fish_poisson.cc

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//LIC// ====================================================================
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//LIC// multi-physics finite-element library, available 
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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
// Driver for solution of 2D Poisson equation in fish-shaped domain with
// adaptivity

 
// Generic oomph-lib headers
#include "generic.h"

// The Poisson equations
#include "poisson.h"

// The fish mesh 
#include "meshes/fish_mesh.h"

using namespace std;

using namespace oomph;


//============ start_of_namespace=====================================
/// Namespace for const source term in Poisson equation
//====================================================================
namespace ConstSourceForPoisson
{ 
 
 /// Strength of source function: default value -1.0
 double Strength=-1.0;

/// Const source function
 void source_function(const Vector<double>& x, double& source)
 {
  source = Strength;
 }

} // end of namespace




//======start_of_problem_class========================================
/// Refineable Poisson problem in fish-shaped domain.
/// Template parameter identifies the element type.
//====================================================================
template<class ELEMENT>
class RefineableFishPoissonProblem : public Problem
{

public:

 /// Constructor
 RefineableFishPoissonProblem();

 /// Destructor: Empty
 virtual ~RefineableFishPoissonProblem(){}

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

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

 /// \short Overloaded version of the problem's access function to 
 /// the mesh. Recasts the pointer to the base Mesh object to 
 /// the actual mesh type.
 RefineableFishMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<RefineableFishMesh<ELEMENT>*>(Problem::mesh_pt());
  }

 /// \short Doc the solution. Output directory and labels are specified 
 /// by DocInfo object
 void doc_solution(DocInfo& doc_info);

}; // end of problem class





//===========start_of_constructor=========================================
/// Constructor for adaptive Poisson problem in fish-shaped
/// domain.
//========================================================================
template<class ELEMENT>
RefineableFishPoissonProblem<ELEMENT>::RefineableFishPoissonProblem()
{ 
    
 // Build fish mesh -- this is a coarse base mesh consisting 
 // of four elements. We'll refine/adapt the mesh later.
 Problem::mesh_pt()=new RefineableFishMesh<ELEMENT>;
 
 // Create/set error estimator
 mesh_pt()->spatial_error_estimator_pt()=new Z2ErrorEstimator;
  
 // Set the boundary conditions for this problem: All nodes are
 // free by default -- just pin the ones that have Dirichlet conditions
 // here. Since the boundary values are never changed, we set
 // them here rather than in actions_before_newton_solve(). 
 unsigned n_bound = mesh_pt()->nboundary();
 for(unsigned i=0;i<n_bound;i++)
  {
   unsigned n_node = mesh_pt()->nboundary_node(i);
   for (unsigned n=0;n<n_node;n++)
    {
     // Pin the single scalar value at this node
     mesh_pt()->boundary_node_pt(i,n)->pin(0); 

     // Assign the homogenous boundary condition for the one and only
     // nodal value
     mesh_pt()->boundary_node_pt(i,n)->set_value(0,0.0); 
    }
  }

 // Loop over elements and set pointers to source function
 unsigned n_element = mesh_pt()->nelement();
 for(unsigned e=0;e<n_element;e++)
  {
   // Upcast from FiniteElement to the present element
   ELEMENT *el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(e));

   //Set the source function pointer
   el_pt->source_fct_pt() = &ConstSourceForPoisson::source_function;
  }

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

} // end of constructor




//=======start_of_doc=====================================================
/// Doc the solution in tecplot format.
//========================================================================
template<class ELEMENT>
void RefineableFishPoissonProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{ 

 ofstream some_file;
 char filename[100];

 // Number of plot points in each coordinate direction.
 unsigned npts;
 npts=5; 

 // 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();
 
} // end of doc

 




//=====================start_of_incremental===============================
/// Demonstrate how to solve 2D Poisson problem in 
/// fish-shaped domain with mesh adaptation. First we solve on the original
/// coarse mesh. Next we do a few uniform refinement steps and re-solve.
/// Finally, we enter into an automatic adapation loop.
//========================================================================
void solve_with_incremental_adaptation()
{
 
