biharmonic_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,
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//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
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//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
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//LIC//====================================================================
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
  #include <oomph-lib-config.h>
#endif

//oomph-lib includes
#include "biharmonic_elements.h"


namespace oomph
{

 /// \short Compute element residual Vector only (if JFLAG=and/or element 
 /// Jacobian matrix 
template<unsigned DIM>
void BiharmonicEquations<DIM>::
fill_in_generic_residual_contribution_biharmonic(
 Vector<double> &residuals, 
 DenseMatrix<double>& jacobian, 
 unsigned JFLAG)
{

 //Find out how many nodes there are
 unsigned n_node = this->nnode();

 //Find out how many values there
 unsigned n_value = this->node_pt(0)->nvalue();

 //Find out how many degrees of freedom are associated with 2nd derivative
 unsigned d2_dof = this->get_d2_dof();
        
 //set up memory for shape and test functions
 Shape psi(n_node,n_value);
 DShape dpsidx(n_node,n_value,DIM);
 DShape d2psidx(n_node,n_value, d2_dof); 
// Shape psi(n_node,n_value);
 DShape dpsids(n_node,n_value,DIM);
 DShape d2psids(n_node,n_value, d2_dof); 
        
 // storage of single local coordinate
 Vector<double> s(DIM);
        
 //number of integration points
 unsigned n_intpt = this->integral_pt()->nweight();
 
 // loop over integration points
 for (unsigned ipt = 0; ipt < n_intpt; ipt++)
  {
   
   // set local coordinates to be intergration scheme knot
   for (unsigned i = 0; i < DIM; i++) s[i] = this->integral_pt()->knot(ipt,i); 
                
   // find weight at knot
   double w = this->integral_pt()->weight(ipt);                 
                        
   // find shape fn and derivate fns at knot point, 
   //and Jacobian of local to global mapping
   double J = this->d2shape_eulerian(s,psi,dpsidx,d2psidx);                    
   this->d2shape_local(s,psi,dpsids,d2psids);

   // premultiply weight by jacobian
   double W = w*J;
                
   // initialise storage for d2u_interpolated
   Vector<double> d2u_interpolated(DIM);
   for (unsigned i = 0; i < DIM; i++)
    {
     d2u_interpolated[i] = 0.0;
    }
 
   // loop over nodes, degrees of freedom, and dimension to calculate 
   // interpolated_d2u
   for (unsigned n = 0; n < n_node; n++)
    {
     for (unsigned k = 0; k < n_value; k++)
      {
       for (unsigned d = 0; d < DIM; d++)
        {
         d2u_interpolated[d] += this->node_pt(n)->value(k)*d2psidx(n,k,d);
        }
      }
    }
   
   // create vector for interpolated position and calculate
   Vector<double> interpolated_position(DIM);
   this->interpolated_x(s,interpolated_position);

   // evaluate source function at knot position
   double source = 0.0; 
   get_source(ipt, interpolated_position, source);

   // loop over nodes
   for (unsigned n1 = 0; n1 < n_node; n1++)
    {

     // loop over types of degrees of freedom
     for (unsigned k1=0; k1 < n_value; k1++)
      {
        
       // determine the local equation number
       int local_eqn_number = this->nodal_local_eqn(n1,k1);
                                                                
       // if local equation number equal to -1 then its a boundary node(pinned)
       if (local_eqn_number >= 0)
        {
                        
         // add source contribution to residual
         residuals[local_eqn_number] -= source*psi(n1,k1)*W;            
         
         // loop over dimension of d2u interpolated                     
         for (unsigned d1 = 0; d1 < DIM; d1++) 
          {
           
           // loop over derivatives of d2psidx
           for (unsigned d2 = 0; d2 < DIM; d2++)
            {
            
            // add residual contribution
            residuals[local_eqn_number] += 
            d2u_interpolated[d1]*d2psidx(n1,k1,d2)*W;   
           
           }                                            
           
           //calculate the jacobian
           if(JFLAG)
            {
             
             // loop over nodes
             for (unsigned n2 = 0; n2 < n_node; n2++)
              {
               
               // loop over types of degrees of freedom
               for (unsigned k2=0; k2 < n_value; k2++)
                {
                 
                 // get local dof, -if -1 then node pinned
                 int local_dof_number = this->nodal_local_eqn(n2,k2); 
                 
                 // if local dof # = -1, then its pinned
                 if (local_dof_number >= 0) 
                  {
                   
                   // loop over derivatives
                   for (unsigned d2 = 0; d2 < DIM; d2++)
                    {
                    
                     // add contribution to jacobian            
                     jacobian(local_eqn_number,local_dof_number) += 
                      d2psidx(n1,k1,d1)*d2psidx(n2,k2,d2)*W;
                   
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }
}

 template class BiharmonicElement<2>;
 template class BiharmonicElement<1>;

}