two_d_poisson.cc

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//LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
//Driver for a simple 2D poisson problem
 
//Generic routines
#include "generic.h"
 
// The Poisson equations
#include "poisson.h"
 
// The mesh
#include "meshes/simple_rectangular_quadmesh.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=1.0;
 
 /// Parameter for angle Phi of "step"
 double TanPhi=0.0;
 
 /// Exact solution as a Vector
 void get_exact_u(const Vector<double>& x, Vector<double>& u)
 {
  u[0]=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }
 
 /// Source function required to make the solution above an exact solution 
 void source_function(const Vector<double>& x, double& source)
 {
  source = 2.0*tanh(-1.0+Alpha*(TanPhi*x[0]-x[1]))*
   (1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*
   Alpha*Alpha*TanPhi*TanPhi+2.0*tanh(-1.0+Alpha*(TanPhi*x[0]-x[1]))*
   (1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*Alpha*Alpha;
 }
 
} // end of namespace
 
 
 
 
 
 
 
 
//====== start_of_problem_class=======================================
/// 2D Poisson problem on rectangular domain, discretised with
/// 2D QPoisson elements. The specific type of element is
/// specified via the template parameter.
//====================================================================
template<class ELEMENT> 
class PoissonProblem : public Problem
{
 
public:
 
 /// Constructor: Pass pointer to source function
 PoissonProblem(PoissonEquations<2>::PoissonSourceFctPt source_fct_pt);
 
 /// Destructor (empty)
 ~PoissonProblem(){}
 
 /// Update the problem specs before solve: Reset boundary conditions
 /// to the values from the exact solution.
 void actions_before_newton_solve();
 
 /// Update the problem 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);
 
private:
 
 /// Pointer to source function
 PoissonEquations<2>::PoissonSourceFctPt Source_fct_pt;
 
}; // end of problem class
 
 
 
 
//=====start_of_constructor===============================================
/// Constructor for Poisson problem: Pass pointer to source function.
//========================================================================
template<class ELEMENT>
PoissonProblem<ELEMENT>::
      PoissonProblem(PoissonEquations<2>::PoissonSourceFctPt source_fct_pt)
       :  Source_fct_pt(source_fct_pt)
{ 
 // Setup mesh
 
 // # of elements in x-direction
 unsigned n_x=4;
 
 // # of elements in y-direction
 unsigned n_y=4;
 
 // Domain length in x-direction
 double l_x=1.0;
 
 // Domain length in y-direction
 double l_y=2.0;
 
 // Build and assign mesh
 Problem::mesh_pt() = new SimpleRectangularQuadMesh<ELEMENT>(n_x,n_y,l_x,l_y);
 
 // Set the boundary conditions for this problem: All nodes are
 // free by default -- only need to pin the ones that have Dirichlet conditions
 // here. 
 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++)
    {
     mesh_pt()->boundary_node_pt(i,n)->pin(0); 
    }
  }
 
 // Complete the build of all elements so they are fully functional
 
 // Loop over the elements to set up element-specific 
 // things that cannot be handled by the (argument-free!) ELEMENT 
 // constructor: Pass pointer to source function
 unsigned n_element = mesh_pt()->nelement();
 for(unsigned i=0;i<n_element;i++)
  {
   // Upcast from GeneralsedElement 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; 
 
} // end of constructor
 
 
 
 
//========================================start_of_actions_before_newton_solve===
/// Update the problem specs before solve: (Re-)set boundary conditions
/// to the values from the exact solution.
//========================================================================
template<class ELEMENT>
void PoissonProblem<ELEMENT>::actions_before_newton_solve()
{
 // How many boundaries are there?
 unsigned n_bound = mesh_pt()->nboundary();
 
 //Loop over the boundaries
 for(unsigned i=0;i<n_bound;i++)
  {
   // How many nodes are there on this boundary?
   unsigned n_node = mesh_pt()->nboundary_node(i);
 
   // Loop over the nodes on boundary
   for (unsigned n=0;n<n_node;n++)
    {
     // Get pointer to node
     Node* nod_pt=mesh_pt()->boundary_node_pt(i,n);
 
     // Extract nodal coordinates from node:
     Vector<double> x(2);
     x[0]=nod_pt->x(0);
     x[1]=nod_pt->x(1);
 
     // Compute the value of the exact solution at the nodal point
     Vector<double> u(1);
     TanhSolnForPoisson::get_exact_u(x,u);
 
     // Assign the value to the one (and only) nodal value at this node
     nod_pt->set_value(0,u[0]);
    }
  } 
}  // end of actions before solve
 
 
 
//===============start_of_doc=============================================
/// Doc the solution: doc_info contains labels/output directory etc.
//========================================================================
template<class ELEMENT>
void PoissonProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{ 
 
 ofstream some_file;
 char filename[100];
 
 // Number of plot points: npts x npts
 unsigned 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 and return of the square of the L2 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();
 
 // Doc L2 error and norm of solution
 cout << "\nNorm of error   : " << sqrt(error) << std::endl; 
 cout << "Norm of solution: " << sqrt(norm) << std::endl << std::endl;
 
} // end of doc
 
 
 
 
 
 
//===== start_of_main=====================================================
/// Driver code for 2D Poisson problem
//========================================================================
int main()
{
 
 //Set up the problem
 //------------------
 
 // Create the problem with 2D nine-node elements from the
 // QPoissonElement family. Pass pointer to source function. 
 PoissonProblem<QPoissonElement<2,3> > 
  problem(&TanhSolnForPoisson::source_function);
 
 // Create label for output
 //------------------------
 DocInfo doc_info;
 
 // Set output directory
 doc_info.set_directory("RESLT");
 
 // Step number
 doc_info.number()=0;
 
 // Check that we're ready to go:
 //----------------------------
 cout << "\n\n\nProblem self-test ";
 if (problem.self_test()==0) 
  {
   cout << "passed: Problem can be solved." << std::endl;
  }
 else 
  {
   throw OomphLibError("Self test failed",
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  }
 
 
 // Set the orientation of the "step" to 45 degrees
 TanhSolnForPoisson::TanPhi=1.0;
 
 // Initial value for the steepness of the "step"
 TanhSolnForPoisson::Alpha=1.0; 
 
 
 // Do a couple of solutions for different forcing functions
 //---------------------------------------------------------
 unsigned nstep=4;
 for (unsigned istep=0;istep<nstep;istep++)
  {
 
   // Increase the steepness of the step:
   TanhSolnForPoisson::Alpha+=1.0;
 
   cout << "\n\nSolving for TanhSolnForPoisson::Alpha="
        << TanhSolnForPoisson::Alpha << std::endl << std::endl;
 
   // Solve the problem
   problem.newton_solve();
 
   //Output the solution
   problem.doc_solution(doc_info);
 
   //Increment counter for solutions 
   doc_info.number()++;
 
  }
 
 
} //end of main