fourier_decomposed_helmholtz_flux_elements.h

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// Header file for elements that are used to apply prescribed flux
// boundary conditions to the Fourier decomposed Helmholtz equations
#ifndef OOMPH_FOURIER_DECOMPOSED_HELMHOLTZ_FLUX_ELEMENTS_HEADER
#define OOMPH_FOURIER_DECOMPOSED_HELMHOLTZ_FLUX_ELEMENTS_HEADER


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

#include "math.h"
#include <complex>

// 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 Fourier decomposed Helmholtz elements.
/// The element geometry is obtained from the  FaceGeometry<ELEMENT> 
/// policy class.
//======================================================================
 template <class ELEMENT>
  class FourierDecomposedHelmholtzFluxElement : 
 public virtual FaceGeometry<ELEMENT>, 
  public virtual FaceElement
  {
   
    public:
   
   /// \short Function pointer to the prescribed-flux function fct(x,f(x)) -- 
   /// x is a Vector and  the flux is a complex
   
   typedef void (*FourierDecomposedHelmholtzPrescribedFluxFctPt)
    (const Vector<double>& x, std::complex<double>& flux);
   
   /// \short Constructor, takes the pointer to the "bulk" element and the 
   /// index of the face to which the element is attached.
   FourierDecomposedHelmholtzFluxElement(FiniteElement* const &bulk_el_pt, 
                                         const int& face_index); 
   
   ///\short  Broken empty constructor
   FourierDecomposedHelmholtzFluxElement()
    {
     throw OomphLibError(
      "Don't call empty constructor for FourierDecomposedHelmholtzFluxElement",
      OOMPH_CURRENT_FUNCTION,
      OOMPH_EXCEPTION_LOCATION);
    }
   
   /// Broken copy constructor
   FourierDecomposedHelmholtzFluxElement(
    const FourierDecomposedHelmholtzFluxElement& dummy) 
    { 
     BrokenCopy::broken_copy("FourierDecomposedHelmholtzFluxElement");
    } 
   
   /// 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 FourierDecomposedHelmholtzFluxElement&) 
    {
     BrokenCopy::broken_assign("FourierDecomposedHelmholtzFluxElement");
     }*/
   
   
   /// Access function for the prescribed-flux function pointer
   FourierDecomposedHelmholtzPrescribedFluxFctPt& 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_fourier_decomposed_helmholtz_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_fourier_decomposed_helmholtz_flux
     (residuals,jacobian,1);
   }
   
   /// Output function -- forward to broken version in FiniteElement
   /// until somebody decides what exactly they want to plot here...
   void output(std::ostream &outfile) {FiniteElement::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)
   {FiniteElement::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) {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);}
   
   
   /// \short Return the index at which the unknown value
   /// is stored. (Real/imag part gives real index of real/imag part).
   virtual inline std::complex<unsigned> 
    u_index_fourier_decomposed_helmholtz() const 
    {
     return std::complex<unsigned>(
      U_index_fourier_decomposed_helmholtz.real(),
      U_index_fourier_decomposed_helmholtz.imag());
    }
   
   
    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, std::complex<double>& flux)
   {
    //If the function pointer is zero return zero
    if(Flux_fct_pt == 0)
     {
      flux = std::complex<double>(0.0,0.0);
     }
    //Otherwise call the function
    else
     {
      (*Flux_fct_pt)(x,flux);
     }
   }
   
   
   /// \short The index at which the real and imag part of the 
   /// unknown is stored at the nodes
   std::complex<unsigned> U_index_fourier_decomposed_helmholtz;
   
   
   /// \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. 
   virtual void 
    fill_in_generic_residual_contribution_fourier_decomposed_helmholtz_flux(
     Vector<double> &residuals, DenseMatrix<double> &jacobian, 
     const unsigned& flag);
   
   
   /// Function pointer to the (global) prescribed-flux function
   FourierDecomposedHelmholtzPrescribedFluxFctPt Flux_fct_pt;
   
  }; 
 
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
 
 
 
//===========================================================================
/// 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>
  FourierDecomposedHelmholtzFluxElement<ELEMENT>::
  FourierDecomposedHelmholtzFluxElement(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);
   
   // Initialise the prescribed-flux function pointer to zero
   Flux_fct_pt = 0;
   

   // Initialise index at which real and imag unknowns are stored
   U_index_fourier_decomposed_helmholtz = std::complex<unsigned>(0,1);
   
   // Now read out indices from bulk element
   FourierDecomposedHelmholtzEquations* eqn_pt = 
    dynamic_cast<FourierDecomposedHelmholtzEquations*>(bulk_el_pt);
   //If the cast has failed die
   if(eqn_pt==0)
    {
     std::string error_string =
      "Bulk element must inherit from FourierDecomposedHelmholtzEquations.";
     throw OomphLibError(
      error_string,
      OOMPH_CURRENT_FUNCTION,
      OOMPH_EXCEPTION_LOCATION);
    }
   else
    {
     //Read the index from the (cast) bulk element
     U_index_fourier_decomposed_helmholtz = 
      eqn_pt->u_index_fourier_decomposed_helmholtz();
    }   

  }

 
//===========================================================================
/// Compute the element's residual vector and the (zero) Jacobian matrix.
//===========================================================================
 template<class ELEMENT>
  void FourierDecomposedHelmholtzFluxElement<ELEMENT>::
  fill_in_generic_residual_contribution_fourier_decomposed_helmholtz_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(1);
   
   //Integers to hold the local equation and unknown numbers
   int local_eqn_real=0 ,local_eqn_imag=0;
   
   //Loop over the integration points
   //--------------------------------
   for(unsigned ipt=0;ipt<n_intpt;ipt++)
    {
     
     //Assign values of s
     for(unsigned i=0;i<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(2,0.0);
     
     //Calculate coordinates
     for(unsigned l=0;l<n_node;l++) 
      {
       //Loop over coordinates
       for(unsigned i=0;i<2;i++)
        {
         interpolated_x[i] += nodal_position(l,i)*psif[l];
        }
      }
     
     //first component
     double r = interpolated_x[0];
     
     //Get the imposed flux
     std::complex<double> flux(0.0,0.0);
     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_real = 
        nodal_local_eqn(l,U_index_fourier_decomposed_helmholtz.real());

       /*IF it's not a boundary condition*/
       if(local_eqn_real >= 0)
        {
         //Add the prescribed flux terms
         residuals[local_eqn_real] -= flux.real()*testf[l]*r*W;
         
         // Imposed traction doesn't depend upon the solution, 
         // --> the Jacobian is always zero, so no Jacobian
         // terms are required
        }
       local_eqn_imag = 
        nodal_local_eqn(l,U_index_fourier_decomposed_helmholtz.imag());

       /*IF it's not a boundary condition*/
       if(local_eqn_imag >= 0)
        {
         //Add the prescribed flux terms
         residuals[local_eqn_imag] -= flux.imag()*testf[l]*r*W;
         
         // Imposed traction doesn't depend upon the solution, 
         // --> the Jacobian is always zero, so no Jacobian
         // terms are required
        }   
      }
    }
  }
 
}

#endif