norms.hh

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*  This file is part of the library KASKADE 7                               */
/*  https://www.zib.de/research/projects/kaskade7-finite-element-toolbox     */
/*                                                                           */
/*  Copyright (C) 2002-2019 Zuse Institute Berlin                            */
/*                                                                           */
/*  KASKADE 7 is distributed under the terms of the ZIB Academic License.    */
/*    see $KASKADE/academic.txt                                              */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
 
#ifndef NORMS_HH
#define NORMS_HH
 
#include <boost/fusion/include/at_c.hpp>
#include <fem/integration.hh>
#include <fem/functionviews.hh>
 
namespace Kaskade
{
  struct L2Norm
  {
    template<typename Function>
    typename Function::Scalar square(Function const& f) const
    {
      Integral<typename Function::Space> integral;
      FunctionViews::AbsSquare<Function> asf(f);
      return integral(asf);
    }
 
    template<typename Function>
    typename Function::Scalar operator()(Function const& f) const
    {
      return std::sqrt(square(f));
    }
  };
 
 
  struct H1SemiNorm
  {
    template<typename Function>
    typename Function::Scalar square(Function const& f) const
    {
      Integral<typename Function::Space> integral;
      FunctionViews::GradientAbsSquare<Function> asf(f);
      return integral(asf);
  //    FunctionViews::Gradient<Function> gf(f);
  //    L2Norm l2Norm;
  //    return l2Norm.square(gf);
    }
 
    template<typename Function>
    typename Function::Scalar operator()(Function const& f) const
    {
      return std::sqrt(square(f));
    }
  };
 
 
 
  struct H1Norm
  {
    template<typename Function>
    typename Function::Scalar square(Function f)
    {
      H1SemiNorm h1Norm;
      L2Norm l2Norm;
      return h1Norm.square(f)+l2Norm.square(f);
    }
 
    template<typename Function>
    typename Function::Scalar operator()(Function f)
    {
      return std::sqrt(square(f));
    }
  };
 
  template<class Space> class LocalIntegral;
  template<class Grid, class T> class CellData;
 
  template<class Function>
  [[deprecated("appears to be outdated and unused - candidate for removal")]]
  typename CellData<typename Function::Space::Grid, typename Function::ValueType>::CellDataVector localH1SemiNorm(Function const& f)
  {
    typedef typename Function::Space Space;
    typedef typename Space::Grid Grid;
    LocalIntegral<Space> localIntegral;
    typename CellData<Grid,typename Function::ValueType>::CellDataVector
      errorIndicator(localIntegral(
                       makeView<FunctionViews::AbsSquare>(makeView<FunctionViews::Gradient>(f))));
    return errorIndicator;
  }
 
  template<class Function>
  [[deprecated("appears to be outdated and unused - candidate for removal")]]
  typename CellData<typename Function::Space::Grid, typename Function::ValueType>::CellDataVector localL2Norm(Function const& f)
  {
    typedef typename Function::Space Space;
    typedef typename Space::Grid Grid;
    LocalIntegral<Space> localIntegral;
    typename CellData<Grid,typename Function::ValueType>::CellDataVector
      errorIndicator(localIntegral(
                       makeView<FunctionViews::AbsSquare>(f)));
    return errorIndicator;
  }
 
 
  template <class FEFunction>
  auto boundaryL2Norm(FEFunction const& function)
  {
    FunctionViews::AbsSquare<FEFunction> functionSquared(function);
    return std::sqrt(integrateOverBoundary(functionSquared));
  }
} // end of namespace Kaskade
#endif