hermite.h (Latest change: Author:Lakshman Anumolu <acrlakshman@yahoo.co.in>, 2019-07-14 14:15:13 -0500, [commit: d5cbae7])

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// Copyright 2019 Lakshman Anumolu, Raunak Bardia.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
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// 1. Redistributions of source code must retain the above copyright notice,
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#pragma once

#include "gals/cpu/levelset.h"
#include "gals/utilities/array.h"
#include "gals/utilities/grid.h"
#include "gals/utilities/mat3.h"
#include "gals/utilities/utilities.h"
#include "gals/utilities/vec3.h"

namespace GALS
{
namespace INTERPOLATION
{
template <typename T>
struct ControlPoints {
  T c_30, c_21, c_12, c_03;
};

// TODO (lakshman): Cleanup below functions.
template <typename T = double>
T B0(T eta)
{
  return cube((T)1.0 - eta);
}

template <typename T = double>
T B1(T eta)
{
  return (T)3.0 * eta * sqr((T)1.0 - eta);
}

template <typename T = double>
T B2(T eta)
{
  return (T)3.0 * sqr(eta) * ((T)1.0 - eta);
}

template <typename T = double>
T B3(T eta)
{
  return cube(eta);
}

template <typename T = double>
T B0_Prime(T eta)
{
  return -(T)3.0 * sqr((T)1.0 - eta);
}

template <typename T = double>
T B1_Prime(T eta)
{
  return (T)3 * ((T)1 - eta) * ((T)1 - (T)3 * eta);
}

template <typename T = double>
T B2_Prime(T eta)
{
  return (T)3 * eta * ((T)2 - (T)3 * eta);
}

template <typename T = double>
T B3_Prime(T eta)
{
  return (T)3 * sqr(eta);
}

template <typename T>
static struct ControlPoints<T> get_control_points(const T &phi_0, const T &phi_x_0, const T &phi_1, const T &phi_x_1,
                                                  const T &dx, bool use_gradient_limiting = false) {
  struct ControlPoints<T> control_points;
  control_points.c_30 = phi_0;
  control_points.c_21 = phi_0 + (phi_x_0 * dx * (T)one_third);
  control_points.c_12 = phi_1 - (phi_x_1 * dx * (T)one_third);
  control_points.c_03 = phi_1;

  if (use_gradient_limiting) {
    // Implementation of gradient limiting algorithm by Bockmann et al. JCP 258(2014)
    T D1 = (T)3.0 * (control_points.c_21 - control_points.c_30);
    T D2 = (T)3.0 * (control_points.c_03 - control_points.c_12);
    T D3 = (T)1.5 * (control_points.c_12 - control_points.c_30);
    T D4 = (T)1.5 * (control_points.c_03 - control_points.c_21);
    T D5 = control_points.c_03 - control_points.c_30;

    if ((D1 - D3) * (D1 - D5) < (T)0)
      control_points.c_12 = (T)2 * control_points.c_21 - control_points.c_30;
    else if ((D2 - D4) * (D2 - D5) < (T)0)
      control_points.c_21 = (T)2 * control_points.c_12 - control_points.c_03;
    else if ((D1 - D5) * (D2 - D5) <= (T)0) {
      control_points.c_21 = (two_thirds * control_points.c_30) + (one_third * control_points.c_03);
      control_points.c_12 = (two_thirds * control_points.c_03) + (one_third * control_points.c_30);
    }
  }

  return control_points;
}

template <typename T, typename T_GRID>
class Hermite;

// Template specialized for 1D
template <typename T>
class Hermite<T, GALS::CPU::Grid<T, 1>>
{
 public:
  using value_type = T;
  using T_GRID = GALS::CPU::Grid<T, 1>;

  Hermite(){};

  ~Hermite(){};

