poisson_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) 2006-2022 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//====================================================================
// Header file for Poisson elements
#ifndef OOMPH_POISSON_ELEMENTS_HEADER
#define OOMPH_POISSON_ELEMENTS_HEADER
 
 
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
#include <sstream>
 
// OOMPH-LIB headers
#include "../generic/projection.h"
#include "../generic/nodes.h"
#include "../generic/Qelements.h"
#include "../generic/oomph_utilities.h"
 
 
namespace oomph
{
  //=============================================================
  //=============================================================
  template<unsigned DIM>
  class PoissonEquations : public virtual FiniteElement
  {
  public:
    typedef void (*PoissonSourceFctPt)(const Vector<double>& x, double& f);
 
 
    typedef void (*PoissonSourceFctGradientPt)(const Vector<double>& x,
                                               Vector<double>& gradient);
 
 
    PoissonEquations() : Source_fct_pt(0), Source_fct_gradient_pt(0) {}
 
    PoissonEquations(const PoissonEquations& dummy) = delete;
 
    void operator=(const PoissonEquations&) = delete;
 
    virtual inline unsigned u_index_poisson() const
    {
      return 0;
    }
 
 
    void point_output_data(const Vector<double>& s, Vector<double>& data)
    {
      // Dimension
      unsigned dim = s.size();
 
      // Resize data for values
      data.resize(dim + 1);
 
      // Write values in the vector
      for (unsigned i = 0; i < dim; i++)
      {
        data[i] = interpolated_x(s, i);
      }
      data[dim] = this->interpolated_u_poisson(s);
    }
 
 
    unsigned nscalar_paraview() const
    {
      return 1;
    }
 
    void scalar_value_paraview(std::ofstream& file_out,
                               const unsigned& i,
                               const unsigned& nplot) const
    {
#ifdef PARANOID
      if (i != 0)
      {
        std::stringstream error_stream;
        error_stream
          << "Poisson elements only store a single field so i must be 0 rather"
          << " than " << i << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      unsigned local_loop = this->nplot_points_paraview(nplot);
      for (unsigned j = 0; j < local_loop; j++)
      {
        // Get the local coordinate of the required plot point
        Vector<double> s(DIM);
        this->get_s_plot(j, nplot, s);
 
        file_out << this->interpolated_u_poisson(s) << std::endl;
      }
    }
 
    std::string scalar_name_paraview(const unsigned& i) const
    {
#ifdef PARANOID
      if (i != 0)
      {
        std::stringstream error_stream;
        error_stream
          << "Poisson elements only store a single field so i must be 0 rather"
          << " than " << i << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      return "Poisson solution";
    }
 
 
    void scalar_value_fct_paraview(
      std::ofstream& file_out,
      const unsigned& i,
      const unsigned& nplot,
      FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
    {
#ifdef PARANOID
      if (i != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson equation has only one field. Can't call "
                     << "this function for value " << i << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      // Vector of local coordinates
      Vector<double> s(DIM);
 
      // Vector for coordinates
      Vector<double> x(DIM);
 
      // Exact solution Vector
      Vector<double> exact_soln(1);
 
      // Loop over plot points
      unsigned num_plot_points = nplot_points_paraview(nplot);
      for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
      {
        // Get local coordinates of plot point
        get_s_plot(iplot, nplot, s);
 
        // Get x position as Vector
        interpolated_x(s, x);
 
        // Get exact solution at this point
        (*exact_soln_pt)(x, exact_soln);
 
        // Write it
        file_out << exact_soln[0] << std::endl;
      }
    }
 
    void output(std::ostream& outfile)
    {
      const unsigned n_plot = 5;
      output(outfile, n_plot);
    }
 
    void output(std::ostream& outfile, const unsigned& n_plot);
 
    void output(FILE* file_pt)
    {
      const unsigned n_plot = 5;
      output(file_pt, n_plot);
    }
 
    void output(FILE* file_pt, const unsigned& n_plot);
 
    void output_fct(std::ostream& outfile,
                    const unsigned& n_plot,
                    FiniteElement::SteadyExactSolutionFctPt exact_soln_pt);
 
    virtual void output_fct(
      std::ostream& outfile,
      const unsigned& n_plot,
      const double& time,
      FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
    {
      throw OomphLibError(
        "There is no time-dependent output_fct() for Poisson elements ",
        OOMPH_CURRENT_FUNCTION,
        OOMPH_EXCEPTION_LOCATION);
    }
 
 
    void compute_norm(double& norm);
 
    void compute_error(std::ostream& outfile,
                       FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
                       double& error,
                       double& norm);
 
 
    void compute_error(std::ostream& outfile,
                       FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt,
                       const double& time,
                       double& error,
                       double& norm)
    {
      throw OomphLibError(
        "There is no time-dependent compute_error() for Poisson elements",
        OOMPH_CURRENT_FUNCTION,
        OOMPH_EXCEPTION_LOCATION);
    }
 
