periodic_orbit_handler.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
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//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
#include "periodic_orbit_handler.h"

namespace oomph
{

 void PeriodicOrbitEquations::orbit_output(GeneralisedElement* const &elem_pt, 
                                           std::ostream &outfile, 
                                           const unsigned &n_plot)
 {
   //Find out how many nodes there are
   const unsigned n_node = nnode();
   
   //Set up memory for the shape and test functions
   Shape psi(n_node);
   DShape dpsidt(n_node,1);
     
   Vector<double> s(1);

   //Cast the element
   PeriodicOrbitBaseElement* const base_el_pt = 
    dynamic_cast<PeriodicOrbitBaseElement*>(elem_pt);
     
   const double inverse_timescale = this->omega();

   //Loop over the plot point
   for(unsigned i=0;i<n_plot;i++)
    {
     //Get the coordinate
     s[0] = -1.0 + 2.0*i/((double)(n_plot-1));

     (void)dshape_eulerian(s,psi,dpsidt);
     
     //Sort out the timestepper weights and the time in here
     //Calculate the time
     double interpolated_time = 0.0;
     for(unsigned l=0;l<n_node;l++)
      {
       interpolated_time += raw_nodal_position(l,0)*psi(l);
      }


     //Need to multiply by period and the set global time
     this->time_pt()->time() = interpolated_time;

     //Set the weights of the timestepper
     this->set_timestepper_weights(psi,dpsidt);

     base_el_pt->spacetime_output(outfile,n_plot, 
                                     interpolated_time/inverse_timescale);
    }
  }

 void PeriodicOrbitEquations::fill_in_generic_residual_contribution_orbit(
  PeriodicOrbitAssemblyHandlerBase* const &assembly_handler_pt,
  GeneralisedElement* const &elem_pt, 
  Vector<double> &residuals, DenseMatrix<double> &jacobian, 
  const unsigned& flag)
  {
   //A simple integration loop
   //Find out how many nodes there are
   const unsigned n_node = nnode();

   //Set up memory for the shape and test functions
   Shape psi(n_node), test(n_node);
   DShape dpsidt(n_node,1), dtestdt(n_node,1);
   
   //Set the value of n_intpt
   const unsigned n_intpt = integral_pt()->nweight();
   
   //Integers to store the local equation and unknown numbers
   int local_eqn=0, local_unknown=0;
   
   //Storage for the underlying element's residuals
   const unsigned n_elem_dof = elem_pt->ndof();
   Vector<double> el_residuals(n_elem_dof);
   DenseMatrix<double> el_mass;
   DenseMatrix<double> el_jacobian;

   if(flag) 
    {
     el_mass.resize(n_elem_dof,n_elem_dof);
     el_jacobian.resize(n_elem_dof,n_elem_dof);
    }

   //Storage for the current value of the unkowns
   Vector<double> u(n_elem_dof);
   //and the derivatives
   Vector<double> du_dt(n_elem_dof);
   //And the previous derivative
   Vector<double> du_dt_old(n_elem_dof);
   //Storage for the inner product matrix
   DenseMatrix<double> inner_product(n_elem_dof);
   //Cast the element
   PeriodicOrbitBaseElement* const base_el_pt = 
    dynamic_cast<PeriodicOrbitBaseElement*>(elem_pt);
   //Get the inner product matrix
   base_el_pt->get_inner_product_matrix(inner_product);
   
   //Storage for "all" unknowns
   Vector<double> all_current_unknowns;
   Vector<double> all_previous_unknowns;

   //Get the value of omega
   const double inverse_timescale = this->omega();
   
   //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 = dshape_and_dtest_eulerian_at_knot_orbit(ipt,psi,dpsidt,
                                                        test,dtestdt);
     
     //Premultiply the weights and the Jacobian
     double W = w*J;
     
     //Sort out the timestepper weights and the time in here
     //Calculate the time
     double interpolated_time = 0.0;
     for(unsigned l=0;l<n_node;l++)
      {
       interpolated_time += raw_nodal_position(l,0)*psi(l);
      }
     
     
     //Need to multiply by period and the set global time
     this->time_pt()->time() = interpolated_time/inverse_timescale;
     //Set the weights of the timestepper
     this->set_timestepper_weights(psi,dpsidt);

     //Get the residuals of the element or residuals and jacobian
     if(flag) 
      {
       elem_pt->get_jacobian_and_mass_matrix(el_residuals,el_jacobian,
                                             el_mass);
      }
      else
       {
        elem_pt->get_residuals(el_residuals);
       }

