poisson_flux_elements.h

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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
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// Header file for elements that are used to apply prescribed flux
// boundary conditions to the Poisson equations
#ifndef OOMPH_POISSON_FLUX_ELEMENTS_HEADER
#define OOMPH_POISSON_FLUX_ELEMENTS_HEADER


// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
  #include <oomph-lib-config.h>
#endif

// oomph-lib includes
#include "../generic/Qelements.h"

namespace oomph
{

//======================================================================
/// \short A class for elements that allow the imposition of an 
/// applied flux on the boundaries of Poisson elements.
/// The element geometry is obtained from the  FaceGeometry<ELEMENT> 
/// policy class.
//======================================================================
template <class ELEMENT>
class PoissonFluxElement : public virtual FaceGeometry<ELEMENT>, 
public virtual FaceElement
{
 
public:

 /// \short Function pointer to the prescribed-flux function fct(x,f(x)) -- 
 /// x is a Vector! 
 typedef void (*PoissonPrescribedFluxFctPt)
  (const Vector<double>& x, double& flux);

 /// \short Constructor, takes the pointer to the "bulk" element and the 
 /// index of the face to which the element is attached.
 PoissonFluxElement(FiniteElement* const &bulk_el_pt, 
                    const int& face_index); 

 ///\short  Broken empty constructor
 PoissonFluxElement()
  {
   throw OomphLibError(
    "Don't call empty constructor for PoissonFluxElement",
    OOMPH_CURRENT_FUNCTION,
    OOMPH_EXCEPTION_LOCATION);
  }

 /// Broken copy constructor
 PoissonFluxElement(const PoissonFluxElement& dummy) 
  { 
   BrokenCopy::broken_copy("PoissonFluxElement");
  } 
 
 /// Broken assignment operator
 void operator=(const PoissonFluxElement&) 
  {
   BrokenCopy::broken_assign("PoissonFluxElement");
  }

 /// \short Specify the value of nodal zeta from the face geometry
 /// The "global" intrinsic coordinate of the element when
 /// viewed as part of a geometric object should be given by
 /// the FaceElement representation, by default (needed to break
 /// indeterminacy if bulk element is SolidElement)
 double zeta_nodal(const unsigned &n, const unsigned &k,           
                          const unsigned &i) const 
  {return FaceElement::zeta_nodal(n,k,i);}     

 /// Access function for the prescribed-flux function pointer
 PoissonPrescribedFluxFctPt& flux_fct_pt() {return Flux_fct_pt;}


 /// Add the element's contribution to its residual vector
 inline void fill_in_contribution_to_residuals(Vector<double> &residuals)
  {
   //Call the generic residuals function with flag set to 0
   //using a dummy matrix argument
   fill_in_generic_residual_contribution_poisson_flux(
    residuals,GeneralisedElement::Dummy_matrix,0);
  }


 /// \short Add the element's contribution to its residual vector and its 
 /// Jacobian matrix
 inline void fill_in_contribution_to_jacobian(Vector<double> &residuals,
                                          DenseMatrix<double> &jacobian)
  {
   //Call the generic routine with the flag set to 1
   fill_in_generic_residual_contribution_poisson_flux(residuals,jacobian,1);
  }

 /// Output function
 void output(std::ostream &outfile)
 {
  const unsigned n_plot=5;
  output(outfile,n_plot);
 }

 /// \short Output function
 void output(std::ostream &outfile, const unsigned &nplot)
  {
   
   // Dimension of element 
   unsigned el_dim=dim();

   //Vector of local coordinates
   Vector<double> s(el_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);
     
     Vector<double> x(el_dim+1);
     for(unsigned i=0;i<el_dim+1;i++) 
      {
       x[i]=interpolated_x(s,i);
       outfile << x[i] << " ";
      }
     double flux=0.0;
     get_flux(x,flux);
     outfile << flux << std::endl;   
    }
   
   // Write tecplot footer (e.g. FE connectivity lists)
   write_tecplot_zone_footer(outfile,nplot);

  }


 /// C-style output function -- forward to broken version in FiniteElement
 /// until somebody decides what exactly they want to plot here...
 void output(FILE* file_pt) {FiniteElement::output(file_pt);}

 /// \short C-style output function -- forward to broken version in 
 /// FiniteElement until somebody decides what exactly they want to plot 
 /// here...
 void output(FILE* file_pt, const unsigned &n_plot)
  {FiniteElement::output(file_pt,n_plot);}


protected:

 /// \short Function to compute the shape and test functions and to return 
 /// the Jacobian of mapping between local and global (Eulerian)
 /// coordinates
 inline double shape_and_test(const Vector<double> &s, Shape &psi, Shape &test)
  const
  {
   //Find number of nodes
   unsigned n_node = nnode();

