manifold_lib.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 1999 - 2022 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_manifold_lib_h
#define dealii_manifold_lib_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/function.h>
#include <deal.II/base/function_parser.h>
 
#include <deal.II/grid/manifold.h>
 
DEAL_II_NAMESPACE_OPEN
 
// forward declaration
namespace internal
{
  namespace MappingQImplementation
  {
    template <int, int>
    class InverseQuadraticApproximation;
  }
} // namespace internal
 
 
template <int dim, int spacedim = dim>
class PolarManifold : public ChartManifold<dim, spacedim, spacedim>
{
public:
  PolarManifold(const Point<spacedim> center = Point<spacedim>());
 
  virtual std::unique_ptr<Manifold<dim, spacedim>>
  clone() const override;
 
  virtual Point<spacedim>
  pull_back(const Point<spacedim> &space_point) const override;
 
  virtual Point<spacedim>
  push_forward(const Point<spacedim> &chart_point) const override;
 
  virtual DerivativeForm<1, spacedim, spacedim>
  push_forward_gradient(const Point<spacedim> &chart_point) const override;
 
  virtual Tensor<1, spacedim>
  normal_vector(
    const typename Triangulation<dim, spacedim>::face_iterator &face,
    const Point<spacedim> &p) const override;
 
  const Point<spacedim> center;
 
private:
  static Tensor<1, spacedim>
  get_periodicity();
};
 
 
 
template <int dim, int spacedim = dim>
class SphericalManifold : public Manifold<dim, spacedim>
{
public:
  SphericalManifold(const Point<spacedim> center = Point<spacedim>());
 
  virtual std::unique_ptr<Manifold<dim, spacedim>>
  clone() const override;
 
  virtual Point<spacedim>
  get_intermediate_point(const Point<spacedim> &p1,
                         const Point<spacedim> &p2,
                         const double           w) const override;
 
  virtual Tensor<1, spacedim>
  get_tangent_vector(const Point<spacedim> &x1,
                     const Point<spacedim> &x2) const override;
 
  virtual Tensor<1, spacedim>
  normal_vector(
    const typename Triangulation<dim, spacedim>::face_iterator &face,
    const Point<spacedim> &p) const override;
 
  virtual void
  get_normals_at_vertices(
    const typename Triangulation<dim, spacedim>::face_iterator &face,
    typename Manifold<dim, spacedim>::FaceVertexNormals &face_vertex_normals)
    const override;
 
  virtual void
  get_new_points(const ArrayView<const Point<spacedim>> &surrounding_points,
                 const Table<2, double> &                weights,
                 ArrayView<Point<spacedim>> new_points) const override;
 
  virtual Point<spacedim>
  get_new_point(const ArrayView<const Point<spacedim>> &vertices,
                const ArrayView<const double> &         weights) const override;
 
  const Point<spacedim> center;
 
private:
  std::pair<double, Tensor<1, spacedim>>
  guess_new_point(const ArrayView<const Tensor<1, spacedim>> &directions,
                  const ArrayView<const double> &             distances,
                  const ArrayView<const double> &             weights) const;
 
  Point<spacedim>
  get_new_point(const ArrayView<const Tensor<1, spacedim>> &directions,
                const ArrayView<const double> &             distances,
                const ArrayView<const double> &             weights,
                const Point<spacedim> &candidate_point) const;
 
  virtual void
  get_new_points(const ArrayView<const Point<spacedim>> &surrounding_points,
                 const ArrayView<const double> &         weights,
                 ArrayView<Point<spacedim>>              new_points) const;
 
  const PolarManifold<spacedim> polar_manifold;
};
 
template <int dim, int spacedim = dim>
class CylindricalManifold : public ChartManifold<dim, spacedim, 3>
{
public:
  CylindricalManifold(const unsigned int axis      = 0,
                      const double       tolerance = 1e-10);
 
  CylindricalManifold(const Tensor<1, spacedim> &direction,
                      const Point<spacedim> &    point_on_axis,
                      const double               tolerance = 1e-10);
 
  virtual std::unique_ptr<Manifold<dim, spacedim>>
  clone() const override;
 
  virtual Point<3>
  pull_back(const Point<spacedim> &space_point) const override;
 
  virtual Point<spacedim>
  push_forward(const Point<3> &chart_point) const override;
 
  virtual DerivativeForm<1, 3, spacedim>
  push_forward_gradient(const Point<3> &chart_point) const override;
 
  virtual Point<spacedim>
  get_new_point(const ArrayView<const Point<spacedim>> &surrounding_points,
                const ArrayView<const double> &         weights) const override;
 
private:
  const Tensor<1, spacedim> normal_direction;
 
  const Tensor<1, spacedim> direction;
 
  const Point<spacedim> point_on_axis;
 
  const double tolerance;
 
  const Tensor<1, spacedim> dxn;
};
 
template <int dim, int spacedim = dim>
class EllipticalManifold : public ChartManifold<dim, spacedim, spacedim>
{
public:
  EllipticalManifold(const Point<spacedim> &    center,
                     const Tensor<1, spacedim> &major_axis_direction,
                     const double               eccentricity);
 
  virtual std::unique_ptr<Manifold<dim, spacedim>>
  clone() const override;
 
  virtual Point<spacedim>
  pull_back(const Point<spacedim> &space_point) const override;
 
  virtual Point<spacedim>
  push_forward(const Point<spacedim> &chart_point) const override;
 
  virtual DerivativeForm<1, spacedim, spacedim>
  push_forward_gradient(const Point<spacedim> &chart_point) const override;
 
 
private:
  Tensor<1, spacedim> direction;
  const Point<spacedim> center;
  const double cosh_u;
  const double sinh_u;
 
  static Tensor<1, spacedim>
  get_periodicity();
};
 
 
template <int dim, int spacedim = dim, int chartdim = dim>
class FunctionManifold : public ChartManifold<dim, spacedim, chartdim>
{
public:
  FunctionManifold(
    const Function<chartdim> & push_forward_function,
    const Function<spacedim> & pull_back_function,
    const Tensor<1, chartdim> &periodicity = Tensor<1, chartdim>(),
    const double               tolerance   = 1e-10);
 
