DerivativeGridFunction.hpp

#pragma once

#include <type_traits>

#include <dune/functions/common/defaultderivativetraits.hh>
#include <dune/grid/utility/hierarchicsearch.hh>

#include <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 DerivativeTraits = Dune::Functions::DefaultDerivativeTraits<RawSignature>;
    using LocalFunction = std::decay_t<decltype(derivative(localFunction(std::declval<GridFunction>())))>;

    enum { hasDerivative = false };

  public:
    /// The Range of the derivative of the GridFunction
    using Range = typename DerivativeTraits::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}
    {
      static_assert(isValidRange<DerivativeTraits>(), "Derivative of GridFunction not defined");
    }

    /// Evaluate derivative in global coordinates. NOTE: expensive
    Range operator()(Domain const& x) const
    {
      auto gv = entitySet().gridView();

      using GridView = decltype(gv);
      using Grid = typename GridView::Grid;
      using IS = typename GridView::IndexSet;

      Dune::HierarchicSearch<Grid,IS> hsearch{gv.grid(), gv.indexSet()};

      auto element = hsearch.findEntity(x);
      auto geometry = element.geometry();
      auto localFct = derivative(localFunction(gridFct_));
      localFct.bind(element);
      return localFct(geometry.local(x));
    }

    /// 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,
            class LocalFct = decltype(localFunction(std::declval<GridFct>())),
    REQUIRES(not GridFct::hasDerivative)>
  auto derivative(GridFct const& gridFct)
  {
    static_assert(Concepts::HasDerivative<LocalFct>, "derivative(LocalFunction) not defined!");
    return DerivativeGridFunction<GridFct>{gridFct};
  }


  template <class Expr>
  struct DerivativePreGridFunction
  {
    using Self = DerivativePreGridFunction;

    struct Creator
    {
      template <class GridView>
      static auto create(Self const& self, GridView const& gridView)
      {
        return derivative(makeGridFunction(self.expr_, gridView));
      }
    };

    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};
  }

  /** @} **/

} // end namespace AMDiS