   //Get the shape functions
   shape(s,psi);

   //Set the test functions to be the same as the shape functions
   for(unsigned i=0;i<n_node;i++) {test[i] = psi[i];}

   //Return the value of the jacobian
   return J_eulerian(s);
  }


 /// \short Function to compute the shape and test functions and to return 
 /// the Jacobian of mapping between local and global (Eulerian)
 /// coordinates
 inline double shape_and_test_at_knot(const unsigned &ipt,
                                      Shape &psi, Shape &test)
  const
  {
   //Find number of nodes
   unsigned n_node = nnode();

   //Get the shape functions
   shape_at_knot(ipt,psi);

   //Set the test functions to be the same as the shape functions
   for(unsigned i=0;i<n_node;i++) {test[i] = psi[i];}

   //Return the value of the jacobian
   return J_eulerian_at_knot(ipt);
  }


 /// Function to calculate the prescribed flux at a given spatial
 /// position
 void get_flux(const Vector<double>& x, double& flux)
  {
   //If the function pointer is zero return zero
   if(Flux_fct_pt == 0)
    {
     flux=0.0;
    }
   //Otherwise call the function
   else
    {
     (*Flux_fct_pt)(x,flux);
    }
  }

private:


 /// \short Add the element's contribution to its residual vector.
 /// flag=1(or 0): do (or don't) compute the contribution to the
 /// Jacobian as well. 
 void fill_in_generic_residual_contribution_poisson_flux(
  Vector<double> &residuals, DenseMatrix<double> &jacobian, 
  const unsigned& flag);
 
 
 /// Function pointer to the (global) prescribed-flux function
 PoissonPrescribedFluxFctPt Flux_fct_pt;

 ///The spatial dimension of the problem
 unsigned Dim;

 ///The index at which the unknown is stored at the nodes
 unsigned U_index_poisson;


}; 

//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////



//===========================================================================
/// Constructor, takes the pointer to the "bulk" element, the 
/// index of the fixed local coordinate and its value represented
/// by an integer (+/- 1), indicating that the face is located
/// at the max. or min. value of the "fixed" local coordinate
/// in the bulk element.
//===========================================================================
template<class ELEMENT>
PoissonFluxElement<ELEMENT>::
PoissonFluxElement(FiniteElement* const &bulk_el_pt, 
                   const int &face_index) : 
  FaceGeometry<ELEMENT>(), FaceElement()
  { 
   // Let the bulk element build the FaceElement, i.e. setup the pointers 
   // to its nodes (by referring to the appropriate nodes in the bulk
   // element), etc.
   bulk_el_pt->build_face_element(face_index,this);
 
#ifdef PARANOID
   {
    //Check that the element is not a refineable 3d element
    ELEMENT* elem_pt = dynamic_cast<ELEMENT*>(bulk_el_pt);
    //If it's three-d
    if(elem_pt->dim()==3)
     {
      //Is it refineable
      RefineableElement* ref_el_pt=dynamic_cast<RefineableElement*>(elem_pt);
      if(ref_el_pt!=0)
       {
        if (this->has_hanging_nodes())
         {
          throw OomphLibError(
           "This flux element will not work correctly if nodes are hanging\n",
           OOMPH_CURRENT_FUNCTION,
           OOMPH_EXCEPTION_LOCATION);
         }
       }
     }
   }
#endif   

   // Initialise the prescribed-flux function pointer to zero
   Flux_fct_pt = 0;

   // Extract the dimension of the problem from the dimension of 
   // the first node
   Dim = this->node_pt(0)->ndim();

   //Set up U_index_poisson. Initialise to zero, which probably won't change
   //in most cases, oh well, the price we pay for generality
   U_index_poisson = 0;

   //Cast to the appropriate PoissonEquation so that we can
   //find the index at which the variable is stored
   //We assume that the dimension of the full problem is the same
   //as the dimension of the node, if this is not the case you will have
   //to write custom elements, sorry
   switch(Dim)
    {
     //One dimensional problem
    case 1:
    {
     PoissonEquations<1>* eqn_pt = 
      dynamic_cast<PoissonEquations<1>*>(bulk_el_pt);
     //If the cast has failed die
     if(eqn_pt==0)
      {
       std::string error_string =
        "Bulk element must inherit from PoissonEquations.";
       error_string += 
        "Nodes are one dimensional, but cannot cast the bulk element to\n";
       error_string += "PoissonEquations<1>\n.";
       error_string += 
        "If you desire this functionality, you must implement it yourself\n";
       
       throw OomphLibError(error_string,
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
      }
     //Otherwise read out the value
     else
      {
       //Read the index from the (cast) bulk element
       U_index_poisson = eqn_pt->u_index_poisson();
      }
    }
    break;
    
