hermite_element_quad_mesh.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//
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// LIC//====================================================================
// This header defines a class for hermite element quad mesh
 
// Include guards
#ifndef OOMPH_HERMITE_ELEMENT_QUAD_MESH_HEADER
#define OOMPH_HERMITE_ELEMENT_QUAD_MESH_HEADER
 
// Config header
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
// oomph-lib headers
#include "generic/hermite_elements.h"
#include "generic/mesh.h"
 
// Include the domain header
#include "topologically_rectangular_domain.h"
 
namespace oomph
{
  //=============================================================================
  /// A two dimensional Hermite bicubic element quadrilateral mesh for
  /// a topologically rectangular domain. The geometry of the problem must be
  /// prescribed using the TopologicallyRectangularDomain. Non uniform node
  /// spacing can be prescribed using a function pointer.
  //=============================================================================
  template<class ELEMENT>
  class HermiteQuadMesh : public Mesh
  {
  public:
    /// Mesh Spacing Function Pointer - an optional function pointer
    /// to prescibe the node spacing in a non-uniformly spaced mesh - takes the
    /// position of a node (in macro element coordinates) in the uniformly
    /// spaced mesh and return the position in the non-uniformly spaced mesh
    typedef void (*MeshSpacingFnPtr)(const Vector<double>& m_uniform_spacing,
                                     Vector<double>& m_non_uniform_spacing);
 
 
    /// Mesh Constructor (for a uniformly spaced mesh). Takes the
    /// following arguments :  nx :              number of elements in x
    /// direction;
    ///              ny :              number of elements in y direction;
    ///              domain :          topologically rectangular domain;
    ///              periodic_in_x :   flag specifying if the mesh is periodic
    ///              in
    ///                                the x direction (default = false);
    ///              time_stepper_pt : pointer to the time stepper (default = no
    ///                                timestepper);
    HermiteQuadMesh(const unsigned& nx,
                    const unsigned& ny,
                    TopologicallyRectangularDomain* domain,
                    const bool& periodic_in_x = false,
                    TimeStepper* time_stepper_pt = &Mesh::Default_TimeStepper)
    {
      // Mesh can only be built with 2D QHermiteElements.
      MeshChecker::assert_geometric_element<QHermiteElementBase, ELEMENT>(2);
 
      // set number of elements in each coordinate direction
      Nelement.resize(2);
      Nelement[0] = nx;
      Nelement[1] = ny;
 
      // set x periodicity
      Xperiodic = periodic_in_x;
 
      // set the domain pointer
      Domain_pt = domain;
 
      // set the node spacing function to zero
      Node_spacing_fn = 0;
 
      // builds the mesh
      build_mesh(time_stepper_pt);
    }
 
 
    /// Mesh Constructor (for a non-uniformly spaced mesh). Takes the
    /// following arguments : nx :              number of elements in x
    /// direction;
    ///                       ny :              number of elements in y
    ///                       direction; domain :          topologically
    ///                       rectangular domain; spacing_fn :      spacing
    ///                       function prescribing a
    ///                                         non-uniformly spaced mesh
    ///                       periodic_in_x :   flag specifying if the mesh is
    ///                                         periodic in the x direction
    ///                                         (default = false);
    ///                       time_stepper_pt : pointer to the time stepper
    ///                                         (default = notimestepper);
    HermiteQuadMesh(const unsigned& nx,
                    const unsigned& ny,
                    TopologicallyRectangularDomain* domain,
                    const MeshSpacingFnPtr spacing_fn,
                    const bool& periodic_in_x = false,
                    TimeStepper* time_stepper_pt = &Mesh::Default_TimeStepper)
    {
      // Mesh can only be built with 2D QHermiteElements.
      MeshChecker::assert_geometric_element<QHermiteElementBase, ELEMENT>(2);
 
      // set number of elements in each coordinate direction
      Nelement.resize(2);
      Nelement[0] = nx;
      Nelement[1] = ny;
 
      // set x periodicity
      Xperiodic = periodic_in_x;
 
      // set the domain pointer
      Domain_pt = domain;
 
      // set the node spacing function to zero
      Node_spacing_fn = spacing_fn;
 
