Tpoisson_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) 2006-2023 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//
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// LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// LIC// Lesser General Public License for more details.
// LIC//
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// LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
// LIC//
// LIC//====================================================================
// Header file for TPoisson elements
#ifndef OOMPH_TPOISSON_ELEMENTS_HEADER
#define OOMPH_TPOISSON_ELEMENTS_HEADER
 
 
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
 
// OOMPH-LIB headers
#include "../generic/nodes.h"
#include "../generic/oomph_utilities.h"
#include "../generic/Telements.h"
#include "../generic/error_estimator.h"
#include "poisson_elements.h"
 
namespace oomph
{
  /// //////////////////////////////////////////////////////////////////////
  /// //////////////////////////////////////////////////////////////////////
  // TPoissonElement
  /// /////////////////////////////////////////////////////////////////////
  /// /////////////////////////////////////////////////////////////////////
 
 
  //======================================================================
  /// TPoissonElement<DIM,NNODE_1D> elements are isoparametric triangular
  /// DIM-dimensional Poisson elements with  NNODE_1D nodal points along each
  /// element edge. Inherits from TElement and PoissonEquations
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  class TPoissonElement : public virtual TElement<DIM, NNODE_1D>,
                          public virtual PoissonEquations<DIM>,
                          public virtual ElementWithZ2ErrorEstimator
  {
  public:
    /// Constructor: Call constructors for TElement and
    /// Poisson equations
    TPoissonElement() : TElement<DIM, NNODE_1D>(), PoissonEquations<DIM>() {}
 
 
    /// Broken copy constructor
    TPoissonElement(const TPoissonElement<DIM, NNODE_1D>& dummy) = delete;
 
    /// Broken assignment operator
    void operator=(const TPoissonElement<DIM, NNODE_1D>&) = delete;
 
    ///  Access function for Nvalue: # of `values' (pinned or dofs)
    /// at node n (always returns the same value at every node, 1)
    inline unsigned required_nvalue(const unsigned& n) const
    {
      return Initial_Nvalue;
    }
 
    /// Output function:
    ///  x,y,u   or    x,y,z,u
    void output(std::ostream& outfile)
    {
      PoissonEquations<DIM>::output(outfile);
    }
 
    ///  Output function:
    ///   x,y,u   or    x,y,z,u at n_plot^DIM plot points
    void output(std::ostream& outfile, const unsigned& n_plot)
    {
      PoissonEquations<DIM>::output(outfile, n_plot);
    }
 
 
    /// C-style output function:
    ///  x,y,u   or    x,y,z,u
    void output(FILE* file_pt)
    {
      PoissonEquations<DIM>::output(file_pt);
    }
 
 
    ///  C-style output function:
    ///   x,y,u   or    x,y,z,u at n_plot^DIM plot points
    void output(FILE* file_pt, const unsigned& n_plot)
    {
      PoissonEquations<DIM>::output(file_pt, n_plot);
    }
 
 
    /// Output function for an exact solution:
    ///  x,y,u_exact
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
    {
      PoissonEquations<DIM>::output_fct(outfile, n_plot, exact_soln_pt);
    }
 
 
    /// Output function for a time-dependent exact solution.
    ///  x,y,u_exact (calls the steady version)
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    const double& time,
                    FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
    {
      PoissonEquations<DIM>::output_fct(outfile, n_plot, time, exact_soln_pt);
    }
 
  protected:
    /// Shape, test functions & derivs. w.r.t. to global coords. Return
    /// Jacobian.
    inline double dshape_and_dtest_eulerian_poisson(const Vector<double>& s,
                                                    Shape& psi,
                                                    DShape& dpsidx,
                                                    Shape& test,
                                                    DShape& dtestdx) const;
 
 
    /// Shape, test functions & derivs. w.r.t. to global coords. Return
    /// Jacobian.
    inline double dshape_and_dtest_eulerian_at_knot_poisson(
      const unsigned& ipt,
      Shape& psi,
      DShape& dpsidx,
      Shape& test,
      DShape& dtestdx) const;
 
    /// Shape/test functions and derivs w.r.t. to global coords at
    /// integration point ipt; return Jacobian of mapping (J). Also compute
    /// derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.
    inline double dshape_and_dtest_eulerian_at_knot_poisson(
      const unsigned& ipt,
      Shape& psi,
      DShape& dpsidx,
      RankFourTensor<double>& d_dpsidx_dX,
      Shape& test,
      DShape& dtestdx,
      RankFourTensor<double>& d_dtestdx_dX,
      DenseMatrix<double>& djacobian_dX) const;
 
    /// Order of recovery shape functions for Z2 error estimation:
    /// Same order as shape functions.
    unsigned nrecovery_order()
    {
      return (NNODE_1D - 1);
    }
 
