refineable_quad_element.h

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// LIC// ====================================================================
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// LIC// multi-physics finite-element library, available
// LIC// at http://www.oomph-lib.org.
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// LIC// Copyright (C) 2006-2023 Matthias Heil and Andrew Hazel
// LIC//
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#ifndef OOMPH_REFINEABLE_QUAD_ELEMENT_HEADER
#define OOMPH_REFINEABLE_QUAD_ELEMENT_HEADER
 
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
 
// oomph-lib headers
#include "quadtree.h"
#include "macro_element.h"
#include "refineable_elements.h"
#include "Qelements.h"
 
namespace oomph
{
  // Forward definition for mesh.
  class Mesh;
 
  //=======================================================================
  /// Refineable version of QElement<2,NNODE_1D>.
  ///
  /// Refinement is performed by quadtree procedures. When the element is
  /// subdivided, the geometry of its sons is established by calls
  /// to their father's
  /// \code  get_x(...) \endcode
  /// function which refers to
  /// - the father element's geometric FE mapping  (this
  ///   is the default)
  /// .
  ///  or
  /// - to a MacroElement 's MacroElement::macro_map (if the pointer
  /// to the macro element is non-NULL)
  ///
  /// The class provides a generic RefineableQElement<2>::build() function
  /// which deals with generic
  /// isoparametric QElements in which all values are associated with
  /// nodes. The RefineableQElement<2>::further_build() function provides
  /// an interface for any element-specific non-generic build operations.
  ///
  //=======================================================================
  template<>
  class RefineableQElement<2> : public virtual RefineableElement,
                                public virtual QuadElementBase
  {
  public:
    /// Shorthand for pointer to an argument-free void member
    /// function of the refineable element
    typedef void (RefineableQElement<2>::*VoidMemberFctPt)();
 
    /// Constructor: Pass refinement level (default 0 = root)
    RefineableQElement() : RefineableElement()
    {
#ifdef LEAK_CHECK
      LeakCheckNames::RefineableQElement<2> _build += 1;
#endif
    }
 
 
    /// Broken copy constructor
    RefineableQElement(const RefineableQElement<2>& 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 RefineableQElement<2>&) = delete;*/
 
    /// Destructor
    virtual ~RefineableQElement()
    {
#ifdef LEAK_CHECK
      LeakCheckNames::RefineableQElement<2> _build -= 1;
#endif
    }
 
    /// A refineable quad element has four sons
    unsigned required_nsons() const
    {
      return 4;
    }
 
    /// If a neighbouring element has already created a node at
    /// a position corresponding to the local fractional position within the
    /// present element, s_fraction, return
    /// a pointer to that node. If not, return NULL (0).
    /// If the node is on a periodic boundary the flag is_periodic is true,
    /// otherwise it will be false.
    virtual Node* node_created_by_neighbour(const Vector<double>& s_fraction,
                                            bool& is_periodic);
 
    /// If a son of a neighbouring element has already created a node at
    /// a position corresponding to the local fractional position within the
    /// present element, s_fraction, return
    /// a pointer to that node. If not, return NULL (0).
    /// If the node is on a periodic boundary the flag is_periodic is true,
    /// otherwise it will be false.
    virtual Node* node_created_by_son_of_neighbour(
      const Vector<double>& s_fraction, bool& is_periodic)
    {
      // It is impossible for this situation to arise in meshes
      // containing elements of uniform p-order. This is here so
      // that it can be overloaded for p-refineable elements.
      return 0;
    }
 
    /// Build the element, i.e. give it nodal positions, apply BCs, etc.
    /// Pointers to any new nodes will be returned in new_node_pt. If
    /// it is open, the positions of the new
    /// nodes will be written to the file stream new_nodes_file
    virtual void build(Mesh*& mesh_pt,
                       Vector<Node*>& new_node_pt,
                       bool& was_already_built,
                       std::ofstream& new_nodes_file);
 
    /// Check the integrity of the element: ensure that the position and
    /// values are continuous across the element edges
    void check_integrity(double& max_error);
 
    ///  Print corner nodes, use colour
    void output_corners(std::ostream& outfile, const std::string& colour) const;
 
    /// Pointer to quadtree representation of this element
    QuadTree* quadtree_pt()
    {
      return dynamic_cast<QuadTree*>(Tree_pt);
    }
 
    /// Pointer to quadtree representation of this element
    QuadTree* quadtree_pt() const
    {
      return dynamic_cast<QuadTree*>(Tree_pt);
    }
 
    /// Markup all hanging nodes & document the results in
    /// the output streams contained in the vector output_stream, if they
    /// are open.
    void setup_hanging_nodes(Vector<std::ofstream*>& output_stream);
 
    /// Perform additional hanging node procedures for variables
    /// that are not interpolated by all nodes (e.g. lower order interpolations
    /// as for the pressure in Taylor Hood).
    virtual void further_setup_hanging_nodes() = 0;
 
  protected:
    /// Coincidence between son nodal points and father boundaries:
    /// Father_bound[node_1d](jnod_son,son_type)={SW/SE/NW/NE/S/E/N/W/OMEGA}
    static std::map<unsigned, DenseMatrix<int>> Father_bound;
 
