linear_wave_elements.cc

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//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
//LIC// $LastChangedDate$
//LIC// 
//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
//LIC// modify it under the terms of the GNU Lesser General Public
//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
//LIC// 
//LIC// This library is distributed in the hope that it will be useful,
//LIC// but WITHOUT ANY WARRANTY; without even the implied warranty of
//LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//LIC// Lesser General Public License for more details.
//LIC// 
//LIC// You should have received a copy of the GNU Lesser General Public
//LIC// License along with this library; if not, write to the Free Software
//LIC// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
//LIC// 02110-1301  USA.
//LIC// 
//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
#include <cmath>

//Non-inline functions for LinearWave elements
#include "linear_wave_elements.h"


namespace oomph
{


///2D LinearWave elements


//======================================================================
// Set the data for the number of Variables at each node
//======================================================================
template<>
const unsigned QLinearWaveElement<1,4>::Initial_Nvalue[4]={1,1,1,1};
template<>
const unsigned QLinearWaveElement<1,3>::Initial_Nvalue[3]={1,1,1};
template<>
const unsigned QLinearWaveElement<1,2>::Initial_Nvalue[2]={1,1};

template<>
const unsigned QLinearWaveElement<2,4>::Initial_Nvalue[16]
={1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1};
template<>
const unsigned QLinearWaveElement<2,3>::Initial_Nvalue[9]
={1,1,1,1,1,1,1,1,1};
template<>
const unsigned QLinearWaveElement<2,2>::Initial_Nvalue[4]
={1,1,1,1};

template<>
const unsigned QLinearWaveElement<3,2>::Initial_Nvalue[8]
={1,1,1,1,1,1,1,1};
template<>
const unsigned QLinearWaveElement<3,3>::Initial_Nvalue[27]
={1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,1};
template<>
const unsigned QLinearWaveElement<3,4>::Initial_Nvalue[64]
={1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1,
  1,1,1,1,1,1,1,1};



//======================================================================
/// Compute element residual Vector and/or element Jacobian matrix 
/// 
/// flag=1: compute both
/// flag=0: compute only residual Vector
///
/// Pure version without hanging nodes
//======================================================================
template <unsigned DIM>
void  LinearWaveEquations<DIM>::
fill_in_generic_residual_contribution_lin_wave(Vector<double> &residuals, 
                                               DenseMatrix<double> &jacobian, 
                                               unsigned flag) 
{
 //Find out how many nodes there are
 unsigned n_node = nnode();

 // Get continuous time from timestepper of first node
 double time=node_pt(0)->time_stepper_pt()->time_pt()->time();
  
 // Find the index at which the linear wave unknown is stored
 unsigned u_nodal_index = u_index_lin_wave();
  
 //Set up memory for the shape and test functions
 Shape psi(n_node), test(n_node);
 DShape dpsidx(n_node,DIM), dtestdx(n_node,DIM);
 
 //Set the value of n_intpt
 unsigned n_intpt = integral_pt()->nweight();
   
 //Set the Vector to hold local coordinates
 Vector<double> s(DIM);

 //Integers to hold the local equation and unknowns
 int local_eqn=0, local_unknown=0;

 //Loop over the integration points
 for(unsigned ipt=0;ipt<n_intpt;ipt++)
  {

   //Assign values of s
   for(unsigned i=0;i<DIM;i++) s[i] = integral_pt()->knot(ipt,i);

   //Get the integral weight
   double w = integral_pt()->weight(ipt);

   //Call the derivatives of the shape and test functions
   double J = 
    dshape_and_dtest_eulerian_at_knot_lin_wave(ipt,psi,dpsidx,test,dtestdx);

   //Premultiply the weights and the Jacobian
   double W = w*J;

   //Allocate memory for local quantities and initialise to zero
   double interpolated_u=0.0;
   double ddudt=0.0;
   Vector<double> interpolated_x(DIM,0.0);
   Vector<double> interpolated_dudx(DIM,0.0);

   //Calculate function value and derivatives:
   // Loop over nodes
   for(unsigned l=0;l<n_node;l++) 
    {
     //Get the nodal value 
     double u_value = raw_nodal_value(l,u_nodal_index);
     interpolated_u += u_value*psi(l);
     ddudt += d2u_dt2_lin_wave(l)*psi(l);
     // Loop over directions
     for(unsigned j=0;j<DIM;j++)
      {
       interpolated_x[j] += raw_nodal_position(l,j)*psi(l);
       interpolated_dudx[j] += u_value*dpsidx(l,j);
      }
    }


   //Get source function
   //-------------------
   double source;
   get_source_lin_wave(time,ipt,interpolated_x,source);

   // Assemble residuals and Jacobian
   //--------------------------------
       
   // Loop over the test functions
   for(unsigned l=0;l<n_node;l++)
    {
     local_eqn = nodal_local_eqn(l,u_nodal_index);
     /*IF it's not a boundary condition*/
     if(local_eqn >= 0)
      {

