biharmonic_problem.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//====================================================================
#ifndef OOMPH_BIHARMONIC_PROBLEM_HEADER
#define OOMPH_BIHARMONIC_PROBLEM_HEADER
 
// Config header generated by autoconfig
#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/problem.h"
#include "../generic/hijacked_elements.h"
#include "../meshes/hermite_element_quad_mesh.template.h"
#include "../meshes/hermite_element_quad_mesh.template.cc"
#include "biharmonic_elements.h"
#include "biharmonic_flux_elements.h"
 
 
namespace oomph
{
  //=============================================================================
  //=============================================================================
  template<unsigned DIM>
  class BiharmonicProblem : public Problem
  {
  public:
    typedef void (*DirichletBCFctPt)(const double& s, double& u);
 
 
    typedef void (*BiharmonicSourceFctPt)(const Vector<double>& x, double& f);
 
    BiharmonicProblem()
    {
      Bulk_element_mesh_pt = 0;
      Face_element_mesh_pt = 0;
    }
 
    virtual ~BiharmonicProblem()
    {
      delete Bulk_element_mesh_pt;
      delete Face_element_mesh_pt;
    };
 
    void actions_before_newton_solve()
    {
#ifdef PARANOID
      if (0 == self_test())
      {
        oomph_info << "self test passed" << std::endl;
      }
      else
      {
        oomph_info << "self test failed" << std::endl;
      }
#endif
    }
 
    void actions_after_newton_solve() {}
 
    void doc_solution(
      DocInfo& doc_info,
      FiniteElement::SteadyExactSolutionFctPt exact_soln_pt = 0);
 
    Mesh* bulk_element_mesh_pt()
    {
      return Bulk_element_mesh_pt;
    }
 
  protected:
    void build_bulk_mesh(
      const unsigned n_x,
      const unsigned n_y,
      TopologicallyRectangularDomain* domain_pt,
      HermiteQuadMesh<BiharmonicElement<2>>::MeshSpacingFnPtr spacing_fn = 0)
    {
      if (spacing_fn == 0)
      {
        Bulk_element_mesh_pt =
          new HermiteQuadMesh<Hijacked<BiharmonicElement<2>>>(
            n_x, n_y, domain_pt);
      }
      else
      {
        Bulk_element_mesh_pt =
          new HermiteQuadMesh<Hijacked<BiharmonicElement<2>>>(
            n_x, n_y, domain_pt, spacing_fn);
      }
      //   add_sub_mesh(Bulk_element_mesh_pt);
      //   build_global_mesh();
    }
 
 
    void build_global_mesh_and_assign_eqn_numbers()
    {
      add_sub_mesh(Bulk_element_mesh_pt);
      if (Face_element_mesh_pt != 0)
      {
        add_sub_mesh(Face_element_mesh_pt);
      }
      build_global_mesh();
      assign_eqn_numbers();
    }
 
    void set_source_function(const BiharmonicSourceFctPt source_fct_pt)
    {
      // number of elements in mesh
      unsigned n_bulk_element = Bulk_element_mesh_pt->nelement();
 
      // loop over bulk elements
      for (unsigned i = 0; i < n_bulk_element; i++)
      {
        // upcast from generalised element to specific element
        BiharmonicElement<2>* element_pt = dynamic_cast<BiharmonicElement<2>*>(
          Bulk_element_mesh_pt->element_pt(i));
 
        // set the source function pointer
        element_pt->source_fct_pt() = source_fct_pt;
      }
    }
 
    void set_dirichlet_boundary_condition(const unsigned& b,
                                          DirichletBCFctPt u_fn = 0,
                                          DirichletBCFctPt dudn_fn = 0);
 
    void set_neumann_boundary_condition(
      const unsigned& b,
      BiharmonicFluxElement<2>::FluxFctPt flux0_fct_pt,
      BiharmonicFluxElement<2>::FluxFctPt flux1_fct_pt = 0);
 
  public:
    // NOTE: these two private meshes are required for the block
    // preconditioners.
 
    Mesh* Bulk_element_mesh_pt;
 
    Mesh* Face_element_mesh_pt;
  };
 
 
  //=============================================================================
  //=============================================================================
  template<unsigned DIM>
  class BiharmonicFluidProblem : public Problem
  {
  public:
    typedef void (*FluidBCFctPt)(const double& s, Vector<double>& u);
 
 
    BiharmonicFluidProblem()
    {
      // initialise the number of non bulk elements
      Npoint_element = 0;
    }
 
 
    void actions_before_newton_solve()
    {
#ifdef PARANOID
      if (0 == self_test())
      {
        oomph_info << "self test passed" << std::endl;
      }
      else
      {
        oomph_info << "self test failed" << std::endl;
      }
#endif
    }
 
 
    void actions_after_newton_solve() {}
 
 
    void doc_solution(
      DocInfo& doc_info,
      FiniteElement::SteadyExactSolutionFctPt exact_soln_pt = 0);
 
 
  protected:
    void impose_solid_boundary_on_edge(const unsigned& b,
                                       const double& psi = 0);
 
    void impose_traction_free_edge(const unsigned& b);
 
 
    void impose_fluid_flow_on_edge(const unsigned& b,
                                   FluidBCFctPt u_imposed_fn);
 
 
  private:
    // number of non-bulk elements - i.e. biharmonic fluid boundary elements
    unsigned Npoint_element;
  };
 
 
  //=============================================================================
  //=============================================================================
  class BiharmonicFluidBoundaryElement : public virtual PointElement
  {
  public:
    // constructor
    BiharmonicFluidBoundaryElement(Node* node_pt, const unsigned s_fixed_index)
    {
      // set the node pt
      this->node_pt(0) = node_pt;
 
      // store fixed index on the boundary
      S_fixed_index = s_fixed_index;
    }
 
    void output(std::ostream& outfile) {}
 
 
    void output(std::ostream& outfile, const unsigned& n_plot) {}
 
 
    void output_fluid_velocity(std::ostream& outfile, const unsigned& n_plot) {}
 
 
    void output(FILE* file_pt) {}
 
 
    void output(FILE* file_pt, const unsigned& n_plot) {}
 
 
    void compute_error(std::ostream& outfile,
                       FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
                       double& error,
                       double& norm)
    {
    }
 
 
    inline void fill_in_contribution_to_residuals(Vector<double>& residuals)
    {
      // create a dummy matrix
      DenseDoubleMatrix dummy(1);
 
      // call the generic residuals functions with flag set to zero
      fill_in_generic_residual_contribution_biharmonic_boundary(
        residuals, dummy, 0);
    }
 
 
    inline void fill_in_contribution_to_jacobian(Vector<double>& residuals,
                                                 DenseMatrix<double>& jacobian)
    {
      // call generic routine with flag set to 1
      fill_in_generic_residual_contribution_biharmonic_boundary(
        residuals, jacobian, 1);
    }
 
 
    virtual void fill_in_generic_residual_contribution_biharmonic_boundary(
      Vector<double>& residuals, DenseMatrix<double>& jacobian, unsigned JFLAG);
 
  private:
    // fixed local coordinate index on boundary
    unsigned S_fixed_index;
  };
 
 
} // namespace oomph
#endif