unsteady_heat_flux_elements.h

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// Header file for elements that are used to apply prescribed flux
// boundary conditions to the UnsteadyHeat equations


#ifndef OOMPH_UNSTEADY_HEAT_FLUX_ELEMENTS_HEADER
#define OOMPH_UNSTEADY_HEAT_FLUX_ELEMENTS_HEADER

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

//Standard libray headers
#include <cmath>

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


namespace oomph
{

//======================================================================
/// \short A class for elements that allow the imposition of an 
/// applied flux on the boundaries of UnsteadyHeat elements.
/// The element geometry is obtained from the  FaceGeometry<ELEMENT> 
/// policy class.
//======================================================================
template <class ELEMENT>
class UnsteadyHeatFluxElement : 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 (*UnsteadyHeatPrescribedFluxFctPt)
  (const double& time, const Vector<double>& x, double& flux);


 /// \short Constructor, takes the pointer to the "bulk" element and the 
 /// index of the face to be created
 UnsteadyHeatFluxElement(FiniteElement* const &bulk_el_pt, 
                         const int &face_index);

 /// Broken copy constructor
 UnsteadyHeatFluxElement(const UnsteadyHeatFluxElement& dummy) 
  { 
   BrokenCopy::broken_copy("UnsteadyHeatFluxElement");
  } 
 
 /// Broken assignment operator
//Commented out broken assignment operator because this can lead to a conflict warning
//when used in the virtual inheritence hierarchy. Essentially the compiler doesn't
//realise that two separate implementations of the broken function are the same and so,
//quite rightly, it shouts.
 /*void operator=(const UnsteadyHeatFluxElement&) 
  {
   BrokenCopy::broken_assign("UnsteadyHeatFluxElement");
   }*/

 /// Access function for the prescribed-flux function pointer
 UnsteadyHeatPrescribedFluxFctPt& flux_fct_pt() {return Flux_fct_pt;}
 
 /// Compute the element 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_ust_heat_flux(
    residuals,GeneralisedElement::Dummy_matrix,0);
  }


 /// Compute the element's 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_ust_heat_flux(residuals,jacobian,1);
  }


 /// \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);}     

 /// Output function -- forward to broken version in FiniteElement
 /// until somebody decides what exactly they want to plot here...
 void output(std::ostream &outfile) {FaceGeometry<ELEMENT>::output(outfile);}

 /// \short Output function -- forward to broken version in FiniteElement
 /// until somebody decides what exactly they want to plot here...
 void output(std::ostream &outfile, const unsigned &n_plot)
  {FaceGeometry<ELEMENT>::output(outfile,n_plot);}

 /// 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) {FaceGeometry<ELEMENT>::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)
  {FaceGeometry<ELEMENT>::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);
  }

 /// Function to calculate the prescribed flux at a given spatial
 /// position and at a gien time
 void get_flux(const double& time, 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)(time,x,flux);
    }
  }


private:


 /// \short Compute the element residual vector.
 /// flag=1(or 0): do (or don't) compute the Jacobian as well. 
 void fill_in_generic_residual_contribution_ust_heat_flux(
  Vector<double> &residuals, DenseMatrix<double> &jacobian, 
  unsigned flag);

 
 /// Function pointer to the (global) prescribed-flux function
 UnsteadyHeatPrescribedFluxFctPt 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_ust_heat;


};

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

//===========================================================================
/// Constructor, takes the pointer to the "bulk" element and the 
/// index of the face to be created.
//===========================================================================
template<class ELEMENT>
UnsteadyHeatFluxElement<ELEMENT>::
UnsteadyHeatFluxElement(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_ust_heat. Initialise to zero, which probably won't change
 //in most cases, oh well, the price we pay for generality
 U_index_ust_heat = 0;
 
 //Cast to the appropriate UnsteadyHeatEquation 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:
  {
   UnsteadyHeatEquations<1>* eqn_pt = 
    dynamic_cast<UnsteadyHeatEquations<1>*>(bulk_el_pt);
   //If the cast has failed die
   if(eqn_pt==0)
    {
     std::string error_string =
      "Bulk element must inherit from UnsteadyHeatEquations.";
     error_string += 
      "Nodes are one dimensional, but cannot cast the bulk element to\n";
     error_string += "UnsteadyHeatEquations<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_ust_heat = eqn_pt->u_index_ust_heat();
    }
  }
  break;
  
  //Two dimensional problem
  case 2:
  {
   UnsteadyHeatEquations<2>* eqn_pt = 
    dynamic_cast<UnsteadyHeatEquations<2>*>(bulk_el_pt);
   //If the cast has failed die
   if(eqn_pt==0)
    {
     std::string error_string =
      "Bulk element must inherit from UnsteadyHeatEquations.";
     error_string += 
      "Nodes are two dimensional, but cannot cast the bulk element to\n";
     error_string += "UnsteadyHeatEquations<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_ust_heat = eqn_pt->u_index_ust_heat();
    }
  }
  break;
  
  //Three dimensional problem
  case 3:
  {
   UnsteadyHeatEquations<3>* eqn_pt = 
    dynamic_cast<UnsteadyHeatEquations<3>*>(bulk_el_pt);
   //If the cast has failed die
   if(eqn_pt==0)
    {
     std::string error_string =
      "Bulk element must inherit from UnsteadyHeatEquations.";
     error_string += 
      "Nodes are three dimensional, but cannot cast the bulk element to\n";
     error_string += "UnsteadyHeatEquations<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_ust_heat = eqn_pt->u_index_ust_heat();
    }
  }
  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 UnsteadyHeatFluxElement<ELEMENT>::
fill_in_generic_residual_contribution_ust_heat_flux(
 Vector<double> &residuals, DenseMatrix<double> &jacobian, 
 unsigned flag)
{
 //Find out how many nodes there are
 const unsigned n_node = nnode();

 // Get continuous time from timestepper of first node
 double time=node_pt(0)->time_stepper_pt()->time_pt()->time();
  
 //Set up memory for the shape and test functions
 Shape psif(n_node), testf(n_node);
 
 //Set the value of n_intpt
 const unsigned n_intpt = integral_pt()->nweight();
 
 //Set the Vector to hold local coordinates
 Vector<double> s(Dim-1);
 
 //Integer to store the local equation and unknowns
 int local_eqn=0;

 // Locally cache the index at which the variable is stored
 const unsigned u_index_ust_heat = U_index_ust_heat;
 
 //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
   Vector<double> interpolated_x(Dim);
   
   //Initialise to zero
   for(unsigned i=0;i<Dim;i++)
    {
     interpolated_x[i] = 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(time,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_ust_heat);
     /*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