ConstantGridFunction.hpp

#pragma once

#include <functional>
#include <type_traits>

#include <dune/common/diagonalmatrix.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>

#include <amdis/common/DerivativeTraits.hpp>
#include <amdis/common/TypeTraits.hpp>
#include <amdis/gridfunctions/AnalyticGridFunction.hpp>
#include <amdis/gridfunctions/GridFunction.hpp>

namespace AMDiS
{
#ifndef DOXYGEN
  template <class Signature, class LocalContext, class Function>
  class ConstantLocalFunction;
#endif

  /// \brief LocalFunction of a Gridfunction returning a constant value.
  template <class R, class D, class LC, class T>
  class ConstantLocalFunction<R(D), LC, T>
  {
  public:
    /// The LocalDomain this LocalFunction can be evaluated in
    using Domain = D;

    /// The range type of the LocalFunction
    using Range = R;

    /// This LocalFunction has its own \ref derivative() function
    enum { hasDerivative = true };

  private:
    using Geometry = typename LC::Geometry;

  public:
    /// \brief Constructor. Stores the constant value.
    ConstantLocalFunction(T const& value)
      : value_(value)
    {}

    void bind(LC const& /*element*/) { /* do nothing */ }
    void unbind() { /* do nothing */ }

    /// Return the constant `value_`.
    Range const& operator()(Domain const& /*local*/) const
    {
      return value_;
    }

    /// \brief Create a \ref ConstantLocalFunction representing the derivative
    /// of a constant function, that ist, the value 0.
    template <class Type>
    auto makeDerivative(Type const& type) const
    {
      using RawSignature = typename Dune::Functions::SignatureTraits<R(D)>::RawSignature;
      using DerivativeRange = typename DerivativeTraits<RawSignature,Type>::Range;
      DerivativeRange diff(0);
      return ConstantLocalFunction<DerivativeRange(D),LC,DerivativeRange>{diff};
    }

    /// Return the constant polynomial order 0.
    int order() const
    {
      return 0;
    }

  private:
    T value_;
  };


  /// \brief Gridfunction returning a constant value.
  /**
   * \ingroup GridFunctions
   *
   * A stored constant is return in global and local evaluation of this functor.
   * Maybe used with arithmetic types and vectors/matrices of arithmetic types.
   * It is also allowed to pass a \ref std::reference_wrapper to allow to
   * modify the value after construction.
   **/
  template <class T, class GridView>
  class ConstantGridFunction
  {
  public:
    using EntitySet = Dune::Functions::GridViewEntitySet<GridView, 0>;
    using Domain = typename EntitySet::GlobalCoordinate;
    using Range = Underlying_t<T>;

    enum { hasDerivative = false };

  private:
    using Element = typename EntitySet::Element;
    using LocalDomain = typename EntitySet::LocalCoordinate;
    using LocalFunction = ConstantLocalFunction<Range(LocalDomain), Element, T>;

  public:
    /// Constructor. Stores the function `fct` and creates an `EntitySet`.
    ConstantGridFunction(T const& value, GridView const& gridView)
      : value_(value)
      , entitySet_(gridView)
    {}

    /// Return the constant `value_`
    Range const& operator()(Domain const& /*x*/) const
    {
      return value_;
    }

    EntitySet const& entitySet() const
    {
      return entitySet_;
    }

    /// \brief Create an \ref ConstantLocalFunction with the stores `value_`.
    LocalFunction makeLocalFunction() const
    {
      return {value_};
    }

  private:
    T value_;
    EntitySet entitySet_;
  };


  namespace Concepts
  {
    /** \addtogroup Concepts
     *  @{
     **/

    namespace Definition
    {
      template <class T>
      struct ConstantToGridFunction
        : std::is_arithmetic<T> {};

      template <class T>
      struct ConstantToGridFunction<std::reference_wrapper<T>>
        : ConstantToGridFunction<T> {};

      template <class T, int N>
      struct ConstantToGridFunction<Dune::FieldVector<T, N>>
        : ConstantToGridFunction<T> {};

      template <class T, int N, int M>
      struct ConstantToGridFunction<Dune::FieldMatrix<T, N, M>>
        : ConstantToGridFunction<T> {};

      template <class T, int N>
      struct ConstantToGridFunction<Dune::DiagonalMatrix<T, N>>
        : ConstantToGridFunction<T> {};

    } // end namespace Definition


    /// \brief Concepts that is true for all ''simple'' types that can be
    /// converted automatically to a GridFunction, e.g. arithmetic types,
    /// FieldVectors, and `std::reference_wrapper`.
    template <class T>
    constexpr bool ConstantToGridFunction =
      Definition::ConstantToGridFunction<T>::value;

    /** @} **/

  } // end namespace Concepts


  template <class Value>
  struct GridFunctionCreator<Value, std::enable_if_t<Concepts::ConstantToGridFunction<Value>>>
  {
    template <class GridView>
    static auto create(Value const& value, GridView const& gridView)
    {
      return ConstantGridFunction<Value,GridView>{value, gridView};
    }
  };

} // end namespace AMDiS