    PoissonSourceFctPt& source_fct_pt()
    {
      return Source_fct_pt;
    }
 
    PoissonSourceFctPt source_fct_pt() const
    {
      return Source_fct_pt;
    }
 
    PoissonSourceFctGradientPt& source_fct_gradient_pt()
    {
      return Source_fct_gradient_pt;
    }
 
    PoissonSourceFctGradientPt source_fct_gradient_pt() const
    {
      return Source_fct_gradient_pt;
    }
 
 
    inline virtual void get_source_poisson(const unsigned& ipt,
                                           const Vector<double>& x,
                                           double& source) const
    {
      // If no source function has been set, return zero
      if (Source_fct_pt == 0)
      {
        source = 0.0;
      }
      else
      {
        // Get source strength
        (*Source_fct_pt)(x, source);
      }
    }
 
 
    inline virtual void get_source_gradient_poisson(
      const unsigned& ipt,
      const Vector<double>& x,
      Vector<double>& gradient) const
    {
      // If no gradient function has been set, FD it
      if (Source_fct_gradient_pt == 0)
      {
        // Reference value
        double source = 0.0;
        get_source_poisson(ipt, x, source);
 
        // FD it
        double eps_fd = GeneralisedElement::Default_fd_jacobian_step;
        double source_pls = 0.0;
        Vector<double> x_pls(x);
        for (unsigned i = 0; i < DIM; i++)
        {
          x_pls[i] += eps_fd;
          get_source_poisson(ipt, x_pls, source_pls);
          gradient[i] = (source_pls - source) / eps_fd;
          x_pls[i] = x[i];
        }
      }
      else
      {
        // Get gradient
        (*Source_fct_gradient_pt)(x, gradient);
      }
    }
 
 
    void get_flux(const Vector<double>& s, Vector<double>& flux) const
    {
      // Find out how many nodes there are in the element
      const unsigned n_node = nnode();
 
      // Get the index at which the unknown is stored
      const unsigned u_nodal_index = u_index_poisson();
 
      // Set up memory for the shape and test functions
      Shape psi(n_node);
      DShape dpsidx(n_node, DIM);
 
      // Call the derivatives of the shape and test functions
      dshape_eulerian(s, psi, dpsidx);
 
      // Initialise to zero
      for (unsigned j = 0; j < DIM; j++)
      {
        flux[j] = 0.0;
      }
 
      // Loop over nodes
      for (unsigned l = 0; l < n_node; l++)
      {
        // Loop over derivative directions
        for (unsigned j = 0; j < DIM; j++)
        {
          flux[j] += this->nodal_value(l, u_nodal_index) * dpsidx(l, j);
        }
      }
    }
 
 
    void get_dflux_dnodal_u(const Vector<double>& s,
                            Vector<Vector<double>>& dflux_dnodal_u) const
    {
      // Find out how many nodes there are in the element
      const unsigned n_node = nnode();
 
      // Set up memory for the shape and test functions
      Shape psi(n_node);
      DShape dpsidx(n_node, DIM);
 
      // Call the derivatives of the shape and test functions
      dshape_eulerian(s, psi, dpsidx);
 
      // And here it is...
      for (unsigned i = 0; i < DIM; i++)
      {
        for (unsigned j = 0; j < n_node; j++)
        {
          dflux_dnodal_u[i][j] = dpsidx(j, i);
        }
      }
    }
 
 
    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_poisson(
        residuals, GeneralisedElement::Dummy_matrix, 0);
    }
 
 
    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_poisson(residuals, jacobian, 1);
    }
 
 
    virtual inline double interpolated_u_poisson(const Vector<double>& s) const
    {
      // Find number of nodes
      const unsigned n_node = nnode();
 
      // Get the index at which the poisson unknown is stored
      const unsigned u_nodal_index = u_index_poisson();
 