       // Add body force/source term and time derivative
       residuals[local_eqn] += (ddudt+source)*test(l)*W;
           
       // Laplace operator
       for(unsigned k=0;k<DIM;k++)
        {
         residuals[local_eqn] += 
          interpolated_dudx[k]*dtestdx(l,k)*W;
        }


       // Calculate the jacobian
       //-----------------------
       if(flag)
        {
         //Loop over the velocity shape functions again
         for(unsigned l2=0;l2<n_node;l2++)
          { 
           local_unknown = nodal_local_eqn(l2,u_nodal_index);
           //If at a non-zero degree of freedom add in the entry
           if(local_unknown >= 0)
            {
             // Mass matrix
             jacobian(local_eqn,local_unknown) 
              += test(l)*psi(l2)*node_pt(l2)->time_stepper_pt()->weight(2,0)*W;

             // Laplace operator
             for(unsigned i=0;i<DIM;i++)
              {
               jacobian(local_eqn,local_unknown) 
                += dpsidx(l2,i)*dtestdx(l,i)*W;
              }
            }
          }
        }
      }
    }


  } // End of loop over integration points
}   




//======================================================================
/// Self-test:  Return 0 for OK
//======================================================================
template <unsigned DIM>
unsigned  LinearWaveEquations<DIM>::self_test()
{

 bool passed=true;

 // Check lower-level stuff
 if (FiniteElement::self_test()!=0)
  {
   passed=false;
  }

 // Return verdict
 if (passed)
  {
   return 0;
  }
 else
  {
   return 1;
  }
   
}



//======================================================================
/// Output function:
///
///   x,y,u   or    x,y,z,u
///
/// nplot points in each coordinate direction
//======================================================================
template <unsigned DIM>
void LinearWaveEquations<DIM>::output(std::ostream &outfile, 
                                      const unsigned &nplot)
{
 //Vector of local coordinates
 Vector<double> s(DIM);
 
 // Tecplot header info
 outfile << tecplot_zone_string(nplot);
 
 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);
   for(unsigned i=0;i<DIM;i++) 
    {
     outfile << interpolated_x(s,i) << " ";
    }
   outfile << interpolated_u_lin_wave(s) << " ";
   outfile << interpolated_du_dt_lin_wave(s) << " ";
   outfile << interpolated_d2u_dt2_lin_wave(s) << std::endl;  
  }

 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(outfile,nplot);

}

//======================================================================
/// C-style output function:
///
///   x,y,u   or    x,y,z,u
///
/// nplot points in each coordinate direction
//======================================================================
template <unsigned DIM>
void  LinearWaveEquations<DIM>::output(FILE* file_pt,
                                 const unsigned &nplot)
{
 //Vector of local coordinates
 Vector<double> s(DIM);
 
 // Tecplot header info
 fprintf(file_pt,"%s",tecplot_zone_string(nplot).c_str());
 
 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {  
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);
   
   for(unsigned i=0;i<DIM;i++) 
    {
     //outfile << interpolated_x(s,i) << " ";
     fprintf(file_pt,"%g ",interpolated_x(s,i));
    }
   //outfile << interpolated_u(s) << std::endl;  
   fprintf(file_pt,"%g \n",interpolated_u_lin_wave(s));
  }

 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(file_pt,nplot);

}



//======================================================================
/// Output exact solution
/// 
/// Solution is provided via function pointer.
/// Plot at a given number of plot points.
///
///   x,y,u_exact    or    x,y,z,u_exact
//======================================================================
template <unsigned DIM>
void LinearWaveEquations<DIM>::output_fct(
 std::ostream &outfile, const unsigned &nplot, 
 FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
{
 //Vector of local coordinates
 Vector<double> s(DIM);

 // Vector for coordintes
 Vector<double> x(DIM);

 // Tecplot header info
 outfile << tecplot_zone_string(nplot);
   
 // Exact solution Vector (value and first and second time derivs)
 Vector<double> exact_soln(3);

 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);

   // Get x position as Vector
   interpolated_x(s,x);

   // Get exact solution at this point
   (*exact_soln_pt)(x,exact_soln);

   //Output x,y,...,u_exact
   for(unsigned i=0;i<DIM;i++)
    {
     outfile << x[i] << " ";
    }
   outfile << exact_soln[0] << std::endl;  
    
  }

 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(outfile,nplot);
}



//======================================================================
/// Output exact solution at time t
/// 
/// Solution is provided via function pointer.
/// Plot at a given number of plot points.
///
///   x,y,u_exact    or    x,y,z,u_exact
//======================================================================
template <unsigned DIM>
void LinearWaveEquations<DIM>::output_fct(
std::ostream &outfile, const unsigned &nplot, const double& time, 
FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
{

 //Vector of local coordinates
 Vector<double> s(DIM);

 // Vector for coordintes
 Vector<double> x(DIM);

 // Tecplot header info
 outfile << tecplot_zone_string(nplot);
   
 // Exact solution Vector u, dudt, d2udt2
 Vector<double> exact_soln(3);