  FunctionManifold(
    std::unique_ptr<Function<chartdim>> push_forward,
    std::unique_ptr<Function<spacedim>> pull_back,
    const Tensor<1, chartdim> &         periodicity = Tensor<1, chartdim>(),
    const double                        tolerance   = 1e-10);
 
  FunctionManifold(
    const std::string          push_forward_expression,
    const std::string          pull_back_expression,
    const Tensor<1, chartdim> &periodicity = Tensor<1, chartdim>(),
    const typename FunctionParser<spacedim>::ConstMap =
      typename FunctionParser<spacedim>::ConstMap(),
    const std::string chart_vars =
      FunctionParser<chartdim>::default_variable_names(),
    const std::string space_vars =
      FunctionParser<spacedim>::default_variable_names(),
    const double tolerance = 1e-10,
    const double h         = 1e-8);
 
  virtual ~FunctionManifold() override;
 
  virtual std::unique_ptr<Manifold<dim, spacedim>>
  clone() const override;
 
  virtual Point<spacedim>
  push_forward(const Point<chartdim> &chart_point) const override;
 
  virtual DerivativeForm<1, chartdim, spacedim>
  push_forward_gradient(const Point<chartdim> &chart_point) const override;
 
  virtual Point<chartdim>
  pull_back(const Point<spacedim> &space_point) const override;
 
private:
  const typename FunctionParser<spacedim>::ConstMap const_map;
 
  SmartPointer<const Function<chartdim>,
               FunctionManifold<dim, spacedim, chartdim>>
    push_forward_function;
 
  SmartPointer<const Function<spacedim>,
               FunctionManifold<dim, spacedim, chartdim>>
    pull_back_function;
 
  const double tolerance;
 
  bool owns_pointers;
 
  const std::string push_forward_expression;
 
  const std::string pull_back_expression;
 
  const std::string chart_vars;
 
  const std::string space_vars;
 
  const double finite_difference_step;
};
 
 
 
template <int dim>
class TorusManifold : public ChartManifold<dim, 3, 3>
{
public:
  static const int chartdim = 3;
  static const int spacedim = 3;
 
  TorusManifold(const double R, const double r);
 
  virtual std::unique_ptr<Manifold<dim, 3>>
  clone() const override;
 
  virtual Point<3>
  pull_back(const Point<3> &p) const override;
 
  virtual Point<3>
  push_forward(const Point<3> &chart_point) const override;
 
  virtual DerivativeForm<1, 3, 3>
  push_forward_gradient(const Point<3> &chart_point) const override;
 
private:
  double r, R;
};
 
 
 
template <int dim, int spacedim = dim>
class TransfiniteInterpolationManifold : public Manifold<dim, spacedim>
{
public:
  TransfiniteInterpolationManifold();
 
  virtual ~TransfiniteInterpolationManifold() override;
 
  virtual std::unique_ptr<Manifold<dim, spacedim>>
  clone() const override;
 
  void
  initialize(const Triangulation<dim, spacedim> &triangulation);
 
  virtual Point<spacedim>
  get_new_point(const ArrayView<const Point<spacedim>> &surrounding_points,
                const ArrayView<const double> &         weights) const override;
 
  virtual void
  get_new_points(const ArrayView<const Point<spacedim>> &surrounding_points,
                 const Table<2, double> &                weights,
                 ArrayView<Point<spacedim>> new_points) const override;
 
private:
  std::array<unsigned int, 20>
  get_possible_cells_around_points(
    const ArrayView<const Point<spacedim>> &surrounding_points) const;
 
  typename Triangulation<dim, spacedim>::cell_iterator
  compute_chart_points(
    const ArrayView<const Point<spacedim>> &surrounding_points,
    ArrayView<Point<dim>>                   chart_points) const;
 
  Point<dim>
  pull_back(const typename Triangulation<dim, spacedim>::cell_iterator &cell,
            const Point<spacedim> &                                     p,
            const Point<dim> &initial_guess) const;
 
  Point<spacedim>
  push_forward(const typename Triangulation<dim, spacedim>::cell_iterator &cell,
               const Point<dim> &chart_point) const;
 
  DerivativeForm<1, dim, spacedim>
  push_forward_gradient(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const Point<dim> &                                          chart_point,
    const Point<spacedim> &pushed_forward_chart_point) const;
 
  const Triangulation<dim, spacedim> *triangulation;
 
  int level_coarse;
 
  std::vector<bool> coarse_cell_is_flat;
 
  FlatManifold<dim> chart_manifold;
 
  std::vector<internal::MappingQImplementation::
                InverseQuadraticApproximation<dim, spacedim>>
    quadratic_approximation;
 
  boost::signals2::connection clear_signal;
};
 
DEAL_II_NAMESPACE_CLOSE
 
#endif