    /// Setup static matrix for coincidence between son
    /// nodal points and father boundaries
    void setup_father_bounds();
 
    /// Determine Vector of boundary conditions along edge (N/S/W/E)
    void get_edge_bcs(const int& edge, Vector<int>& bound_cons) const;
 
  public:
    /// Determine set of (mesh) boundaries that the
    /// element edge/vertex lives on
    void get_boundaries(const int& edge, std::set<unsigned>& boundaries) const;
 
    /// Determine Vector of boundary conditions along edge
    /// (or on vertex) bound (S/W/N/E/SW/SE/NW/NE): For value ival
    /// on this boundary, bound_cons[ival]=1 if pinned and 0 if free.
    void get_bcs(int bound, Vector<int>& bound_cons) const;
 
    /// Return the value of the intrinsic boundary coordinate
    /// interpolated along the edge (S/W/N/E)
    void interpolated_zeta_on_edge(const unsigned& boundary,
                                   const int& edge,
                                   const Vector<double>& s,
                                   Vector<double>& zeta);
 
  protected:
    /// Internal helper function that is used to construct the
    /// hanging node schemes for the value_id-th interpolated value
    void setup_hang_for_value(const int& value_id);
 
    /// Internal helper function that is used to construct the
    /// hanging node schemes for the positions.
    virtual void quad_hang_helper(const int& value_id,
                                  const int& my_edge,
                                  std::ofstream& output_hangfile);
  };
 
 
  //========================================================================
  /// Refineable version of Solid quad elements
  //========================================================================
  template<>
  class RefineableSolidQElement<2> : public virtual RefineableQElement<2>,
                                     public virtual RefineableSolidElement,
                                     public virtual QSolidElementBase
  {
  public:
    /// Constructor, just call the constructor of the RefineableQElement<2>
    RefineableSolidQElement()
      : RefineableQElement<2>(), RefineableSolidElement()
    {
    }
 
 
    /// Broken copy constructor
    RefineableSolidQElement(const RefineableSolidQElement<2>& dummy) = delete;
 
    /// Broken assignment operator
    /*void operator=(const RefineableSolidQElement<2>&) = delete;*/
 
    /// Virtual Destructor
    virtual ~RefineableSolidQElement() {}
 
 
    /// Final over-ride: Use version in QSolidElementBase
    void set_macro_elem_pt(MacroElement* macro_elem_pt)
    {
      QSolidElementBase::set_macro_elem_pt(macro_elem_pt);
    }
 
    /// Final over-ride: Use version in QSolidElementBase
    void set_macro_elem_pt(MacroElement* macro_elem_pt,
                           MacroElement* undeformed_macro_elem_pt)
    {
      QSolidElementBase::set_macro_elem_pt(macro_elem_pt,
                                           undeformed_macro_elem_pt);
    }
 
    /// Use the generic finite difference routine defined in
    /// RefineableSolidElement to calculate the Jacobian matrix
    void get_jacobian(Vector<double>& residuals, DenseMatrix<double>& jacobian)
    {
      RefineableSolidElement::get_jacobian(residuals, jacobian);
    }
 
    /// Determine vector of solid (positional) boundary conditions
    /// along edge (N/S/W/E) [Pressure does not have to be included
    /// since it can't be subjected to bc at more than one node anyway]
    void get_edge_solid_bcs(const int& edge,
                            Vector<int>& solid_bound_cons) const;
 
    /// Determine vector of solid (positional) boundary conditions
    /// along edge (or on vertex) bound (S/W/N/E/SW/SE/NW/NE): For direction i,
    /// solid_bound_cons[i]=1 if displacement in this coordinate direction
    /// is pinned and 0 if it's free.
    void get_solid_bcs(int bound, Vector<int>& solid_bound_cons) const;
 
 
    /// Build the element, i.e. give it nodal positions, apply BCs, etc.
    /// Incl. documention into new_nodes_file
    // NOTE: FOR SOME REASON THIS NEEDS TO LIVE IN *.H TO WORK ON INTEL
    void build(Mesh*& mesh_pt,
               Vector<Node*>& new_node_pt,
               bool& was_already_built,
               std::ofstream& new_nodes_file)
    {
      using namespace QuadTreeNames;
 
      // Call the standard (non-elastic) build function
      RefineableQElement<2>::build(
        mesh_pt, new_node_pt, was_already_built, new_nodes_file);
 
      // Are we done?
      if (was_already_built) return;
 
      // Now need to loop over the nodes again and set solid variables
 
      // What type of son am I? Ask my quadtree representation...
      int son_type = Tree_pt->son_type();
 
      // Which element (!) is my father? (We must have a father
      // since was_already_built is false...)
      RefineableSolidQElement<2>* father_el_pt =
        dynamic_cast<RefineableSolidQElement<2>*>(
          Tree_pt->father_pt()->object_pt());
 