      /// build the mesh
      build_mesh(time_stepper_pt);
    }
 
    /// Destructor - does nothing - handled in mesh base class
    ~HermiteQuadMesh() {};
 
    /// Access function for number of elements in mesh in each dimension
    unsigned& nelement_in_dim(const unsigned& d)
    {
      return Nelement[d];
    }
 
  private:
    /// returns the macro element position of the node that is the x-th
    /// node along from the LHS and the y-th node up from the lower edge
    void macro_coordinate_position(const unsigned& node_num_x,
                                   const unsigned& node_num_y,
                                   Vector<double>& macro_element_position)
    {
      // compute macro element position in uniformly spaced mesh
      macro_element_position[0] = 2 * node_num_x / double(Nelement[0]) - 1;
      macro_element_position[1] = 2 * node_num_y / double(Nelement[1]) - 1;
 
      // if a non unform spacing function is provided
      if (Node_spacing_fn != 0)
      {
        Vector<double> temp(macro_element_position);
        (*Node_spacing_fn)(temp, macro_element_position);
      }
    }
 
 
    /// sets the generalised position of the node (i.e. - x_i, dx_i/ds_0,
    /// dx_i/ds_1 & d2x_i/ds_0ds_1 for i = 1,2). Takes the x,y coordinates of
    /// the node from which its position can be determined.
    void set_position_of_node(const unsigned& node_num_x,
                              const unsigned& node_num_y,
                              Node* node_pt);
 
 
    /// sets the generalised position of the node (i.e. - x_i, dx_i/ds_0,
    /// dx_i/ds_1 & d2x_i/ds_0ds_1 for i = 1,2). Takes the x,y coordinates of
    /// the node from which its position can be determined. Also sets
    /// coordinates on boundary vector for the node to be the generalised
    /// position of the node in macro element coordinates
    void set_position_of_boundary_node(const unsigned& node_num_x,
                                       const unsigned& node_num_y,
                                       BoundaryNode<Node>* node_pt);
 
 
    /// computes the generalised position of the node at position
    /// (node_num_x, node_num_y) in the macro element coordinate scheme.
    ///     index 0 of m_gen : 0 - m_i
    ///                        1 - dm_i/ds_0
    ///                        2 - dm_i/ds_1
    ///                        3 - d2m_i/ds_0ds_1    (where i is index 1 of
    ///                        m_gen)
    void generalised_macro_element_position_of_node(const unsigned& node_num_x,
                                                    const unsigned& node_num_y,
                                                    DenseMatrix<double>& m_gen);
 
 
    /// Generic mesh construction function to build the mesh
    virtual void build_mesh(TimeStepper* time_stepper_pt);
 
    /// Setup lookup schemes which establish whic elements are located
    /// next to mesh's boundaries (wrapper to suppress doc).
    /// Specific version for HermiteQuadMesh to ensure that the order of the
    /// elements in Boundary_element_pt matches the actual order along the
    /// boundary. This is required when hijacking the BiharmonicElement to apply
    /// the BiharmonicFluidBoundaryElement in
    /// BiharmonicFluidProblem::impose_traction_free_edge(...)
    virtual void setup_boundary_element_info()
    {
      std::ofstream outfile;
      setup_boundary_element_info(outfile);
    }
 
 
    /// Setup lookup schemes which establish which elements are located
    /// next to which boundaries (Doc to outfile if it's open).
    /// Specific version for HermiteQuadMesh to ensure that the order of the
    /// elements in Boundary_element_pt matches the actual order along the
    /// boundary. This is required when hijacking the BiharmonicElement to apply
    /// the BiharmonicFluidBoundaryElement in
    /// BiharmonicFluidProblem::impose_traction_free_edge(...)
    virtual void setup_boundary_element_info(std::ostream& outfile);
 
 
    /// number of elements in each coordinate direction
    Vector<unsigned> Nelement;
 
    /// boolean variable to determine whether the mesh is periodic in the
    /// x-direction
    bool Xperiodic;
 
    /// Pointer to the topologically rectangular domain which prescribes
    /// the problem domain
    TopologicallyRectangularDomain* Domain_pt;
 
    /// non uniform mesh spacing function pointer
    MeshSpacingFnPtr Node_spacing_fn;
  };
} // namespace oomph
#include "hermite_element_quad_mesh.template.cc"
#endif