refineable_helmholtz_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.
//LIC// 
//LIC//====================================================================
#include "refineable_helmholtz_elements.h"


namespace oomph
{



//========================================================================
/// Add element's contribution to the elemental 
/// residual vector and/or Jacobian matrix.
/// flag=1: compute both
/// flag=0: compute only residual vector
//========================================================================
template<unsigned DIM>
void RefineableHelmholtzEquations<DIM>::
fill_in_generic_residual_contribution_helmholtz(Vector<double> &residuals, 
                                              DenseMatrix<double> &jacobian, 
                                              const unsigned& flag)
{

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

//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();

//Integers to store the local equation and unknown numbers
int local_eqn_real=0, local_unknown_real=0;
int local_eqn_imag=0, local_unknown_imag=0;

// Local storage for pointers to hang_info objects
 HangInfo *hang_info_pt=0, *hang_info2_pt=0;

//Loop over the integration points
for(unsigned ipt=0;ipt<n_intpt;ipt++)
{
 //Get the integral weight
 double w = integral_pt()->weight(ipt);
 
 //Call the derivatives of the shape and test functions
 double J = 
  this->dshape_and_dtest_eulerian_at_knot_helmholtz(ipt,psi,dpsidx,
                                                    test,dtestdx);
 
 //Premultiply the weights and the Jacobian
 double W = w*J;
 
 // Position and gradient
 std::complex<double> interpolated_u(0.0,0.0);
 Vector<double> interpolated_x(DIM,0.0);
 Vector<std::complex<double> > interpolated_dudx(DIM);
 
 //Calculate function value and derivatives:
 //-----------------------------------------
 
 // Loop over nodes
 for(unsigned l=0;l<n_node;l++) 
  {
   // Loop over directions
   for(unsigned j=0;j<DIM;j++)
    {
     interpolated_x[j] += nodal_position(l,j)*psi(l);
    }
   //Get the nodal value of the helmholtz unknown
   const std::complex<double> u_value(
    nodal_value(l,this->u_index_helmholtz().real()),
    nodal_value(l,this->u_index_helmholtz().imag()));
   //Add to the interpolated value
   interpolated_u += u_value*psi(l);
   
   // Loop over directions
   for(unsigned j=0;j<DIM;j++)
    {
     interpolated_dudx[j] += u_value*dpsidx(l,j);
    } 
  }
 
 //Get body force
 std::complex<double> source(0.0,0.0);
 this->get_source_helmholtz(ipt,interpolated_x,source);
 
 
 // Assemble residuals and Jacobian
 
 // Loop over the nodes for the test functions 
 for(unsigned l=0;l<n_node;l++)
  {
   //Local variables used to store the number of master nodes and the
   //weight associated with the shape function if the node is hanging
   unsigned n_master=1; double hang_weight=1.0;
   
   //Local bool (is the node hanging)
   bool is_node_hanging = this->node_pt(l)->is_hanging();
   
   //If the node is hanging, get the number of master nodes
   if(is_node_hanging)
    {
     hang_info_pt = this->node_pt(l)->hanging_pt();
     n_master = hang_info_pt->nmaster();
    }
   //Otherwise there is just one master node, the node itself
   else
    {
     n_master = 1;
    }
   
   //Loop over the master nodes
   for(unsigned m=0;m<n_master;m++)
    {  
     //Get the local equation number and hang_weight
     //If the node is hanging
     if(is_node_hanging)
      {
       //Read out the local equation number from the m-th master node
       local_eqn_real=this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                           this->u_index_helmholtz().real());
       local_eqn_imag=this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                           this->u_index_helmholtz().imag());
       
       //Read out the weight from the master node
       hang_weight = hang_info_pt->master_weight(m);
      }
     //If the node is not hanging
     else
      {
       //The local equation number comes from the node itself
       local_eqn_real=this->nodal_local_eqn(l,this->u_index_helmholtz().real());
       local_eqn_imag=this->nodal_local_eqn(l,this->u_index_helmholtz().imag());
       
       //The hang weight is one
       hang_weight = 1.0;
      }
     
     //If the nodal equation is not a boundary condition
     if(local_eqn_real >= 0)
      {
       // Add body force/source term here and Helmholtz bit
       residuals[local_eqn_real] += 
        (source.real()-this->k_squared()*interpolated_u.real())*
        test(l)*W*hang_weight;
       
       // The Helmholtz bit itself
       for(unsigned k=0;k<DIM;k++)
        {
         residuals[local_eqn_real] += 
          interpolated_dudx[k].real()*dtestdx(l,k)*W*hang_weight;
        }
       
       // Calculate the Jacobian
       if(flag)
        {
         //Local variables to store the number of master nodes
         //and the weights associated with each hanging node
         unsigned n_master2=1; double hang_weight2=1.0;
         
