filter.h

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/*
 * Copyright (c) 2013-2014:  G-CSC, Goethe University Frankfurt
 * Author: Christian Wehner
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Lesser General Public License for more details.
 */
 
#ifndef __H__UG__NAVIER_STOKES__INCOMPRESSIBLE__FILTER__
#define __H__UG__NAVIER_STOKES__INCOMPRESSIBLE__FILTER__
 
#include <vector>
#include "lib_disc/function_spaces/approximation_space.h"
#include "lib_grid/tools/periodic_boundary_manager.h"
#include "lib_grid/lg_base.h"
#include "common/profiler/profiler.h"
#include "lib_disc/spatial_disc/disc_util/fvcr_geom.h"
#include "lib_disc/spatial_disc/disc_util/fv1_geom.h"
#include "lib_disc/local_finite_element/local_finite_element_provider.h"
#include "lib_grid/algorithms/attachment_util.h"
#include "fvcr/disc_constraint_fvcr.h"
 
namespace ug{
namespace NavierStokes{
 
template <typename TGridFunction>
class WallObject{
public:
  inline int si(){return m_subset_index;}
  inline number coord(){return m_coord;}
  inline size_t direction(){return m_direction;}
  number dist(MathVector<TGridFunction::dim> co){
    return std::abs(co[m_direction]-m_coord);
  }
  number dist(MathVector<TGridFunction::dim> co) {…}
  WallObject(SmartPtr<TGridFunction> u,size_t direction,number coord,const char* subset){
    m_subset_index = u->subset_id_by_name(subset);
    m_direction=direction;
    m_coord=coord;
  }
  WallObject(SmartPtr<TGridFunction> u,size_t direction,number coord,const char* subset) {…}
private:
  int m_subset_index;
  size_t m_direction;
  number m_coord;
};
class WallObject {…};
 
template <int dim,typename elem_type,typename TGridFunction>
void copyAttachmentToGridFunction(SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<elem_type,Attachment<MathVector<dim> > >& aaU){
  typedef typename TGridFunction::template traits<elem_type>::const_iterator ElemIterator;
  typedef typename TGridFunction::domain_type domain_type;
  //  get domain
  domain_type& domain = *u->domain().get();
  //  create Multiindex
  std::vector<DoFIndex> multInd;
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    ElemIterator iter = u->template begin<elem_type>(si);
    ElemIterator iterEnd = u->template end<elem_type>(si);
    for(  ;iter !=iterEnd; ++iter)
    {
      elem_type* elem = *iter;
      for (int d=0;d<dim;d++){
        u->dof_indices(elem, d, multInd);
        DoFRef(*u,multInd[0])=aaU[elem][d];
      }
    }
  }
}
void copyAttachmentToGridFunction(SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<elem_type,Attachment<MathVector<dim> > >& aaU) {…}
 
template <int dim,typename elem_type,typename TGridFunction>
void copyGridFunctionToAttachment(PeriodicAttachmentAccessor<elem_type,Attachment<MathVector<dim> > >& aaU,SmartPtr<TGridFunction> u){
  typedef typename TGridFunction::template traits<elem_type>::const_iterator ElemIterator;
  typedef typename TGridFunction::domain_type domain_type;
  //  get domain
  domain_type& domain = *u->domain().get();
  //  create Multiindex
  std::vector<DoFIndex> multInd;
  for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si){
    ElemIterator iter = u->template begin<elem_type>(si);
    ElemIterator iterEnd = u->template end<elem_type>(si);
    for(  ;iter !=iterEnd; ++iter)
    {
      elem_type* elem = *iter;
      for (int d=0;d<dim;d++){
        u->dof_indices(elem, d, multInd);
        aaU[elem][d]=DoFRef(*u,multInd[0]);
      }
    }
  }
}
void copyGridFunctionToAttachment(PeriodicAttachmentAccessor<elem_type,Attachment<MathVector<dim> > >& aaU,SmartPtr<TGridFunction> u) {…}
  
template <typename elem_type,typename attachment_type,typename grid_type>
void initAttachment(PeriodicAttachmentAccessor<elem_type,attachment_type >& accessor,
          attachment_type& attachment,
          grid_type& grid
          ){
  grid.template attach_to<elem_type>(attachment);
  accessor.access(grid,attachment);
};
void initAttachment(PeriodicAttachmentAccessor<elem_type,attachment_type >& accessor, {…}
    
template <typename TGridFunction>
class FilterBaseClass{
public:
  static const size_t dim = TGridFunction::dim;
 
