DerivativeGridFunction.hpp

#pragma once

#include <type_traits>

#include <dune/functions/common/defaultderivativetraits.hh>

#include <dune/amdis/gridfunctions/GridFunctionConcepts.hpp>

namespace AMDiS
{
  /**
    * \addtogroup GridFunctions
    * @{
    **/

  /// \brief A Gridfunction that returns the derivative when calling localFunction.
  /**
   * Wrapps the GridFunction so that \ref localFunction returns a LocalFunction
   * representing the derivative of the LocalFunction of the GridFunction.
   *
   * \tparam GridFunction The GridFunction that is wrapped.
   *
   * **Requirements:**
   * - `GridFunction` models \ref Concepts::GridFunction and the LocalFunction has a derivative.
   **/
  template <class GridFunction>
  class DerivativeGridFunction
  {
    using GridFctRange = typename GridFunction::Range;
    using GridFctDomain = typename GridFunction::Domain;
    using RawSignature = typename Dune::Functions::SignatureTraits<GridFctRange(GridFctDomain)>::RawSignature;
    using LocalFunction = std::decay_t<decltype(derivative(localFunction(std::declval<GridFunction>())))>;

  public:
    /// The Range of the derivative of the GridFunction
    using Range = typename Dune::Functions::DefaultDerivativeTraits<RawSignature>::Range;
    /// The domain of the GridFunction
    using Domain = GridFctDomain;
    /// The EntitySet of the GridFunction
    using EntitySet = typename GridFunction::EntitySet;

  public:
    /// Constructor. Stores a copy of gridFct.
    explicit DerivativeGridFunction(GridFunction const& gridFct)
      : gridFct_(gridFct)
    {}

    /// NOTE: no global derivative available
    Range operator()(Domain const& x) const
    {
      error_exit("Not implemented");
      return Range(0);
    }

    /// Return the derivative-localFunction of the GridFunction.
    friend LocalFunction localFunction(DerivativeGridFunction const& gf)
    {
      return derivative(localFunction(gf.gridFct_));
    }

    /// Return the \ref EntitySet of the \ref GridFunction.
    EntitySet const& entitySet() const
    {
      return gridFct_.entitySet();
    }

  private:
    GridFunction gridFct_;
  };


#ifndef DOXYGEN
  template <class GridFct,
    REQUIRES(not Concepts::HasDerivative<GridFct> &&
                Concepts::HasLocalFunctionDerivative<GridFct>)>
  auto derivative(GridFct const& gridFct)
  {
    return DerivativeGridFunction<GridFct>{gridFct};
  }


  template <class Expr>
  struct DerivativePreGridFunction
  {
    Expr expr;
  };

  namespace Traits
  {
    template <class Expr>
    struct IsPreGridFunction<DerivativePreGridFunction<Expr>>
      : std::true_type {};
  }
#endif


  /// \brief Generator function for DerivativeGridFunction expressions. \relates DerivativeGridFunction
  /**
   * Generates a derivative of a GridFunction. See \ref DerivativeGridFunction.
   *
   * **Examples:**
   * - `gradientAtQP(prob.getSolution(_0))`
   * - `gradientAtQP(X(0) + X(1) + prob.getSolution(_0))`
   **/
  template <class Expr>
  auto gradientAtQP(Expr const& expr)
  {
    return DerivativePreGridFunction<Expr>{expr};
  }

  /** @} **/

  namespace Impl
  {
    /// Generator function for \ref AnalyticGridFunction expressions from \ref AnalyticPreGridFunction.
    template <class Expr, class GridView>
    auto makeGridFunctionImpl(DerivativePreGridFunction<Expr> const& pre, GridView const& gridView, Dune::PriorityTag<3>)
    {
      return derivative(Impl::makeGridFunctionImpl(pre.expr, gridView, Dune::PriorityTag<10>{}));
    }

  } // end namespace Impl
} // end namespace AMDiS