         //Loop over the nodes for the variables
         for(unsigned l2=0;l2<n_node;l2++)
          { 
           //Local bool (is the node hanging)
           bool is_node2_hanging = this->node_pt(l2)->is_hanging();
           
           //If the node is hanging, get the number of master nodes
           if(is_node2_hanging)
            {
             hang_info2_pt = this->node_pt(l2)->hanging_pt();
             n_master2 = hang_info2_pt->nmaster();
            }
           //Otherwise there is one master node, the node itself
           else
            {
             n_master2 = 1;
            }
           
           //Loop over the master nodes
           for(unsigned m2=0;m2<n_master2;m2++)
            {
             //Get the local unknown and weight
             //If the node is hanging
             if(is_node2_hanging)
              {
               //Read out the local unknown from the master node
               local_unknown_real = 
                this->local_hang_eqn(hang_info2_pt->master_node_pt(m2),
                                     this->u_index_helmholtz().real());
              
               //Read out the hanging weight from the master node
               hang_weight2 = hang_info2_pt->master_weight(m2);
              }
             //If the node is not hanging
             else
              {
               //The local unknown number comes from the node
               local_unknown_real = 
                this->nodal_local_eqn(l2,this->u_index_helmholtz().real());
               
               //The hang weight is one
               hang_weight2 = 1.0;
              }
             
             //If the unknown is not pinned
             if(local_unknown_real >= 0)
              {
               //Add contribution to Elemental Matrix
               for(unsigned i=0;i<DIM;i++)
                {
                 jacobian(local_eqn_real,local_unknown_real) += 
                  dpsidx(l2,i)*dtestdx(l,i)*W*hang_weight*hang_weight2;
                }
               
               // Add the helmholtz contribution
               jacobian(local_eqn_real,local_unknown_real)      -= 
                this->k_squared()*psi(l2)*test(l)*W*
                hang_weight*hang_weight2;
              }
            } //End of loop over master nodes
          } //End of loop over nodes
        } //End of Jacobian calculation 
      } //End of case when residual equation is not pinned
     
     
     if(local_eqn_imag >= 0)
      {
       // Add body force/source term here and Helmholtz bit
       residuals[local_eqn_imag] += 
        (source.imag()-this->k_squared()*interpolated_u.imag())*
        test(l)*W*hang_weight;
       
       // The Helmholtz bit itself
       for(unsigned k=0;k<DIM;k++)
        {
         residuals[local_eqn_imag] += 
          interpolated_dudx[k].imag()*dtestdx(l,k)*W*hang_weight;
        }
       
       // Calculate the Jacobian
       if(flag)
        {
         //Local variables to store the number of master nodes
         //and the weights associated with each hanging node
         unsigned n_master2=1; double hang_weight2=1.0;
         
         //Loop over the nodes for the variables
         for(unsigned l2=0;l2<n_node;l2++)
          { 
           //Local bool (is the node hanging)
           bool is_node2_hanging = this->node_pt(l2)->is_hanging();
           
           //If the node is hanging, get the number of master nodes
           if(is_node2_hanging)
            {
             hang_info2_pt = this->node_pt(l2)->hanging_pt();
             n_master2 = hang_info2_pt->nmaster();
            }
           //Otherwise there is one master node, the node itself
           else
            {
             n_master2 = 1;
            }
           
           //Loop over the master nodes
           for(unsigned m2=0;m2<n_master2;m2++)
            {
             //Get the local unknown and weight
             //If the node is hanging
             if(is_node2_hanging)
              {
               //Read out the local unknown from the master node
               local_unknown_imag = 
                this->local_hang_eqn(hang_info2_pt->master_node_pt(m2),
                                     this->u_index_helmholtz().imag());
               
               //Read out the hanging weight from the master node
               hang_weight2 = hang_info2_pt->master_weight(m2);
              }
             //If the node is not hanging
             else
              {
               //The local unknown number comes from the node
              
               local_unknown_imag = 
                this->nodal_local_eqn(l2,this->u_index_helmholtz().imag());

               //The hang weight is one
               hang_weight2 = 1.0;
              }
 
             if(local_unknown_imag >= 0)
              {
               //Add contribution to Elemental Matrix
               for(unsigned i=0;i<DIM;i++)
                {
                 jacobian(local_eqn_imag,local_unknown_imag) += 
                  dpsidx(l2,i)*dtestdx(l,i)*W*hang_weight*hang_weight2;
                }
               
               // Add the helmholtz contribution
               jacobian(local_eqn_imag,local_unknown_imag)      -= 
                this->k_squared()*psi(l2)*test(l)*W*
                hang_weight*hang_weight2;
              }
            } //End of loop over master nodes
          } //End of loop over nodes
        } //End of Jacobian calculation 
      }
    } //End of loop over master nodes for residual
  } //End of loop over nodes
 
} // End of loop over integration points
}
 

 
 

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

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

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

}