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
 
  typedef typename TGridFunction::domain_type domain_type;
 
  typedef typename domain_type::grid_type grid_type;
 
  typedef typename elem_type::side side_type;
 
  // vertex type
  typedef Vertex vertex_type;
 
  // data types used in attachments
  typedef MathVector<dim> type0;
  typedef number type1;
  typedef MathSymmetricMatrix<dim> type2;
 
  // filter for side attachment
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat,
      PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaU){}
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat, {…}
 
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type1> >& aaUHat,
      PeriodicAttachmentAccessor<side_type,Attachment<type1> >& aaU){}
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type1> >& aaUHat, {…}
  
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type2> >& aaUHat,
      PeriodicAttachmentAccessor<side_type,Attachment<type2> >& aaU){}
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type2> >& aaUHat, {…}
 
  // filter for crouzeix-raviart type grid function
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat,
      SmartPtr<TGridFunction> u){}
  virtual void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat, {…}
 
  // filter for vertex attachment
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat,
             PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaU){}
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat, {…}
 
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type1> >& aaUHat,
             PeriodicAttachmentAccessor<vertex_type,Attachment<type1> >& aaU){}
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type1> >& aaUHat, {…}
  
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type2> >& aaUHat,
             PeriodicAttachmentAccessor<vertex_type,Attachment<type2> >& aaU){}
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type2> >& aaUHat, {…}
 
  // filter for general grid function, result stored in nodes
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat,
             SmartPtr<TGridFunction> u){}
  virtual void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat, {…}
 
  // filter grid function
  virtual void apply(SmartPtr<TGridFunction> u){}
  
  virtual number width(vertex_type* vrt){return -1;}
  
  virtual number width(side_type* side){return -1;}
  
  virtual void compute_filterwidth(){}
  
  FilterBaseClass(){}
  virtual ~FilterBaseClass(){}
};
class FilterBaseClass {…};
 
// wrapper class for filtering
template <typename TImpl,typename TGridFunction>
class FilterImplBaseClass
: public FilterBaseClass<TGridFunction>
{
  public:
  static const size_t dim = TGridFunction::dim;
  
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
  
  typedef typename TGridFunction::domain_type domain_type;
 
  typedef typename domain_type::grid_type grid_type;
 
  typedef typename elem_type::side side_type;
  
  // vertex type
  typedef Vertex vertex_type;
  
  // data types
  typedef typename FilterBaseClass<TGridFunction>::type0 type0;
  typedef typename FilterBaseClass<TGridFunction>::type1 type1;
  typedef typename FilterBaseClass<TGridFunction>::type2 type2;
  
  // filter for side attachment
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat,
         PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaU){
    getImpl().apply_filter(aaUHat,SPNULL,aaU);
  }
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat, {…}
  
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type1> >& aaUHat,
         PeriodicAttachmentAccessor<side_type,Attachment<type1> >& aaU){
    getImpl().apply_filter(aaUHat,SPNULL,aaU);
  }
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type1> >& aaUHat, {…}
  
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type2> >& aaUHat,
         PeriodicAttachmentAccessor<side_type,Attachment<type2> >& aaU){
    getImpl().apply_filter(aaUHat,SPNULL,aaU);
  }
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type2> >& aaUHat, {…}
  
  // filter for crouzeix-raviart type grid function
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat,
      SmartPtr<TGridFunction> u){
      UG_LOG("son class\n");
      getImpl().apply_filter(aaUHat,u,aaUHat);
  }
  void apply(PeriodicAttachmentAccessor<side_type,Attachment<type0> >& aaUHat, {…}
  
