation numbering scheme
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl; 

}

#ifdef ADAPT
//========================================================================
/// Actions performed after the adaptation steps
//========================================================================
template<class ELEMENT>
void PoissonProblem<ELEMENT>::actions_after_adapt()
{
 // Since the mesh adaptation strategy is based on mesh re-generation
 // we need to pin the nodes in the new regenerated mesh, and pass the
 // source function to the elements

 // Set the boundary conditions for this problem: All nodes are free
 // by default -- just pin the ones that have Dirichlet conditions
 // here.
 unsigned num_bound = mesh_pt()->nboundary();
 for(unsigned ibound=0;ibound<num_bound;ibound++)
  {
   unsigned num_nod= mesh_pt()->nboundary_node(ibound);
   for (unsigned inod=0;inod<num_nod;inod++)
   {
     mesh_pt()->boundary_node_pt(ibound,inod)->pin(0);
   }
 }

 // Complete the build of all elements so they are fully functional

 //Find number of elements in mesh
 unsigned n_element = mesh_pt()->nelement();

 // Loop over the elements to set up element-specific 
 // things that cannot be handled by constructor
 for(unsigned i=0;i<n_element;i++)
  {
   // Upcast from GeneralElement to the present element
   ELEMENT* el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(i));

   //Set the source function pointer
   el_pt->source_fct_pt() = Source_fct_pt;
  }

 // Setup equation numbering scheme
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl; 
}
#endif


//========================================================================
/// Doc the solution
//========================================================================
template<class ELEMENT>
void PoissonProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{ 

 ofstream some_file;
 char filename[100];

 // Number of plot points
 unsigned npts;
 npts=5;



 // Output boundaries
 //------------------
 sprintf(filename,"%s/boundaries.dat",doc_info.directory().c_str());
 some_file.open(filename);
 mesh_pt()->output_boundaries(some_file);
 some_file.close();


 // Output solution
 //----------------
 sprintf(filename,"%s/soln%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 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);
 mesh_pt()->output_fct(some_file,npts,TanhSolnForPoisson::get_exact_u); 
 some_file.close();


 // Doc error
 //----------
 double error,norm;
 sprintf(filename,"%s/error%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 mesh_pt()->compute_error(some_file,TanhSolnForPoisson::get_exact_u,
                          error,norm); 
 some_file.close();
 cout << "error: " << sqrt(error) << std::endl; 
 cout << "norm : " << sqrt(norm) << std::endl << std::endl;


 // Get norm of solution
 sprintf(filename,"%s/norm%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 double norm_soln=0.0;
 mesh_pt()->compute_norm(norm_soln);  
 some_file << sqrt(norm_soln) << std::endl;
 cout << "Norm of computed solution: "   << sqrt(norm_soln)  << endl;
 some_file.close();
 
}

 



//========================================================================
/// Demonstrate how to solve Poisson problem
//========================================================================
int main(int argc, char* argv[])
{
 // Store command line arguments
 CommandLineArgs::setup(argc,argv);

 // Check number of command line arguments: Need exactly two.
 if (argc!=4)
  {
   std::string error_message =
    "Wrong number of command line arguments.\n";
   error_message +=
    "Must specify the following file names  \n";
   error_message += 
    "filename.node then filename.ele then filename.poly\n";

   throw OomphLibError(error_message,
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  }

#ifdef ADAPT
 const unsigned max_adapt = 3;
#endif
 
 // Convert arguments to strings that specify the input file names
 string node_file_name(argv[1]);
 string element_file_name(argv[2]);
 string poly_file_name(argv[3]);

 // Label for output
 DocInfo doc_info;
 
 // Output directory
 doc_info.set_directory("RESLT");
 
#ifndef ADAPT
 // Do the problem with cubic elements
 //-----------------------------------
 {
  cout << std::endl << "Cubic elements" << std::endl;
  cout <<         "==============" << std::endl << std::endl;
  
  //Set up the problem
  PoissonProblem<TPoissonElement<2,4> > 
   problem(&TanhSolnForPoisson::get_source,node_file_name,
           element_file_name,
           poly_file_name);
  
  // Solve the problem
  problem.newton_solve();
  
  //Output solution
  problem.doc_solution(doc_info);
  
  //Increment counter for solutions 
  doc_info.number()++;
 }
#endif
 
 
 // Do the problem with quadratic elements
 //---------------------------------------
 {
  cout << std::endl  << "Quadratic elements" << std::endl;
  cout <<               "===================" << std::endl << std::endl;

#ifdef ADAPT
  //Set up the problem
  PoissonProblem<ProjectablePoissonElement<TPoissonElement<2,3> > >
   problem(&TanhSolnForPoisson::get_source,node_file_name,
           element_file_name,
           poly_file_name);
#else
  //Set up the problem
  PoissonProblem<TPoissonElement<2,3> > 
   problem(&TanhSolnForPoisson::get_source,node_file_name,
           element_file_name,
           poly_file_name);
#endif
    
#ifdef ADAPT
  // Solve the problem with adaptation
  problem.newton_solve(max_adapt);
#else
  // Solve the problem
  problem.newton_solve();
#endif
  
  //Output solution
  problem.doc_solution(doc_info);
  
  //Increment counter for solutions 
  doc_info.number()++;
 }



 // Do the problem with linear elements
 //------------------------------------
 {
  cout << std::endl << "Linear elements" << std::endl;
  cout <<              "===============" << std::endl << std::endl;

#ifdef ADAPT
  //Set up the problem
  PoissonProblem<ProjectablePoissonElement<TPoissonElement<2,2> > > 
   problem(&TanhSolnForPoisson::get_source,node_file_name,
           element_file_name,
           poly_file_name);
#else
  //Set up the problem
  PoissonProblem<TPoissonElement<2,2> > 
   problem(&TanhSolnForPoisson::get_source,node_file_name,
           element_file_name,
           poly_file_name);
#endif
  
#ifdef ADAPT
  // Solve the problem with adaptation
  problem.newton_solve(max_adapt);
#else
  // Solve the problem
  problem.newton_solve();
#endif
  
  //Output solution
  problem.doc_solution(doc_info);
  
  //Increment counter for solutions 
  doc_info.number()++;
 }

}