 
#ifdef PARANOID
      // Currently we can't handle the case of generalised coordinates
      // since we haven't established how they should be interpolated
      // Buffer this case:
      if (static_cast<SolidNode*>(father_el_pt->node_pt(0))
            ->nlagrangian_type() != 1)
      {
        throw OomphLibError(
          "We can't handle generalised nodal positions (yet).\n",
          OOMPH_CURRENT_FUNCTION,
          OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      Vector<double> s_lo(2);
      Vector<double> s_hi(2);
      Vector<double> s(2);
      Vector<double> xi(2);
      Vector<double> xi_fe(2);
      Vector<double> x(2);
      Vector<double> x_fe(2);
 
      // Setup vertex coordinates in father element:
      //--------------------------------------------
      switch (son_type)
      {
        case SW:
          s_lo[0] = -1.0;
          s_hi[0] = 0.0;
          s_lo[1] = -1.0;
          s_hi[1] = 0.0;
          break;
 
        case SE:
          s_lo[0] = 0.0;
          s_hi[0] = 1.0;
          s_lo[1] = -1.0;
          s_hi[1] = 0.0;
          break;
 
        case NE:
          s_lo[0] = 0.0;
          s_hi[0] = 1.0;
          s_lo[1] = 0.0;
          s_hi[1] = 1.0;
          break;
 
        case NW:
          s_lo[0] = -1.0;
          s_hi[0] = 0.0;
          s_lo[1] = 0.0;
          s_hi[1] = 1.0;
          break;
      }
 
      // Pass the undeformed macro element onto the son
      // hierher why can I read this?
      if (father_el_pt->Undeformed_macro_elem_pt != 0)
      {
        Undeformed_macro_elem_pt = father_el_pt->Undeformed_macro_elem_pt;
        for (unsigned i = 0; i < 2; i++)
        {
          s_macro_ll(i) =
            father_el_pt->s_macro_ll(i) +
            0.5 * (s_lo[i] + 1.0) *
              (father_el_pt->s_macro_ur(i) - father_el_pt->s_macro_ll(i));
          s_macro_ur(i) =
            father_el_pt->s_macro_ll(i) +
            0.5 * (s_hi[i] + 1.0) *
              (father_el_pt->s_macro_ur(i) - father_el_pt->s_macro_ll(i));
        }
      }
 
      // Local node number
      unsigned n = 0;
 
      // Find number of 1D nodes in element
      unsigned n_p = nnode_1d();
 
      // Loop over nodes in element
      for (unsigned i0 = 0; i0 < n_p; i0++)
      {
        // Local coordinate in father element
        s[0] = s_lo[0] + (s_hi[0] - s_lo[0]) * double(i0) / double(n_p - 1);
 
        for (unsigned i1 = 0; i1 < n_p; i1++)
        {
          // Local coordinate in father element
          s[1] = s_lo[1] + (s_hi[1] - s_lo[1]) * double(i1) / double(n_p - 1);
 
          // Local node number
          n = i0 + n_p * i1;
 
          // Get position from father element -- this uses the macro
          // element representation(s) if appropriate. If the node
          // turns out to be a hanging node later on, then
          // its position gets adjusted in line with its
          // hanging node interpolation.
          father_el_pt->get_x_and_xi(s, x_fe, x, xi_fe, xi);
 
          // Cast the node to an Solid node
          SolidNode* elastic_node_pt = static_cast<SolidNode*>(node_pt(n));
 
          for (unsigned i = 0; i < 2; i++)
          {
            // x_fe is the FE representation -- this is all we can
            // work with in a solid mechanics problem. If you wish
            // to reposition nodes on curvilinear boundaries of
            // a domain to their exact positions on those boundaries
            // you'll have to do this yourself! [Note: We used to
            // use the macro-element-based representation
            // to assign the position of pinned nodes but this is not always
            // correct since pinning doesn't mean "pin in place" or
            // "pin to the curvilinear boundary". For instance, we could impose
            // the boundary displacement manually.
            // x_fe is the FE representation
            elastic_node_pt->x(i) = x_fe[i];
 
            // Lagrangian coordinates can come from undeformed macro element
 
            if (Use_undeformed_macro_element_for_new_lagrangian_coords)
            {
              elastic_node_pt->xi(i) = xi[i];
            }
            else
            {
              elastic_node_pt->xi(i) = xi_fe[i];
            }
          }
 
 
          // Are there any history values to be dealt with?
          TimeStepper* time_stepper_pt =
            father_el_pt->node_pt(0)->time_stepper_pt();
 
          // Number of history values (incl. present)
          unsigned ntstorage = time_stepper_pt->ntstorage();
          if (ntstorage != 1)
          {
            // Loop over # of history values (excluding present which has been
            // done above)
            for (unsigned t = 1; t < ntstorage; t++)
            {
              // History values can (and in the case of Newmark timestepping,
              // the scheme most likely to be used for Solid computations, do)
              // include non-positional values, e.g. velocities and
              // accelerations.
 
              // Set previous positions of the new node
              for (unsigned i = 0; i < 2; i++)
              {
                elastic_node_pt->x(t, i) =
                  father_el_pt->interpolated_x(t, s, i);
              }
            }
          }
 
        } // End of vertical loop over nodes in element
 
      } // End of horizontal loop over nodes in element
    }
  };
 
} // namespace oomph
 
#endif