  // filter for vertex attachment
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat,
         PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaU){
    getImpl().apply_filter(aaUHat,SPNULL,aaU);
  }
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat, {…}
  
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type1> >& aaUHat,
         PeriodicAttachmentAccessor<vertex_type,Attachment<type1> >& aaU){
    getImpl().apply_filter(aaUHat,SPNULL,aaU);
  }
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type1> >& aaUHat, {…}
  
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type2> >& aaUHat,
         PeriodicAttachmentAccessor<vertex_type,Attachment<type2> >& aaU){
    getImpl().apply_filter(aaUHat,SPNULL,aaU);
  }
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type2> >& aaUHat, {…}
  
  // filter for general grid function, result stored in nodes
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat,
      SmartPtr<TGridFunction> u){
      if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
        getImpl().apply_filter(aaUHat,u);
      } else {
        getImpl().apply_filter(aaUHat,u,aaUHat);
      }
  }
  void apply(PeriodicAttachmentAccessor<vertex_type,Attachment<type0> >& aaUHat, {…}
 
  template <typename TElem>
  void apply_(SmartPtr<TGridFunction> u){
    // define attachment types
    Attachment<MathVector<dim> > aUHat;
    PeriodicAttachmentAccessor<TElem,Attachment<MathVector<dim> > > acUHat;
 
    domain_type& domain = *u->domain().get();
    grid_type& grid = *domain.grid();
 
    // attach
    grid.template attach_to<TElem>(aUHat);
    acUHat.access(grid,aUHat);
    getImpl().apply_filter(acUHat,u,acUHat);
    copyAttachmentToGridFunction<dim,TElem,TGridFunction>(u,acUHat);
    grid.template detach_from<TElem>(aUHat);
  }
  void apply_(SmartPtr<TGridFunction> u) {…}
 
  // filter grid function
  void apply(SmartPtr<TGridFunction> u){
    if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      apply_<side_type>(u);
    } else {
      apply_<vertex_type>(u);
    }
  }
  void apply(SmartPtr<TGridFunction> u) {…}
  
  template<typename VType,typename TElem>
  void copyWallData(PeriodicAttachmentAccessor<TElem,Attachment<VType> >& acUHat,SmartPtr<TGridFunction> u,std::vector<WallObject<TGridFunction> > walls){
    typedef typename TGridFunction::domain_type TDomain;
    typedef typename TDomain::grid_type TGrid;
    TDomain domain = *u->domain().get();
    typedef typename TGridFunction::template traits<TElem>::const_iterator ElemIterator;
    PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
    std::vector<DoFIndex> dofInd;
    for (int j=0;j<(int)walls.size();j++){
      int si = walls[j].si();
      ElemIterator elemIter = u->template begin<TElem>(si);
      ElemIterator elemIterEnd = u->template end<TElem>(si);
      for(  ;elemIter !=elemIterEnd; elemIter++)
      {
        TElem* elem = *elemIter;
        if (pbm && pbm->is_slave(elem)) continue;
        VType localValue;
        for (int d=0;d<TGridFunction::dim;d++){
          u->dof_indices(elem, d, dofInd);
          assignVal(localValue,d,DoFRef(*u,dofInd[0]));
        }
        acUHat[elem]=localValue;
      }
    }
  }
  void copyWallData(PeriodicAttachmentAccessor<TElem,Attachment<VType> >& acUHat,SmartPtr<TGridFunction> u,std::vector<WallObject<TGridFunction> > walls) {…}
 
