helmholtz_flux_elements.h

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// LIC// ====================================================================
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// LIC//
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// Header file for elements that are used to apply prescribed flux
// boundary conditions to the Helmholtz equations
#ifndef OOMPH_HELMHOLTZ_FLUX_ELEMENTS_HEADER
#define OOMPH_HELMHOLTZ_FLUX_ELEMENTS_HEADER
 
 
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
// oomph-lib ncludes
#include "../generic/Qelements.h"
#include "math.h"
#include <complex>
 
namespace oomph
{
  //======================================================================
  /// A class for elements that allow the imposition of an
  /// applied flux on the boundaries of Helmholtz elements.
  /// The element geometry is obtained from the  FaceGeometry<ELEMENT>
  /// policy class.
  //======================================================================
  template<class ELEMENT>
  class HelmholtzFluxElement : public virtual FaceGeometry<ELEMENT>,
                               public virtual FaceElement
  {
  public:
    /// Function pointer to the prescribed-flux function fct(x,f(x)) --
    /// x is a Vector and  the flux is a complex
 
    typedef void (*HelmholtzPrescribedFluxFctPt)(const Vector<double>& x,
                                                 std::complex<double>& flux);
 
    /// Constructor, takes the pointer to the "bulk" element and the
    /// index of the face to which the element is attached.
    HelmholtzFluxElement(FiniteElement* const& bulk_el_pt,
                         const int& face_index);
 
    /// Broken empty constructor
    HelmholtzFluxElement()
    {
      throw OomphLibError(
        "Don't call empty constructor for HelmholtzFluxElement",
        OOMPH_CURRENT_FUNCTION,
        OOMPH_EXCEPTION_LOCATION);
    }
 
    /// Broken copy constructor
    HelmholtzFluxElement(const HelmholtzFluxElement& dummy) = delete;
 
    /// 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 HelmholtzFluxElement&) = delete;*/
 
 
    /// Access function for the prescribed-flux function pointer
    HelmholtzPrescribedFluxFctPt& 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_helmholtz_flux(
        residuals, GeneralisedElement::Dummy_matrix, 0);
    }
 
 
    /// 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_helmholtz_flux(
        residuals, jacobian, 1);
    }
 
 
    /// 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)
    {
      FiniteElement::output(outfile);
    }
 
    /// 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);
    }
 
    /// 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);
    }
 
 
    /// Return the index at which the unknown value
    /// is stored.
    virtual inline std::complex<unsigned> u_index_helmholtz() const
    {
      return std::complex<unsigned>(U_index_helmholtz.real(),
                                    U_index_helmholtz.imag());
    }
 
 
  protected:
    /// 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 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);
      }
    }
 
 
    /// The index at which the real and imag part of the unknown is
    /// stored at the nodes
    std::complex<unsigned> U_index_helmholtz;
 
 
    /// 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_helmholtz_flux(
      Vector<double>& residuals,
      DenseMatrix<double>& jacobian,
      const unsigned& flag);
 
 
    /// Function pointer to the (global) prescribed-flux function
    HelmholtzPrescribedFluxFctPt Flux_fct_pt;
 
    /// The spatial dimension of the problem
    unsigned Dim;
  };
 
  /// ///////////////////////////////////////////////////////////////////
  /// ///////////////////////////////////////////////////////////////////
  /// ///////////////////////////////////////////////////////////////////
 
 
  //===========================================================================
  /// 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>
  HelmholtzFluxElement<ELEMENT>::HelmholtzFluxElement(
    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_helmholtz. Initialise to zero, which probably won't change
    // in most cases, oh well, the price we pay for generality
    U_index_helmholtz = std::complex<unsigned>(0, 1);
 
    // Cast to the appropriate HelmholtzEquation 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:
      {
        HelmholtzEquations<1>* eqn_pt =
          dynamic_cast<HelmholtzEquations<1>*>(bulk_el_pt);
        // If the cast has failed die
        if (eqn_pt == 0)
        {
          std::string error_string =
            "Bulk element must inherit from HelmholtzEquations.";
          error_string +=
            "Nodes are one dimensional, but cannot cast the bulk element to\n";
          error_string += "HelmholtzEquations<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_helmholtz = eqn_pt->u_index_helmholtz();
        }
      }
      break;
 
      // Two dimensional problem
      case 2:
      {
        HelmholtzEquations<2>* eqn_pt =
          dynamic_cast<HelmholtzEquations<2>*>(bulk_el_pt);
        // If the cast has failed die
        if (eqn_pt == 0)
        {
          std::string error_string =
            "Bulk element must inherit from HelmholtzEquations.";
          error_string +=
            "Nodes are two dimensional, but cannot cast the bulk element to\n";
          error_string += "HelmholtzEquations<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_helmholtz = eqn_pt->u_index_helmholtz();
        }
      }
 
      break;
 
      // Three dimensional problem
      case 3:
      {
        HelmholtzEquations<3>* eqn_pt =
          dynamic_cast<HelmholtzEquations<3>*>(bulk_el_pt);
        // If the cast has failed die
        if (eqn_pt == 0)
        {
          std::string error_string =
            "Bulk element must inherit from HelmholtzEquations.";
          error_string += "Nodes are three dimensional, but cannot cast the "
                          "bulk element to\n";
          error_string += "HelmholtzEquations<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_helmholtz = eqn_pt->u_index_helmholtz();
        }
      }
      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 HelmholtzFluxElement<ELEMENT>::
    fill_in_generic_residual_contribution_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(Dim - 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 < (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 Eulerian position of integration point
      for (unsigned l = 0; l < n_node; l++)
      {
        for (unsigned i = 0; i < Dim; i++)
        {
          interpolated_x[i] += nodal_position(l, i) * psif[l];
        }
      }
 
      // 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_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] * 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_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] * W;
 
          // Imposed traction doesn't depend upon the solution,
          // --> the Jacobian is always zero, so no Jacobian
          // terms are required
        }
      }
    }
  }
 
 
} // namespace oomph
 
#endif