    /// Number of 'flux' terms for Z2 error estimation
    unsigned num_Z2_flux_terms()
    {
      return DIM;
    }
 
    /// Get 'flux' for Z2 error recovery:  Standard flux.from Poisson equations
    void get_Z2_flux(const Vector<double>& s, Vector<double>& flux)
    {
      this->get_flux(s, flux);
    }
 
    /// Number of vertex nodes in the element
    unsigned nvertex_node() const
    {
      return TElement<DIM, NNODE_1D>::nvertex_node();
    }
 
    /// Pointer to the j-th vertex node in the element
    Node* vertex_node_pt(const unsigned& j) const
    {
      return TElement<DIM, NNODE_1D>::vertex_node_pt(j);
    }
 
  private:
    /// Static unsigned that holds the (same) number of variables at every node
    static const unsigned Initial_Nvalue;
  };
 
 
  // Inline functions:
 
 
  //======================================================================
  /// Define the shape functions and test functions and derivatives
  /// w.r.t. global coordinates and return Jacobian of mapping.
  ///
  /// Galerkin: Test functions = shape functions
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  double TPoissonElement<DIM, NNODE_1D>::dshape_and_dtest_eulerian_poisson(
    const Vector<double>& s,
    Shape& psi,
    DShape& dpsidx,
    Shape& test,
    DShape& dtestdx) const
  {
    unsigned n_node = this->nnode();
 
    // Call the geometrical shape functions and derivatives
    double J = this->dshape_eulerian(s, psi, dpsidx);
 
    // Loop over the test functions and derivatives and set them equal to the
    // shape functions
    for (unsigned i = 0; i < n_node; i++)
    {
      test[i] = psi[i];
      dtestdx(i, 0) = dpsidx(i, 0);
      dtestdx(i, 1) = dpsidx(i, 1);
    }
 
    // Return the jacobian
    return J;
  }
 
 
  //======================================================================
  /// Define the shape functions and test functions and derivatives
  /// w.r.t. global coordinates and return Jacobian of mapping.
  ///
  /// Galerkin: Test functions = shape functions
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  double TPoissonElement<DIM, NNODE_1D>::
    dshape_and_dtest_eulerian_at_knot_poisson(const unsigned& ipt,
                                              Shape& psi,
                                              DShape& dpsidx,
                                              Shape& test,
                                              DShape& dtestdx) const
  {
    // Call the geometrical shape functions and derivatives
    double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
 
    // Set the pointers of the test functions
    test = psi;
    dtestdx = dpsidx;
 
    // Return the jacobian
    return J;
  }
 
 
  //======================================================================
  /// Define the shape functions (psi) and test functions (test) and
  /// their derivatives w.r.t. global coordinates (dpsidx and dtestdx)
  /// and return Jacobian of mapping (J). Additionally compute the
  /// derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.
  ///
  /// Galerkin: Test functions = shape functions
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  double TPoissonElement<DIM, NNODE_1D>::
    dshape_and_dtest_eulerian_at_knot_poisson(
      const unsigned& ipt,
      Shape& psi,
      DShape& dpsidx,
      RankFourTensor<double>& d_dpsidx_dX,
      Shape& test,
      DShape& dtestdx,
      RankFourTensor<double>& d_dtestdx_dX,
      DenseMatrix<double>& djacobian_dX) const
  {
    // Call the geometrical shape functions and derivatives
    const double J = this->dshape_eulerian_at_knot(
      ipt, psi, dpsidx, djacobian_dX, d_dpsidx_dX);
 
    // Set the pointers of the test functions
    test = psi;
    dtestdx = dpsidx;
    d_dtestdx_dX = d_dpsidx_dX;
 
    // Return the jacobian
    return J;
  }
 
 
  //=======================================================================
  /// Face geometry for the TPoissonElement elements: The spatial
  /// dimension of the face elements is one lower than that of the
  /// bulk element but they have the same number of points
  /// along their 1D edges.
  //=======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  class FaceGeometry<TPoissonElement<DIM, NNODE_1D>>
    : public virtual TElement<DIM - 1, NNODE_1D>
  {
  public:
    /// Constructor: Call the constructor for the
    /// appropriate lower-dimensional TElement
    FaceGeometry() : TElement<DIM - 1, NNODE_1D>() {}
  };
 
  //=======================================================================
  /// Face geometry for the 1D TPoissonElement elements: Point elements
  //=======================================================================
  template<unsigned NNODE_1D>
  class FaceGeometry<TPoissonElement<1, NNODE_1D>> : public virtual PointElement
  {
  public:
    /// Constructor: Call the constructor for the
    /// appropriate lower-dimensional TElement
    FaceGeometry() : PointElement() {}
  };
 
 
} // namespace oomph
 
#endif