  template<typename VType,typename TElem>
  void copyWallData(PeriodicAttachmentAccessor<TElem,Attachment<VType> >& acUHat,PeriodicAttachmentAccessor<TElem,Attachment<VType> >&  acU,
          SmartPtr<TGridFunction> u,std::vector<WallObject<TGridFunction> > walls){
    typedef typename TGridFunction::domain_type TDomain;
    typedef typename TDomain::grid_type TGrid;
    TDomain domain = *u->domain().get();
    typedef typename TGridFunction::template traits<TElem>::const_iterator ElemIterator;
    PeriodicBoundaryManager* pbm = (domain.grid())->periodic_boundary_manager();
    std::vector<DoFIndex> dofInd;
    for (int j=0;j<(int)walls.size();j++){
      int si = walls[j].si();
      ElemIterator elemIter = u->template begin<TElem>(si);
      ElemIterator elemIterEnd = u->template end<TElem>(si);
      for(  ;elemIter !=elemIterEnd; elemIter++)
      {
        TElem* elem = *elemIter;
        if (pbm && pbm->is_slave(elem)) continue;
        acUHat[elem]=acU[elem];
      }
    }
  }
  void copyWallData(PeriodicAttachmentAccessor<TElem,Attachment<VType> >& acUHat,PeriodicAttachmentAccessor<TElem,Attachment<VType> >&  acU, {…}
  
  void assignVal(number& v,size_t ind,number value){
    v=value;  
  }
  void assignVal(number& v,size_t ind,number value) {…}
  
  void assignVal(MathVector<2>& v,size_t ind,number value){
    v[ind]=value;
  }
  void assignVal(MathVector<2>& v,size_t ind,number value) {…}
  
  void assignVal(MathVector<3>& v,size_t ind,number value){
    v[ind]=value;
  }
  void assignVal(MathVector<3>& v,size_t ind,number value) {…}
  
  void assignVal(MathSymmetricMatrix<2>& v,size_t ind,number value){
    v[ind]=value;
  }
  void assignVal(MathSymmetricMatrix<2>& v,size_t ind,number value) {…}
  
  void assignVal(MathSymmetricMatrix<3>& v,size_t ind,number value){
    v[ind]=value;
  }
  void assignVal(MathSymmetricMatrix<3>& v,size_t ind,number value) {…}
  
  protected:
    TImpl& getImpl() {return static_cast<TImpl&>(*this);}
 
    const TImpl& getImpl() const {return static_cast<const TImpl&>(*this);}
};
class FilterImplBaseClass {…};
  
template <int dim>
struct Region{
  size_t firstIndex;
  MathVector<dim> periodicOffset;
};
struct Region {…};
  
// Box filter with constant filter width
template <typename TGridFunction>
class ConstantBoxFilter
  : public FilterImplBaseClass<ConstantBoxFilter<TGridFunction>,TGridFunction>
{
public:
  // base type
  typedef FilterImplBaseClass<ConstantBoxFilter<TGridFunction>,TGridFunction> base_type;
  
  // dimension
  static const size_t dim = TGridFunction::dim;
  
    // element type
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
  
  //  domain type
  typedef typename TGridFunction::domain_type domain_type;
  
  // side type
  typedef typename elem_type::side side_type;
  
  // vertex type
  typedef Vertex vertex_type;
  
  //  grid type
  typedef typename domain_type::grid_type grid_type;  
  
  //  position accessor type
  typedef typename domain_type::position_accessor_type position_accessor_type;
 
  typedef typename TGridFunction::template dim_traits<dim>::const_iterator ElemIterator;
 
  typedef typename TGridFunction::template traits<side_type>::const_iterator SideIterator;
 
  typedef typename TGridFunction::template traits<vertex_type>::const_iterator VertexIterator;
 
  // accessor types
  typedef PeriodicAttachmentAccessor<side_type,ANumber > aSideNumber;
  typedef PeriodicAttachmentAccessor<vertex_type,ANumber > aVertexNumber;
 
  // filter for crouzeix-raviart type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,
         SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaU);
      
  // filter for fv1 type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaU){
              UG_THROW("not implemented");
            };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
 
  // filter for crouzeix-raviart grid function with output in node attachment
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
         SmartPtr<TGridFunction> u){
              UG_THROW("not implemented");
            };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
  
  // compute average mesh size
  number compute_average_element_size(SmartPtr<TGridFunction> u);
  
  inline number width(vertex_type* vrt){ return m_width; }
  
  inline number width(side_type* side){ return m_width; }
  
  void add_wall(WallObject<TGridFunction> w){
    m_walls.push_back(w);
  }
  void add_wall(WallObject<TGridFunction> w) {…}
  