    //Two dimensional problem
    case 2:
    {
     PoissonEquations<2>* eqn_pt = 
      dynamic_cast<PoissonEquations<2>*>(bulk_el_pt);
     //If the cast has failed die
     if(eqn_pt==0)
      {
       std::string error_string =
        "Bulk element must inherit from PoissonEquations.";
       error_string += 
        "Nodes are two dimensional, but cannot cast the bulk element to\n";
       error_string += "PoissonEquations<2>\n.";
       error_string += 
        "If you desire this functionality, you must implement it yourself\n";
       
       throw OomphLibError(error_string,
                           OOMPH_CURRENT_FUNCTION,
                        OOMPH_EXCEPTION_LOCATION);
      }
     else
      {
       //Read the index from the (cast) bulk element.
       U_index_poisson = eqn_pt->u_index_poisson();
      }
    }
    break;
    
    //Three dimensional problem
    case 3:
    {
     PoissonEquations<3>* eqn_pt = 
      dynamic_cast<PoissonEquations<3>*>(bulk_el_pt);
     //If the cast has failed die
     if(eqn_pt==0)
      {
       std::string error_string =
        "Bulk element must inherit from PoissonEquations.";
       error_string += 
        "Nodes are three dimensional, but cannot cast the bulk element to\n";
       error_string += "PoissonEquations<3>\n.";
       error_string += 
        "If you desire this functionality, you must implement it yourself\n";
       
       throw OomphLibError(error_string,
                           OOMPH_CURRENT_FUNCTION,
                        OOMPH_EXCEPTION_LOCATION);
       
      }
     else
      {
       //Read the index from the (cast) bulk element.
       U_index_poisson = eqn_pt->u_index_poisson();
      }
    }
    break;

    //Any other case is an error
    default:
     std::ostringstream error_stream; 
     error_stream <<  "Dimension of node is " << Dim 
                  << ". It should be 1,2, or 3!" << std::endl;
     
     throw OomphLibError(error_stream.str(),
                         OOMPH_CURRENT_FUNCTION,
                         OOMPH_EXCEPTION_LOCATION);
     break;
    }
  }


//===========================================================================
/// Compute the element's residual vector and the (zero) Jacobian matrix.
//===========================================================================
template<class ELEMENT>
void PoissonFluxElement<ELEMENT>::
fill_in_generic_residual_contribution_poisson_flux(
 Vector<double> &residuals, DenseMatrix<double> &jacobian, 
 const unsigned& flag)
{
 //Find out how many nodes there are
 const unsigned n_node = nnode();
  
 //Set up memory for the shape and test functions
 Shape psif(n_node), testf(n_node);
 
 //Set the value of Nintpt
 const unsigned n_intpt = integral_pt()->nweight();
 
 //Set the Vector to hold local coordinates
 Vector<double> s(Dim-1);
 
 //Integers to hold the local equation and unknown numbers
 int local_eqn=0;

 // Locally cache the index at which the variable is stored
 const unsigned u_index_poisson = U_index_poisson;

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

   //Assign values of s
   for(unsigned i=0;i<(Dim-1);i++) {s[i] = integral_pt()->knot(ipt,i);}
   
   //Get the integral weight
   double w = integral_pt()->weight(ipt);
   
   //Find the shape and test functions and return the Jacobian
   //of the mapping
   double J = shape_and_test(s,psif,testf);
   
   //Premultiply the weights and the Jacobian
   double W = w*J;
   
   //Need to find position to feed into flux function, initialise to zero
   Vector<double> interpolated_x(Dim,0.0);
   
   //Calculate velocities and derivatives
   for(unsigned l=0;l<n_node;l++) 
    {
     //Loop over velocity components
     for(unsigned i=0;i<Dim;i++)
      {
       interpolated_x[i] += nodal_position(l,i)*psif[l];
      }
    }
   
   //Get the imposed flux
   double flux;
   get_flux(interpolated_x,flux);
   
   //Now add to the appropriate equations
   
   //Loop over the test functions
   for(unsigned l=0;l<n_node;l++)
    {
     local_eqn = nodal_local_eqn(l,u_index_poisson);
     /*IF it's not a boundary condition*/
     if(local_eqn >= 0)
      {
       //Add the prescribed flux terms
       residuals[local_eqn] -= flux*testf[l]*W;
         
       // Imposed traction doesn't depend upon the solution, 
       // --> the Jacobian is always zero, so no Jacobian
       // terms are required
      }
    }
  }
}


}

#endif