 //Set up the problem with nine-node refineable Poisson elements
 RefineableFishPoissonProblem<RefineableQPoissonElement<2,3> > problem;
 
 // Setup labels for output
 //------------------------
 DocInfo doc_info;
 
 // Set output directory
 doc_info.set_directory("RESLT_incremental"); 
 
 // Step number
 doc_info.number()=0;
  
  
 // Doc (default) refinement targets
 //----------------------------------
 problem.mesh_pt()->doc_adaptivity_targets(cout);
 
 // Solve/doc the problem on the initial, very coarse mesh
 //-------------------------------------------------------
 
 // Solve the problem
 problem.newton_solve();
 
 //Output solution
 problem.doc_solution(doc_info);
 
 //Increment counter for solutions 
 doc_info.number()++;


 // Do three rounds of uniform mesh refinement and re-solve
 //--------------------------------------------------------
 problem.refine_uniformly();
 problem.refine_uniformly();
 problem.refine_uniformly();
 
 // Solve the problem 
 problem.newton_solve();
 
 //Output solution
 problem.doc_solution(doc_info);
 
 //Increment counter for solutions 
 doc_info.number()++;
 
 
 // Now do (up to) four rounds of fully automatic adapation in response to 
 //-----------------------------------------------------------------------
 // error estimate
 //---------------
 unsigned max_solve=4;
 for (unsigned isolve=0;isolve<max_solve;isolve++)
  {
   // Adapt problem/mesh
   problem.adapt(); 
         
   // Re-solve the problem if the adaptation has changed anything
   if ((problem.mesh_pt()->nrefined()  !=0)||
       (problem.mesh_pt()->nunrefined()!=0))
    {
     problem.newton_solve();
    }
   else
    {
     cout << "Mesh wasn't adapted --> we'll stop here" << std::endl;
     break;
    }
   
   //Output solution
   problem.doc_solution(doc_info);
   
   //Increment counter for solutions 
   doc_info.number()++;
  }
 
 
} // end of incremental






//================================start_black_box=========================
/// Demonstrate how to solve 2D Poisson problem in 
/// fish-shaped domain with fully automatic mesh adaptation
//========================================================================
void solve_with_fully_automatic_adaptation()
{

  //Set up the problem with nine-node refineable Poisson elements
  RefineableFishPoissonProblem<RefineableQPoissonElement<2,3> > problem;
  
  // Setup labels for output
  //------------------------
  DocInfo doc_info;
  
  // Set output directory
  doc_info.set_directory("RESLT_fully_automatic"); 
  
  // Step number
  doc_info.number()=0;


  // Doc (default) refinement targets
  //----------------------------------
  problem.mesh_pt()->doc_adaptivity_targets(cout);

  
  // Solve/doc the problem with fully automatic adaptation
  //------------------------------------------------------

  // Maximum number of adaptations:
  unsigned max_adapt=5;

  // Solve the problem; perform up to specified number of adaptations.
  problem.newton_solve(max_adapt);
  
  //Output solution
  problem.doc_solution(doc_info);   

} // end black box




//=================start_of_main==========================================
/// Demonstrate how to solve 2D Poisson problem in 
/// fish-shaped domain with mesh adaptation.
//========================================================================
int main()
{
 // Solve with adaptation, docing the intermediate steps
 solve_with_incremental_adaptation();

 // Solve directly, with fully automatic adaptation
 solve_with_fully_automatic_adaptation();

} // end of main




//  //Do few unrefinements and keep doc-ing
//  for (unsigned i=0;i<5;i++)
//   {
//    problem.unrefine_uniformly();
   
//    //Output solution
//    problem.doc_solution(doc_info);
   
//    //Increment counter for solutions 
//    doc_info.number()++;
//   }