eighth_sphere_poisson.cc

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//LIC//====================================================================
//Driver for a 3D poisson problem
 
//Generic routines
#include "generic.h"
 
// The Poisson equations
#include "poisson.h"
 
// The mesh
#include "meshes/eighth_sphere_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=1;
 
 /// Orientation (non-normalised x-component of unit vector in direction
 /// of step plane)
 double N_x=-1.0;
 
 /// Orientation (non-normalised y-component of unit vector in direction
 /// of step plane)
 double N_y=-1.0;
 
 /// Orientation (non-normalised z-component of unit vector in direction
 /// of step plane)
 double N_z=1.0;
 
 
 /// Orientation (x-coordinate of step plane) 
 double X_0=0.0;
 
 /// Orientation (y-coordinate of step plane) 
 double Y_0=0.0;
 
 /// 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
 
 
 
 
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
 
 
 
//=======start_of_class_definition====================================
/// Poisson problem in refineable eighth of a sphere mesh.
//====================================================================
template<class ELEMENT>
class EighthSpherePoissonProblem : public Problem
{
 
public:
 
 /// Constructor: Pass pointer to source function
 EighthSpherePoissonProblem(
  PoissonEquations<3>::PoissonSourceFctPt source_fct_pt);
 
 /// Destructor: Empty
 ~EighthSpherePoissonProblem(){}
 
 /// Overload generic access function by one that returns
 /// a pointer to the specific  mesh
 RefineableEighthSphereMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<RefineableEighthSphereMesh<ELEMENT>*>(Problem::mesh_pt());
  }
 
 /// Update the problem specs after solve (empty)
 void actions_after_newton_solve()  {}
 
 /// Update the problem specs before solve: 
 /// Set Dirchlet boundary conditions from exact solution.
 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);
    }
   }
 }
 
 /// Doc the solution
 void doc_solution(DocInfo& doc_info);
 
private:
 
 /// Pointer to source function
 PoissonEquations<3>::PoissonSourceFctPt Source_fct_pt;
 
}; // end of class definition
 
 
 
 
 
//====================start_of_constructor================================
/// Constructor for Poisson problem on eighth of a sphere mesh
//========================================================================
template<class ELEMENT>
EighthSpherePoissonProblem<ELEMENT>::EighthSpherePoissonProblem(
   PoissonEquations<3>::PoissonSourceFctPt source_fct_pt) : 
         Source_fct_pt(source_fct_pt)
{ 
 
 // Setup parameters for exact tanh solution
 // Steepness of step
 TanhSolnForPoisson::Alpha=50.0;
 
 /// Create mesh for sphere of radius 5
 double radius=5.0; 
 Problem::mesh_pt() = new RefineableEighthSphereMesh<ELEMENT>(radius);
 
 // Set error estimator 
 Z2ErrorEstimator* error_estimator_pt=new Z2ErrorEstimator;
 mesh_pt()->spatial_error_estimator_pt()=error_estimator_pt;
 
 // Adjust error targets for adaptive refinement
 if (CommandLineArgs::Argc>1)
  {
   // Validation: Relax tolerance to get nonuniform refinement during
   // first step
   mesh_pt()->max_permitted_error()=0.7;
   mesh_pt()->min_permitted_error()=0.5;
  }
 else
  {
   mesh_pt()->max_permitted_error()=0.01;
   mesh_pt()->min_permitted_error()=0.001;
  } // end adjustment
 
 //Doc the mesh boundaries
 ofstream some_file;
 some_file.open("boundaries.dat");
 mesh_pt()->output_boundaries(some_file);
 some_file.close();
 
 // Set the boundary conditions for this problem: All nodes are
 // free by default -- just pin the ones that have Dirichlet conditions
 // here (all the nodes on the boundary)
 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); 
    }
  } // end of pinning
 
 
 //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 FiniteElement 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 
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl; 
 
} // end of constructor
 
 
 
//========================start_of_doc====================================
/// Doc the solution
//========================================================================
template<class ELEMENT>
void EighthSpherePoissonProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{
 ofstream some_file;
 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);
 mesh_pt()->output(some_file,npts);
 some_file.close();
 
 
 // Output exact solution 
 //----------------------
 snprintf(filename, sizeof(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;
 snprintf(filename, sizeof(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
 
 
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
 
 
 
//=========start_of_main=============================================
/// Driver for 3D Poisson problem in eighth of a sphere. Solution 
/// has a sharp step. If there are
/// any command line arguments, we regard this as a validation run
/// and perform only a single adaptation.
//===================================================================
int main(int argc, char *argv[]) 
{ 
 
 // Store command line arguments
 CommandLineArgs::setup(argc,argv);
 
 // Set up the problem with 27-node brick elements, pass pointer to 
 // source function
 EighthSpherePoissonProblem<RefineableQPoissonElement<3,3> >
  problem(&TanhSolnForPoisson::get_source);
 
 // Setup labels for output
  DocInfo doc_info;
 
 // Output directory
 doc_info.set_directory("RESLT");
 
 // Step number
 doc_info.number()=0;
 
 // Check if we're ready to go
 cout << "Self test: " << problem.self_test() << std::endl;
 
 // Solve the problem
 problem.newton_solve();
 
 //Output solution
 problem.doc_solution(doc_info);
 
 //Increment counter for solutions 
 doc_info.number()++;
 
 // Now do (up to) three rounds of fully automatic adapation in response to 
 // error estimate
 unsigned max_solve;
 if (CommandLineArgs::Argc>1)
  {
   // Validation run: Just one adaptation
   max_solve=1;
   cout << "Only doing one adaptation for validation" << std::endl;
  }
 else
  {
   // Up to four adaptations
   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()++;
  }
 
// pause("done");
 
} // end of main