 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {
     
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);

   // Get x position as Vector
   interpolated_x(s,x);

   // Get exact solution at this point
   (*exact_soln_pt)(time,x,exact_soln);

   //Output x,y,...,u_exact
   for(unsigned i=0;i<DIM;i++)
    {
     outfile << x[i] << " ";
    }
   outfile << exact_soln[0] << " " 
           << exact_soln[1] << " " 
           << exact_soln[2] << " " 
           << std::endl;   
  }

 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(outfile,nplot);
}




//======================================================================
/// Validate against exact solution
/// 
/// Solution is provided via function pointer.
/// Plot error at a given number of plot points.
///
//======================================================================
template <unsigned DIM>
void LinearWaveEquations<DIM>::compute_error(
 std::ostream &outfile, 
 FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
 double& error, double& norm)
{ 

 // Initialise
 error=0.0;
 norm=0.0;

 //Vector of local coordinates
 Vector<double> s(DIM);

 // Vector for coordintes
 Vector<double> x(DIM);


 //Find out how many nodes there are in the element
 unsigned n_node = nnode();

 Shape psi(n_node);

 //Set the value of n_intpt
 unsigned n_intpt = integral_pt()->nweight();

 // Tecplot header info
 outfile << "ZONE" << std::endl;
   
 // Exact solution Vector (value, and first and second time derivs)
 Vector<double> exact_soln(3);

 //Loop over the integration points
 for(unsigned ipt=0;ipt<n_intpt;ipt++)
  {

   //Assign values of s
   for(unsigned i=0;i<DIM;i++)
    {
     s[i] = integral_pt()->knot(ipt,i);
    }

   //Get the integral weight
   double w = integral_pt()->weight(ipt);

   // Get jacobian of mapping
   double J=J_eulerian(s);

   //Premultiply the weights and the Jacobian
   double W = w*J;

   // Get x position as Vector
   interpolated_x(s,x);

   // Get FE function value
   double u_fe=interpolated_u_lin_wave(s);

   // Get exact solution at this point
   (*exact_soln_pt)(x,exact_soln);

   //Output x,y,...,error
   for(unsigned i=0;i<DIM;i++)
    {
     outfile << x[i] << " ";
    }
   outfile << exact_soln[0] << " " << exact_soln[0]-u_fe << std::endl;  

   // Add to error and norm
   norm+=exact_soln[0]*exact_soln[0]*W;
   error+=(exact_soln[0]-u_fe)*(exact_soln[0]-u_fe)*W;
  }
}




//======================================================================
/// Validate against exact solution at time t.
/// 
/// Solution is provided via function pointer.
/// Plot error at a given number of plot points.
///
//======================================================================
template <unsigned DIM>
void LinearWaveEquations<DIM>::compute_error(
 std::ostream &outfile, 
 FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt,
 const double& time, double& error, double& norm)

{ 

 // Initialise
 error=0.0;
 norm=0.0;

 //Vector of local coordinates
 Vector<double> s(DIM);

 // Vector for coordintes
 Vector<double> x(DIM);

 //Find out how many nodes there are in the element
 unsigned n_node = nnode();

 Shape psi(n_node);

 //Set the value of n_intpt
 unsigned n_intpt = integral_pt()->nweight();   
     
 // Tecplot header info
 outfile << "ZONE" << std::endl;
   
 // Exact solution Vector (value, and first and second time derivs)
 Vector<double> exact_soln(3);

 //Loop over the integration points
 for(unsigned ipt=0;ipt<n_intpt;ipt++)
  {

   //Assign values of s
   for(unsigned i=0;i<DIM;i++)
    {
     s[i] = integral_pt()->knot(ipt,i);
    }

   //Get the integral weight
   double w = integral_pt()->weight(ipt);

   // Get jacobian of mapping
   double J=J_eulerian(s);

   //Premultiply the weights and the Jacobian
   double W = w*J;

   // Get x position as Vector
   interpolated_x(s,x);

   // Get FE function value
   double u_fe=interpolated_u_lin_wave(s);

   // Get exact solution at this point
   (*exact_soln_pt)(time,x,exact_soln);

   //Output x,y,...,error
   for(unsigned i=0;i<DIM;i++)
    {
     outfile << x[i] << " ";
    }
   outfile << exact_soln[0] << " " << exact_soln[0]-u_fe << std::endl;  

   // Add to error and norm
   norm+=exact_soln[0]*exact_soln[0]*W;
   error+=(exact_soln[0]-u_fe)*(exact_soln[0]-u_fe)*W;

  }
}




//====================================================================
// Force build of templates
//====================================================================
template class QLinearWaveElement<1,2>;
template class QLinearWaveElement<1,3>;
template class QLinearWaveElement<1,4>;

template class QLinearWaveElement<2,2>;
template class QLinearWaveElement<2,3>;
template class QLinearWaveElement<2,4>;

template class QLinearWaveElement<3,2>;
template class QLinearWaveElement<3,3>;
template class QLinearWaveElement<3,4>;


}