rectangle_with_hole_domain.h

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// LIC// ====================================================================
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// LIC// multi-physics finite-element library, available
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// LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
// LIC//
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#ifndef OOMPH_RECTANGLE_WITH_HOLE_DOMAIN_HEADER
#define OOMPH_RECTANGLE_WITH_HOLE_DOMAIN_HEADER
 
// Generic includes
#include "generic/quadtree.h"
#include "generic/geom_objects.h"
#include "generic/macro_element.h"
#include "generic/domain.h"
 
namespace oomph
{
  //===========================================================
  /// Rectangular domain with circular whole
  //===========================================================
  class RectangleWithHoleDomain : public Domain
  {
  public:
    /// Constructor. Pass pointer to geometric object that
    /// represents the cylinder, the length of the (square) domain.
    /// The GeomObject must be parametrised such that
    /// \f$\zeta \in [0,2\pi]\f$ sweeps around the circumference
    /// in anticlockwise direction.
    RectangleWithHoleDomain(GeomObject* cylinder_pt, const double& length)
      : Cylinder_pt(cylinder_pt)
    {
      // Vertices of rectangle
      Lower_left.resize(2);
      Lower_left[0] = -0.5 * length;
      Lower_left[1] = -0.5 * length;
 
      Upper_left.resize(2);
      Upper_left[0] = -0.5 * length;
      Upper_left[1] = 0.5 * length;
 
      Lower_right.resize(2);
      Lower_right[0] = 0.5 * length;
      Lower_right[1] = -0.5 * length;
 
      Upper_right.resize(2);
      Upper_right[0] = 0.5 * length;
      Upper_right[1] = 0.5 * length;
 
      // Coordinates of points where the "radial" lines from central
      // cylinder meet the upper and lower boundaries
      Lower_mid_left.resize(2);
      Lower_mid_left[0] = -0.5 * length;
      Lower_mid_left[1] = -0.5 * length;
 
      Upper_mid_left.resize(2);
      Upper_mid_left[0] = -0.5 * length;
      Upper_mid_left[1] = 0.5 * length;
 
      Lower_mid_right.resize(2);
      Lower_mid_right[0] = 0.5 * length;
      Lower_mid_right[1] = -0.5 * length;
 
      Upper_mid_right.resize(2);
      Upper_mid_right[0] = 0.5 * length;
      Upper_mid_right[1] = 0.5 * length;
 
      // There are four macro elements
      Macro_element_pt.resize(4);
 
      // Build the 2D macro elements
      for (unsigned i = 0; i < 4; i++)
      {
        Macro_element_pt[i] = new QMacroElement<2>(this, i);
      }
    }
 
    /// Destructor: Empty; cleanup done in base class
    ~RectangleWithHoleDomain() {}
 
    /// Helper function to interpolate linearly between the
    /// "right" and "left" points; \f$ s \in [-1,1] \f$
    void linear_interpolate(Vector<double> left,
                            Vector<double> right,
                            const double& s,
                            Vector<double>& f)
    {
      for (unsigned i = 0; i < 2; i++)
      {
        f[i] = left[i] + (right[i] - left[i]) * 0.5 * (s + 1.0);
      }
    }
 
 
    /// Parametrisation of macro element boundaries: f(s) is the position
    /// vector to macro-element m's boundary in the specified direction
    /// [N/S/E/W] at the specfied discrete time level (time=0: present; time>0:
    /// previous)
    void macro_element_boundary(const unsigned& time,
                                const unsigned& m,
                                const unsigned& direction,
                                const Vector<double>& s,
                                Vector<double>& f)
    {
#ifdef WARN_ABOUT_SUBTLY_CHANGED_OOMPH_INTERFACES
      // Warn about time argument being moved to the front
      OomphLibWarning(
        "Order of function arguments has changed between versions 0.8 and 0.85",
        "RectangleWithHoleDomain::macro_element_boundary(...)",
        OOMPH_EXCEPTION_LOCATION);
#endif
 
      // Lagrangian coordinate along surface of cylinder
      Vector<double> xi(1);
 
      // Point on circle
      Vector<double> point_on_circle(2);
 
      using namespace QuadTreeNames;
 