     //Get the current value of the unknown time derivatives
     base_el_pt->get_non_external_ddofs_dt(du_dt);

     //Multiply the elemental residuals by the appropriate test functions
     for(unsigned l=0;l<n_node;l++)
      {
       //Get the local equation number
       local_eqn = nodal_local_eqn(l,0);
       //If it's not a boundary condition (it will never be)
       if(local_eqn >= 0)
        {
         //Work out the offset which is the GLOBAL time unknown
         //multiplied by the number of elemental unknowns
         unsigned offset = this->eqn_number(local_eqn)*n_elem_dof;
         //Add to the appropriate residuals
         for(unsigned i=0;i<n_elem_dof;i++)
          {
           residuals[i + offset] += el_residuals[i]*psi(l)*W;
          }

         
         //Add the jacobian contributions
         if(flag)
          {
           //The form of the equations is -M du/dt + R = 0
             
           //Now add the contribution to the jacobian
           for(unsigned l2=0;l2<n_node;l2++)
            {
             local_unknown = nodal_local_eqn(l2,0);
             if(local_unknown >= 0)
              {
               //Work out the second offset
               unsigned offset2 = this->eqn_number(local_unknown)*n_elem_dof;
               //Add to the appropriate jacobian terms
               for(unsigned i=0;i<n_elem_dof;i++)
                {
                 for(unsigned j=0;j<n_elem_dof;j++)
                  {
                   //Add in the Jacobian terms
                   jacobian(i + offset, j+ offset2) += 
                    el_jacobian(i,j)*psi(l2)*psi(l)*W;
                   
                   //Add the time derivative terms, 
                   jacobian(i + offset, j + offset2) -= el_mass(i,j)*
                    dpsidt(l2,0)*inverse_timescale*psi(l)*W;
                  }
                }
              }
            }
           
           
           //Add the variation of the period
           for(unsigned i=0;i<n_elem_dof;i++)
            {
             for(unsigned j=0;j<n_elem_dof;j++)
              {
               jacobian(i + offset, Ntstorage*n_elem_dof)
                -= el_mass(i,j)*(du_dt[j]/inverse_timescale)*psi(l)*W;
              }
            }
          } //End of Jacobian flag
        }
      }

     //Sort out the phase condition

     //Get the current value of the unknowns
     base_el_pt->get_non_external_dofs(u);

     //Now get the unknowns required by the assembly handler
     //i.e. including all values throughout the period for backup
     assembly_handler_pt->get_dofs_for_element(elem_pt,
                                               all_current_unknowns);
     //Get the previous values as stored by the assembly handler
     assembly_handler_pt->get_previous_dofs_for_element(elem_pt,
                                                        all_previous_unknowns);
     
     //Now set the elemental values to the previous values
     assembly_handler_pt->set_dofs_for_element(elem_pt,all_previous_unknowns);
     //Get the previous time derivatives
     base_el_pt->get_non_external_ddofs_dt(du_dt_old);
     //Reset the element's values to the current 
     assembly_handler_pt->set_dofs_for_element(elem_pt,all_current_unknowns);


     //Assemble the inner product
     double sum = 0.0;
     for(unsigned i=0;i<n_elem_dof;i++)
      {
       for(unsigned j=0;j<n_elem_dof;j++)
        {
         sum += u[i]*inner_product(i,j)*du_dt_old[j];
        }
      }
     
     //Add to the residuals 
     residuals[Ntstorage*n_elem_dof] += sum*W;

     //Sort out the jacobian
     if(flag)
      {
       //Loop over the unknown time points
       for(unsigned l2=0;l2<n_node;l2++)
        {
         //Get the local unknown
         local_unknown = nodal_local_eqn(l2,0);
         if(local_unknown >= 0)
          {
           //Work out the offset
           unsigned offset2 = this->eqn_number(local_unknown)*n_elem_dof;
           //Now add in the appropriate jacobian terms
           for(unsigned i2=0;i2<n_elem_dof;i2++)
            {
             double sum2 = 0.0;
             for(unsigned j=0;j<n_elem_dof;j++)
              {
               sum2 += inner_product(i2,j)*du_dt_old[j];
              }
             jacobian(Ntstorage*n_elem_dof,i2 + offset2) += psi(l2)*sum2*W;
            }
          }
        }
      } //End of jacobian calculation

    } //End of loop over time period integration points
  }



}