mesh_from_tetgen_poisson.cc

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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
// Driver function for a simple test poisson problem using a mesh
// generated from an input file generated by the tetrahedra mesh generator.
// the files .node,  .ele and .face should be specified in this order

//Generic routines
#include "generic.h"

// Poisson equations
#include "poisson.h"

// Get the mesh
#include "meshes/tetgen_mesh.h"

using namespace std;

using namespace oomph;

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

 /// Parameter for steepness of step
 double Alpha=3;

 ///\short Orientation (non-normalised x-component of unit vector in direction
 /// of step plane)
 double N_x=-1.0;

 ///\short Orientation (non-normalised y-component of unit vector in direction
 /// of step plane)
 double N_y=-1.0;

 ///\short Orientation (non-normalised z-component of unit vector in direction
 /// of step plane)
 double N_z=1.0;


 ///\short Orientation (x-coordinate of step plane) 
 double X_0=0.0;

 ///\short Orientation (y-coordinate of step plane) 
 double Y_0=0.0;

 ///\short Orientation (z-coordinate of step plane) 
 double Z_0=0.0;


 // Exact solution as a Vector
 void get_exact_u(const Vector<double>& x, Vector<double>& u)
 {
  u[0] = tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-Y_0)*
                    N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*
                     N_z/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)));
 }

 /// Exact solution as a scalar
 void get_exact_u(const Vector<double>& x, double& u)
 {
  u = tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-Y_0)*
                     N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*
                     N_z/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)));
 }


 /// Source function to make it an exact solution 
 void get_source(const Vector<double>& x, double& source)
 {

  double s1,s2,s3,s4;

  s1 = -2.0*tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-
 Y_0)*N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*N_z/sqrt(N_x*N_x+N_y*N_y+N_z*
 N_z)))*(1.0-pow(tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-
 Y_0)*N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*N_z/sqrt(N_x*N_x+N_y*N_y+N_z*
 N_z))),2.0))*Alpha*Alpha*N_x*N_x/(N_x*N_x+N_y*N_y+N_z*N_z);
      s3 = -2.0*tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-
 Y_0)*N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*N_z/sqrt(N_x*N_x+N_y*N_y+N_z*
 N_z)))*(1.0-pow(tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-
 Y_0)*N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*N_z/sqrt(N_x*N_x+N_y*N_y+N_z*
 N_z))),2.0))*Alpha*Alpha*N_y*N_y/(N_x*N_x+N_y*N_y+N_z*N_z);
     s4 = -2.0*tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-
 Y_0)*N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*N_z/sqrt(N_x*N_x+N_y*N_y+N_z*
 N_z)))*(1.0-pow(tanh(Alpha*((x[0]-X_0)*N_x/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[1]-
 Y_0)*N_y/sqrt(N_x*N_x+N_y*N_y+N_z*N_z)+(x[2]-Z_0)*N_z/sqrt(N_x*N_x+N_y*N_y+N_z*
 N_z))),2.0))*Alpha*Alpha*N_z*N_z/(N_x*N_x+N_y*N_y+N_z*N_z);
      s2 = s3+s4;
      source = s1+s2;
 }


} // end of namespace





//====================================================================
/// Micky mouse Poisson problem.
//====================================================================
template<class ELEMENT> 
class PoissonProblem : public Problem
{

public:


 /// Constructor
  PoissonProblem(PoissonEquations<3>::PoissonSourceFctPt source_fct_pt,
                 const string& node_file_name,
                 const string& element_file_name,
                 const string& face_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(3);
       x[0]=nod_pt->x(0);
       x[1]=nod_pt->x(1);
       x[2]=nod_pt->x(2);
       TanhSolnForPoisson::get_exact_u(x,u);
       nod_pt->set_value(0,u);
      }
    }
  }

 /// Update the problem specs before solve (empty)
 void actions_after_newton_solve(){}


 //Access function for the specific mesh
TetgenMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<TetgenMesh<ELEMENT>*>(Problem::mesh_pt());
  }

  /// Doc the solution
 void doc_solution(const unsigned& nplot, DocInfo& doc_info);

private:

 /// Pointer to source function
 PoissonEquations<3>::PoissonSourceFctPt Source_fct_pt;

};



//========================================================================
/// Constructor for Poisson problem
//========================================================================
template<class ELEMENT>
PoissonProblem<ELEMENT>::
 PoissonProblem(PoissonEquations<3>::PoissonSourceFctPt source_fct_pt,
                const string& node_file_name,
                const string& element_file_name,
                const string& face_file_name)
        : Source_fct_pt(source_fct_pt)
{ 

 // Setup parameters for exact tanh solution

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


 //Create mesh
 Problem::mesh_pt() = new TetgenMesh<ELEMENT>(node_file_name,
                                              element_file_name,
                                              face_file_name);

 // 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; 

}



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

 ofstream some_file;
 char filename[100];


 // Doc local node numbering
 //-------------------------
 sprintf(filename,"%s/node_numbering%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 FiniteElement* el_pt=mesh_pt()->finite_element_pt(0);
 unsigned nnode=el_pt->nnode();
 unsigned ndim=el_pt->node_pt(0)->ndim();
 for (unsigned j=0;j<nnode;j++)
  {
   for (unsigned i=0;i<ndim;i++)
    {
     some_file << el_pt->node_pt(j)->x(i) << " " ;
    }
   some_file << j << std::endl;
  }
 some_file.close();

 // Output boundaries
 //------------------
 sprintf(filename,"%s/boundaries%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 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,nplot);
 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,nplot,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;

} // end of doc




//========================================================================
/// 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 three.
 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.face\n";

   throw OomphLibError(error_message,
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  }

 // Convert arguments to strings that specify the input file names
 string node_file_name(argv[1]);
 string element_file_name(argv[2]);
 string face_file_name(argv[3]);


 // Label for output
 DocInfo doc_info;
 
 // Output directory
 doc_info.set_directory("RESLT");
  
 // Number of output points per edge
 unsigned nplot=2;

 // Do the problem with linear elements
 //------------------------------------
 {
  PoissonProblem<TPoissonElement<3,2> > 
   problem(&TanhSolnForPoisson::get_source,
           node_file_name,element_file_name,face_file_name);

  // Solve the problem
  problem.newton_solve();
  
  //Output solution with 2 points per edge
  nplot=2;
  problem.doc_solution(nplot,doc_info);
    
  //Increment counter for solutions 
  doc_info.number()++;

  //Output solution with 5 points per edge
  nplot=5;
  problem.doc_solution(nplot,doc_info);
    
  //Increment counter for solutions 
  doc_info.number()++;


 }



 // Do the problem with quadratic elements
 //---------------------------------------
 {
  PoissonProblem<TPoissonElement<3,3> > 
   problem(&TanhSolnForPoisson::get_source,
           node_file_name,element_file_name,face_file_name);
  
  // Solve the problem
  problem.newton_solve();

  //Output solution with 2 points per edge
  nplot=2;
  problem.doc_solution(nplot,doc_info);
    
  //Increment counter for solutions 
  doc_info.number()++;

  //Output solution with 5 points per edge
  nplot=5;
  problem.doc_solution(nplot,doc_info);
    
  //Increment counter for solutions 
  doc_info.number()++;

 }


}