      // Switch on the macro element
      switch (m)
      {
          // Macro element 0, is is immediately left of the cylinder
        case 0:
 
          switch (direction)
          {
            case N:
              xi[0] = 3.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(Upper_mid_left, point_on_circle, s[0], f);
              break;
 
            case S:
              xi[0] = -3.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(Lower_mid_left, point_on_circle, s[0], f);
              break;
 
            case W:
              linear_interpolate(Lower_mid_left, Upper_mid_left, s[0], f);
              break;
 
            case E:
              xi[0] = 5.0 * atan(1.0) - 2.0 * atan(1.0) * 0.5 * (1.0 + s[0]);
              Cylinder_pt->position(time, xi, f);
              break;
 
            default:
 
              std::ostringstream error_stream;
              error_stream << "Direction is incorrect:  " << direction
                           << std::endl;
              throw OomphLibError(error_stream.str(),
                                  OOMPH_CURRENT_FUNCTION,
                                  OOMPH_EXCEPTION_LOCATION);
          }
 
          break;
 
        // Macro element 1, is immediately above the cylinder
        case 1:
 
          switch (direction)
          {
            case N:
              linear_interpolate(Upper_mid_left, Upper_mid_right, s[0], f);
              break;
 
            case S:
              xi[0] = 3.0 * atan(1.0) - 2.0 * atan(1.0) * 0.5 * (1.0 + s[0]);
              Cylinder_pt->position(time, xi, f);
              break;
 
            case W:
              xi[0] = 3.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(point_on_circle, Upper_mid_left, s[0], f);
              break;
 
            case E:
              xi[0] = 1.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(point_on_circle, Upper_mid_right, s[0], f);
              break;
 
            default:
 
              std::ostringstream error_stream;
              error_stream << "Direction is incorrect:  " << direction
                           << std::endl;
              throw OomphLibError(error_stream.str(),
                                  OOMPH_CURRENT_FUNCTION,
                                  OOMPH_EXCEPTION_LOCATION);
          }
 
          break;
 
          // Macro element 2, is immediately right of the cylinder
        case 2:
 
          switch (direction)
          {
            case N:
              xi[0] = 1.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(point_on_circle, Upper_mid_right, s[0], f);
              break;
 
            case S:
              xi[0] = -1.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(point_on_circle, Lower_mid_right, s[0], f);
              break;
 
            case W:
              xi[0] = -atan(1.0) + 2.0 * atan(1.0) * 0.5 * (1.0 + s[0]);
              Cylinder_pt->position(time, xi, f);
              break;
 
            case E:
              linear_interpolate(Lower_mid_right, Upper_mid_right, s[0], f);
              break;
 
            default:
 
              std::ostringstream error_stream;
              error_stream << "Direction is incorrect:  " << direction
                           << std::endl;
              throw OomphLibError(error_stream.str(),
                                  OOMPH_CURRENT_FUNCTION,
                                  OOMPH_EXCEPTION_LOCATION);
          }
 
          break;
 
          // Macro element 3, is immediately below cylinder
        case 3:
 
          switch (direction)
          {
            case N:
              xi[0] = -3.0 * atan(1.0) + 2.0 * atan(1.0) * 0.5 * (1.0 + s[0]);
              Cylinder_pt->position(time, xi, f);
              break;
 
            case S:
              linear_interpolate(Lower_mid_left, Lower_mid_right, s[0], f);
              break;
 
            case W:
              xi[0] = -3.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(Lower_mid_left, point_on_circle, s[0], f);
              break;
 
            case E:
              xi[0] = -1.0 * atan(1.0);
              Cylinder_pt->position(time, xi, point_on_circle);
              linear_interpolate(Lower_mid_right, point_on_circle, s[0], f);
              break;
 
            default:
 
              std::ostringstream error_stream;
              error_stream << "Direction is incorrect:  " << direction
                           << std::endl;
              throw OomphLibError(error_stream.str(),
                                  OOMPH_CURRENT_FUNCTION,
                                  OOMPH_EXCEPTION_LOCATION);
          }
 
          break;
 
        default:
 
          std::ostringstream error_stream;
          error_stream << "Wrong macro element number" << m << std::endl;
          throw OomphLibError(error_stream.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
      }
    }
 
  private:
    /// Lower left corner of rectangle
    Vector<double> Lower_left;
 
    /// Lower right corner of rectangle
    Vector<double> Lower_right;
 
    /// Where the "radial" line from circle meets lower boundary on left
    Vector<double> Lower_mid_left;
 
    /// Where the "radial" line from circle meets lower boundary on right
    Vector<double> Lower_mid_right;
 
    /// Upper left corner of rectangle
    Vector<double> Upper_left;
 
    /// Upper right corner of rectangle
    Vector<double> Upper_right;
 
    /// Where the "radial" line from circle meets upper boundary on left
    Vector<double> Upper_mid_left;
 
    /// Where the "radial" line from circle meets upper boundary on right
    Vector<double> Upper_mid_right;
 
    /// Pointer to geometric object that represents the central cylinder
    GeomObject* Cylinder_pt;
  };
 
} // namespace oomph
#endif