  // constructors 
  ConstantBoxFilter(SmartPtr<TGridFunction> u,number width){
    m_width = width;
    m_uInfo = u;
    domain_type& domain = *u->domain().get();
    if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      domain.grid()->template attach_to<side_type>(m_aSideVolume);
      m_acSideVolume.access(*domain.grid(),m_aSideVolume);
    } else {
      domain.grid()->template attach_to<vertex_type>(m_aVertexVolume);
      m_acSideVolume.access(*domain.grid(),m_aVertexVolume);
    }
  }
  ConstantBoxFilter(SmartPtr<TGridFunction> u,number width) {…}
  
  ConstantBoxFilter(SmartPtr<TGridFunction> u){
    m_uInfo = u;
    domain_type& domain = *u->domain().get();
    if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      domain.grid()->template attach_to<side_type>(m_aSideVolume);
      m_acSideVolume.access(*domain.grid(),m_aSideVolume);
    } else {
      domain.grid()->template attach_to<vertex_type>(m_aVertexVolume);
      m_acSideVolume.access(*domain.grid(),m_aVertexVolume);
    }
    m_width = pow(compute_average_element_size(u),(number)1.0/dim);
  }
  ConstantBoxFilter(SmartPtr<TGridFunction> u) {…}
  
  ~ConstantBoxFilter(){
    domain_type& domain = *m_uInfo->domain().get();
    domain.grid()->template detach_from<side_type>(m_aSideVolume);
    domain.grid()->template detach_from<vertex_type>(m_aVertexVolume);
  }
  ~ConstantBoxFilter() {…}
  
private:
  template <typename VType>
  void collectSides(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& acUHat,
            PeriodicAttachmentAccessor<side_type,Attachment<number> >& acVolume,
            std::vector< MathVector<dim> >& coord,
            VType values[DimFV1Geometry<dim>::maxNumSCV],
            number volumes[DimFV1Geometry<dim>::maxNumSCV],
            std::vector<side_type*>& sides
            );
  
  //  volume attachment
  ANumber m_aSideVolume;
  aSideNumber m_acSideVolume;
  ANumber m_aVertexVolume;
  aVertexNumber m_acVertexVolume;
 
  number m_width;
  
  position_accessor_type m_posAcc;
 
  // grid function
  SmartPtr<TGridFunction> m_uInfo;
  
  std::vector<WallObject<TGridFunction> > m_walls;
  
  using base_type::assignVal;
  using base_type::copyWallData;
};
class ConstantBoxFilter {…};
  
// Box filter with constant filter width
template <typename TGridFunction>
class VariableBoxFilter
: public FilterImplBaseClass<VariableBoxFilter<TGridFunction>,TGridFunction>
{
public:
  // base type
  typedef FilterImplBaseClass<VariableBoxFilter<TGridFunction>,TGridFunction> base_type;
  
  // dimension
  static const size_t dim = TGridFunction::dim;
    
  // element type
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
    
  //  domain type
  typedef typename TGridFunction::domain_type domain_type;
    
  // side type
  typedef typename elem_type::side side_type;
    
  // vertex type
  typedef Vertex vertex_type;
    
  //  grid type
  typedef typename domain_type::grid_type grid_type;  
    
  //  position accessor type
  typedef typename domain_type::position_accessor_type position_accessor_type;
    
  typedef typename TGridFunction::template dim_traits<dim>::const_iterator ElemIterator;
    
  typedef typename TGridFunction::template traits<side_type>::const_iterator SideIterator;
    
  typedef typename TGridFunction::template traits<vertex_type>::const_iterator VertexIterator;
    
  // accessor types
  typedef PeriodicAttachmentAccessor<side_type,ANumber > aSideNumber;
  typedef PeriodicAttachmentAccessor<vertex_type,ANumber > aVertexNumber;
    
  // filter for crouzeix-raviart type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaU);
    
