biharmonic_flux_elements.h

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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// Copyright (C) 2006-2025 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
// LIC// 02110-1301  USA.
// LIC//
// LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
// LIC//
// LIC//====================================================================
#ifndef OOMPH_BIHARMONIC_FLUX_ELEMENTS_HEADER
#define OOMPH_BIHARMONIC_FLUX_ELEMENTS_HEADER
 
// Config header
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
#ifdef OOMPH_HAS_MPI
// mpi headers
#include "mpi.h"
#endif
 
// Generic C++ headers
#include <iostream>
#include <math.h>
 
// oomph-lib headers
#include "generic/matrices.h"
#include "generic/elements.h"
#include "generic/hermite_elements.h"
#include "biharmonic_elements.h"
 
 
// oomph namespace
namespace oomph
{
  //============================================================================
  /// face geometry for biharmonic elements - template parameter
  /// indicates dimension of problem (i.e. bulk element),  not the face elements
  //============================================================================
  template<unsigned DIM>
  class FaceGeometry<BiharmonicElement<DIM>>
    : public virtual QHermiteElement<DIM - 1>
  {
  public:
    /// Constructor: Call the constructor for the
    /// appropriate lower-dimensional BiharmonicElement
    FaceGeometry() : QHermiteElement<DIM - 1>() {}
  };
 
  template<>
  class FaceGeometry<BiharmonicElement<1>> : public virtual PointElement
  {
  public:
    /// Constructor: Call the constructor for the
    /// appropriate lower-dimensional BiharmonicElement
    FaceGeometry() : PointElement() {}
  };
 
 
  //=============================================================================
  /// Biharmonic Flux Element
  //=============================================================================
  template<unsigned DIM>
  class BiharmonicFluxElement
    : public virtual FaceGeometry<BiharmonicElement<2>>,
      public virtual FaceElement
  {
  public:
    /// definition of flux function pointer, flux must be parametised in terms
    /// of the macro element coordinate position (s) along the problem edge
    typedef void (*FluxFctPt)(const double& s, double& flux);
 
    /// constructor
    BiharmonicFluxElement(FiniteElement* const& bulk_el_pt,
                          const int& face_index,
                          const unsigned& b);
 
 
    /// Broken empty constructor
    BiharmonicFluxElement()
    {
      throw OomphLibError("Don't call empty constructor for PoissonFluxElement",
                          OOMPH_CURRENT_FUNCTION,
                          OOMPH_EXCEPTION_LOCATION);
    }
 
 
    /// Broken copy constructor
    BiharmonicFluxElement(const BiharmonicFluxElement& dummy) = delete;
 
 
    /// Broken assignment operator
    void operator=(const BiharmonicFluxElement&) = delete;
 
    /// Access function for the flux0 function pointer
    FluxFctPt& flux0_fct_pt()
    {
      return Flux0_fct_pt;
    }
 
    /// Access function for the flux1 function pointer
    FluxFctPt& flux1_fct_pt()
    {
      return Flux1_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
      fill_in_generic_residual_contribution_biharmonic_flux(residuals);
    }
 
 
    /// Add the element's contribution to its residual vector and its
    /// Jacobian matrix (note - no contributions are made to the jacobian)
    inline void fill_in_contribution_to_jacobian(Vector<double>& residuals,
                                                 DenseMatrix<double>& jacobian)
    {
      // Call the generic residuals routine
      fill_in_generic_residual_contribution_biharmonic_flux(residuals);
    }
 
 
    /// 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 -- does nothing
    void output(std::ostream& outfile) {}
 
 
    /// Output function -- does nothing
    void output(std::ostream& outfile, const unsigned& n_plot) {}
 
 
    /// C-style output function -- does nothing
    void output(FILE* file_pt) {}
 
 
    /// C-style output function -- does nothing
    void output(FILE* file_pt, const unsigned& n_plot) {}
 
 
    /// compute_error -- does nothing
    void compute_error(std::ostream& outfile,
                       FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
                       double& error,
                       double& norm)
    {
    }
 
 
    virtual void output_fct(
      std::ostream& outfile,
      const unsigned& nplot,
      FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
    {
    }
 
  private:
    /// Function to return the prescribed flux at a given macro element
    /// coordinate position
    void get_flux0(const double& s, double& flux)
    {
      // If the function pointer is zero return zero
      if (Flux0_fct_pt == 0)
      {
        flux = 0.0;
      }
      // Otherwise call the function
      else
      {
        (*Flux0_fct_pt)(s, flux);
      }
    }
 
    /// Function to return the prescribed flux at a given macro element
    /// coordinate position
    void get_flux1(const double& s, double& flux)
    {
      // If the function pointer is zero return zero
      if (Flux1_fct_pt == 0)
      {
        flux = 0.0;
      }
      // Otherwise call the function
      else
      {
        (*Flux1_fct_pt)(s, flux);
      }
    }
 
    /// Calculate the Jacobian of the mapping between local and global
    /// coordinates at the position s for face elements
    double J_eulerian(const Vector<double>& s) const;
 
    /// Add the element's contribution to its residual vector. Flux
    /// elements only make contribution to the residual vector
    void fill_in_generic_residual_contribution_biharmonic_flux(
      Vector<double>& residuals);
 
    /// Function pointer to the prescribed flux
    FluxFctPt Flux0_fct_pt;
 
    /// Function pointer to the prescribed flux
    FluxFctPt Flux1_fct_pt;
 
    /// the number of nodal degrees of freedom for the face element basis
    /// functions
    unsigned Nface_nodal_dof;
 
    /// Boundary ID
    unsigned Boundary;
  };
 
 
} // namespace oomph
#endif