      // Local shape function
      Shape psi(n_node);
 
      // Find values of shape function
      shape(s, psi);
 
      // Initialise value of u
      double interpolated_u = 0.0;
 
      // Loop over the local nodes and sum
      for (unsigned l = 0; l < n_node; l++)
      {
        interpolated_u += this->nodal_value(l, u_nodal_index) * psi[l];
      }
 
      return (interpolated_u);
    }
 
 
    virtual void get_dresidual_dnodal_coordinates(
      RankThreeTensor<double>& dresidual_dnodal_coordinates);
 
    unsigned self_test();
 
 
  protected:
    virtual double dshape_and_dtest_eulerian_poisson(const Vector<double>& s,
                                                     Shape& psi,
                                                     DShape& dpsidx,
                                                     Shape& test,
                                                     DShape& dtestdx) const = 0;
 
 
    virtual double dshape_and_dtest_eulerian_at_knot_poisson(
      const unsigned& ipt,
      Shape& psi,
      DShape& dpsidx,
      Shape& test,
      DShape& dtestdx) const = 0;
 
    virtual 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 = 0;
 
    virtual void fill_in_generic_residual_contribution_poisson(
      Vector<double>& residuals,
      DenseMatrix<double>& jacobian,
      const unsigned& flag);
 
    PoissonSourceFctPt Source_fct_pt;
 
    PoissonSourceFctGradientPt Source_fct_gradient_pt;
  };
 
 
 
 
  //======================================================================
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  class QPoissonElement : public virtual QElement<DIM, NNODE_1D>,
                          public virtual PoissonEquations<DIM>
  {
  private:
    static const unsigned Initial_Nvalue;
 
  public:
    QPoissonElement() : QElement<DIM, NNODE_1D>(), PoissonEquations<DIM>() {}
 
    QPoissonElement(const QPoissonElement<DIM, NNODE_1D>& dummy) = delete;
 
    void operator=(const QPoissonElement<DIM, NNODE_1D>&) = delete;
 
    inline unsigned required_nvalue(const unsigned& n) const
    {
      return Initial_Nvalue;
    }
 
    void output(std::ostream& outfile)
    {
      PoissonEquations<DIM>::output(outfile);
    }
 
 
    void output(std::ostream& outfile, const unsigned& n_plot)
    {
      PoissonEquations<DIM>::output(outfile, n_plot);
    }
 
 
    void output(FILE* file_pt)
    {
      PoissonEquations<DIM>::output(file_pt);
    }
 
 
    void output(FILE* file_pt, const unsigned& n_plot)
    {
      PoissonEquations<DIM>::output(file_pt, n_plot);
    }
 
 
    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);
    }
 
 
    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:
    inline double dshape_and_dtest_eulerian_poisson(const Vector<double>& s,
                                                    Shape& psi,
                                                    DShape& dpsidx,
                                                    Shape& test,
                                                    DShape& dtestdx) const;
 
 
    inline double dshape_and_dtest_eulerian_at_knot_poisson(
      const unsigned& ipt,
      Shape& psi,
      DShape& dpsidx,
      Shape& test,
      DShape& dtestdx) const;
 
    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;
  };
 
 
  // Inline functions:
 
 
  //======================================================================
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  double QPoissonElement<DIM, NNODE_1D>::dshape_and_dtest_eulerian_poisson(
    const Vector<double>& s,
    Shape& psi,
    DShape& dpsidx,
    Shape& test,
    DShape& dtestdx) const
  {
    // Call the geometrical shape functions and derivatives
    const double J = this->dshape_eulerian(s, psi, dpsidx);
 
    // Set the test functions equal to the shape functions
    test = psi;
    dtestdx = dpsidx;
 
    // Return the jacobian
    return J;
  }
 
 
  //======================================================================
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  double QPoissonElement<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
    const 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;
  }
 
 
  //======================================================================
  //======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  double QPoissonElement<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;
  }
 
 
 
 
  //=======================================================================
  //=======================================================================
  template<unsigned DIM, unsigned NNODE_1D>
  class FaceGeometry<QPoissonElement<DIM, NNODE_1D>>
    : public virtual QElement<DIM - 1, NNODE_1D>
  {
  public:
    FaceGeometry() : QElement<DIM - 1, NNODE_1D>() {}
  };
 
 
 