  CPU::InterpolatedFields<CPU::Vec3<T>> interpolate(
      const GALS::CPU::Grid<typename GALS::CPU::Grid<T, 1>::value_type, GALS::CPU::Grid<T, 1>::dim> &grid,
      const typename GALS::CPU::Grid<T, 1>::position_type &x_interp,
      const CPU::Levelset<GALS::CPU::Grid<T, 1>, T> &levelset, const bool use_gradient_limiting = false);

  void compute(const GALS::CPU::Array<GALS::CPU::Grid<T, 1>, typename GALS::CPU::Grid<T, 1>::position_type> &x_interp,
               CPU::Levelset<GALS::CPU::Grid<T, 1>, T> &levelset);

  void operator()(
      const GALS::CPU::Array<GALS::CPU::Grid<T, 1>, typename GALS::CPU::Grid<T, 1>::position_type> &x_interp,
      CPU::Levelset<GALS::CPU::Grid<T, 1>, T> &levelset)
  {
    compute(x_interp, levelset);
  }

  void operator()(
      const GALS::CPU::Array<GALS::CPU::Grid<T, 1>, typename GALS::CPU::Grid<T, 1>::position_type> &x_interp,
      const GALS::CPU::Array<GALS::CPU::Grid<T, 1>, T> &alpha,
      GALS::CPU::Array<GALS::CPU::Grid<T, 1>, T> &alpha_interpolated)
  {
    GALS_FUNCTION_NOT_IMPLEMENTED();
  }
};

// Template specialized for 2D
template <typename T>
class Hermite<T, GALS::CPU::Grid<T, 2>>
{
 public:
  using value_type = T;
  using T_GRID = GALS::CPU::Grid<T, 2>;

  Hermite(){};

  ~Hermite(){};

  CPU::InterpolatedFields<CPU::Vec3<T>> interpolate(
      const GALS::CPU::Grid<typename GALS::CPU::Grid<T, 2>::value_type, GALS::CPU::Grid<T, 2>::dim> &grid,
      const typename GALS::CPU::Grid<T, 2>::position_type &x_interp,
      const CPU::Levelset<GALS::CPU::Grid<T, 2>, T> &levelset, const bool use_gradient_limiting = false);

  void compute(const GALS::CPU::Array<GALS::CPU::Grid<T, 2>, typename GALS::CPU::Grid<T, 2>::position_type> &x_interp,
               CPU::Levelset<GALS::CPU::Grid<T, 2>, T> &levelset);

  void operator()(
      const GALS::CPU::Array<GALS::CPU::Grid<T, 2>, typename GALS::CPU::Grid<T, 2>::position_type> &x_interp,
      CPU::Levelset<GALS::CPU::Grid<T, 2>, T> &levelset)
  {
    compute(x_interp, levelset);
  }

  void operator()(
      const GALS::CPU::Array<GALS::CPU::Grid<T, 2>, typename GALS::CPU::Grid<T, 2>::position_type> &x_interp,
      const GALS::CPU::Array<GALS::CPU::Grid<T, 2>, T> &alpha,
      GALS::CPU::Array<GALS::CPU::Grid<T, 2>, T> &alpha_interpolated)
  {
    GALS_FUNCTION_NOT_IMPLEMENTED();
  }
};

// Template specialized for 3D
template <typename T>
class Hermite<T, GALS::CPU::Grid<T, 3>>
{
 public:
  using value_type = T;
  using T_GRID = GALS::CPU::Grid<T, 3>;

  Hermite(){};

  ~Hermite(){};

  CPU::InterpolatedFields<CPU::Vec3<T>> interpolate(
      const GALS::CPU::Grid<typename GALS::CPU::Grid<T, 3>::value_type, GALS::CPU::Grid<T, 3>::dim> &grid,
      const typename GALS::CPU::Grid<T, 3>::position_type &x_interp,
      const CPU::Levelset<GALS::CPU::Grid<T, 3>, T> &levelset, const bool use_gradient_limiting = false);

  void compute(const GALS::CPU::Array<GALS::CPU::Grid<T, 3>, typename GALS::CPU::Grid<T, 3>::position_type> &x_interp,
               CPU::Levelset<GALS::CPU::Grid<T, 3>, T> &levelset);

  void operator()(
      const GALS::CPU::Array<GALS::CPU::Grid<T, 3>, typename GALS::CPU::Grid<T, 3>::position_type> &x_interp,
      CPU::Levelset<GALS::CPU::Grid<T, 3>, T> &levelset)
  {
    compute(x_interp, levelset);
  }

  void operator()(
      const GALS::CPU::Array<GALS::CPU::Grid<T, 3>, typename GALS::CPU::Grid<T, 3>::position_type> &x_interp,
      const GALS::CPU::Array<GALS::CPU::Grid<T, 3>, T> &alpha,
      GALS::CPU::Array<GALS::CPU::Grid<T, 3>, T> &alpha_interpolated)
  {
    GALS_FUNCTION_NOT_IMPLEMENTED();
  }
};

}  // namespace INTERPOLATION
}  // namespace GALS