  //=======================================================================
  //=======================================================================
  template<unsigned NNODE_1D>
  class FaceGeometry<QPoissonElement<1, NNODE_1D>> : public virtual PointElement
  {
  public:
    FaceGeometry() : PointElement() {}
  };
 
 
 
 
  //==========================================================
  //==========================================================
  template<class POISSON_ELEMENT>
  class ProjectablePoissonElement
    : public virtual ProjectableElement<POISSON_ELEMENT>
  {
  public:
    Vector<std::pair<Data*, unsigned>> data_values_of_field(const unsigned& fld)
    {
#ifdef PARANOID
      if (fld != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson elements only store a single field so fld "
                        "must be 0 rather"
                     << " than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      // Create the vector
      unsigned nnod = this->nnode();
      Vector<std::pair<Data*, unsigned>> data_values(nnod);
 
      // Loop over all nodes
      for (unsigned j = 0; j < nnod; j++)
      {
        // Add the data value associated field: The node itself
        data_values[j] = std::make_pair(this->node_pt(j), fld);
      }
 
      // Return the vector
      return data_values;
    }
 
    unsigned nfields_for_projection()
    {
      return 1;
    }
 
    unsigned nhistory_values_for_projection(const unsigned& fld)
    {
#ifdef PARANOID
      if (fld != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson elements only store a single field so fld "
                        "must be 0 rather"
                     << " than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      return this->node_pt(0)->ntstorage();
    }
 
    unsigned nhistory_values_for_coordinate_projection()
    {
      return this->node_pt(0)->position_time_stepper_pt()->ntstorage();
    }
 
    double jacobian_and_shape_of_field(const unsigned& fld,
                                       const Vector<double>& s,
                                       Shape& psi)
    {
#ifdef PARANOID
      if (fld != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson elements only store a single field so fld "
                        "must be 0 rather"
                     << " than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      unsigned n_dim = this->dim();
      unsigned n_node = this->nnode();
      Shape test(n_node);
      DShape dpsidx(n_node, n_dim), dtestdx(n_node, n_dim);
      double J =
        this->dshape_and_dtest_eulerian_poisson(s, psi, dpsidx, test, dtestdx);
      return J;
    }
 
 
    double get_field(const unsigned& t,
                     const unsigned& fld,
                     const Vector<double>& s)
    {
#ifdef PARANOID
      if (fld != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson elements only store a single field so fld "
                        "must be 0 rather"
                     << " than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      // Find the index at which the variable is stored
      unsigned u_nodal_index = this->u_index_poisson();
 
      // Local shape function
      unsigned n_node = this->nnode();
      Shape psi(n_node);
 
      // Find values of shape function
      this->shape(s, psi);
 
      // Initialise value of u
      double interpolated_u = 0.0;
 
      // Sum over the local nodes
      for (unsigned l = 0; l < n_node; l++)
      {
        interpolated_u += this->nodal_value(l, u_nodal_index) * psi[l];
      }
      return interpolated_u;
    }
 
 
    unsigned nvalue_of_field(const unsigned& fld)
    {
#ifdef PARANOID
      if (fld != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson elements only store a single field so fld "
                        "must be 0 rather"
                     << " than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      return this->nnode();
    }
 
 
    int local_equation(const unsigned& fld, const unsigned& j)
    {
#ifdef PARANOID
      if (fld != 0)
      {
        std::stringstream error_stream;
        error_stream << "Poisson elements only store a single field so fld "
                        "must be 0 rather"
                     << " than " << fld << std::endl;
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
      const unsigned u_nodal_index = this->u_index_poisson();
      return this->nodal_local_eqn(j, u_nodal_index);
    }
  };
 
 
  //=======================================================================
  //=======================================================================
  template<class ELEMENT>
  class FaceGeometry<ProjectablePoissonElement<ELEMENT>>
    : public virtual FaceGeometry<ELEMENT>
  {
  public:
    FaceGeometry() : FaceGeometry<ELEMENT>() {}
  };
 
 
  //=======================================================================
  //=======================================================================
  template<class ELEMENT>
  class FaceGeometry<FaceGeometry<ProjectablePoissonElement<ELEMENT>>>
    : public virtual FaceGeometry<FaceGeometry<ELEMENT>>
  {
  public:
    FaceGeometry() : FaceGeometry<FaceGeometry<ELEMENT>>() {}
  };
 
 
} // namespace oomph
 
#endif