  // filter for fv1 type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaU){
      UG_THROW("not implemented");
  };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
    
  // filter for crouzeix-raviart grid function with output in node attachment
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u){
      UG_THROW("not implemented");
  };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
    
  // compute average mesh size
  number compute_average_element_size(SmartPtr<TGridFunction> u);
    
  inline number width(vertex_type* vrt){ 
    std::vector<DoFIndex> multInd; 
    m_width->inner_dof_indices(vrt,0, multInd);
    return DoFRef(*m_width,multInd[0]); 
  }
  inline number width(vertex_type* vrt) {…}
  
  inline number width(side_type* side){
    std::vector<DoFIndex> multInd; 
    m_width->inner_dof_indices(side,0, multInd);
    return DoFRef(*m_width,multInd[0]);
  }
  inline number width(side_type* side) {…}
  
  template <typename TElem>
  void init_width(number width){
    domain_type& domain = *m_width->domain().get();
    std::vector<DoFIndex> multInd; 
    for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
    {
      //  get iterators
      ElemIterator iter = m_width->template begin<elem_type>(si);
      ElemIterator iterEnd = m_width->template end<elem_type>(si);
      
      //  loop elements of dimension
      for(  ;iter !=iterEnd; ++iter)
      {
        //  get Elem
        elem_type* elem = *iter;
        m_width->inner_dof_indices(elem,0, multInd);
        DoFRef(*m_width,multInd[0])=width;
      }
    }
  }
  void init_width(number width) {…}
  
  template <typename TElem>
  number max_width(number width){
    domain_type& domain = *m_width->domain().get();
    std::vector<DoFIndex> multInd; 
    number maxwidth = 0;
    for(int si = 0; si < domain.subset_handler()->num_subsets(); ++si)
    {
      //  get iterators
      ElemIterator iter = m_width->template begin<elem_type>(si);
      ElemIterator iterEnd = m_width->template end<elem_type>(si);
      
      //  loop elements of dimension
      for(  ;iter !=iterEnd; ++iter)
      {
        //  get Elem
        elem_type* elem = *iter;
        m_width->inner_dof_indices(elem,0, multInd);
        maxwidth=std::max(DoFRef(*m_width,multInd[0]),maxwidth);
      }
    }
    m_maxwidth = maxwidth;
    return maxwidth;
  }
  number max_width(number width) {…}
  
  void add_wall(WallObject<TGridFunction> w){
    m_walls.push_back(w);
  }
  void add_wall(WallObject<TGridFunction> w) {…}
  
  template <typename VType,typename TElem>
  void check_volume_sizes(PeriodicAttachmentAccessor<TElem,Attachment<VType> >& acUHat,SmartPtr<TGridFunction> u){
    domain_type& domain = *m_width->domain().get();
    
  }
  void check_volume_sizes(PeriodicAttachmentAccessor<TElem,Attachment<VType> >& acUHat,SmartPtr<TGridFunction> u) {…}
 
  // constructors 
  VariableBoxFilter(SmartPtr<TGridFunction> u,SmartPtr<TGridFunction> fwidth,bool initWidth=false){
    m_width = fwidth;
    m_uInfo = u;
    domain_type& domain = *u->domain().get();
    if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      domain.grid()->template attach_to<side_type>(m_aSideVolume);
      m_acSideVolume.access(*domain.grid(),m_aSideVolume);
    } else {
      domain.grid()->template attach_to<vertex_type>(m_aVertexVolume);
      m_acSideVolume.access(*domain.grid(),m_aVertexVolume);
    }
    if (initWidth){
      number width = pow(compute_average_element_size(u),(number)1.0/dim);
      if (m_width->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
        init_width<side_type>(width);
      }
      if (m_width->local_finite_element_id(0) == LFEID(LFEID::LAGRANGE, dim, 1)){
        init_width<vertex_type>(width);
      }
    }
  }
  VariableBoxFilter(SmartPtr<TGridFunction> u,SmartPtr<TGridFunction> fwidth,bool initWidth=false) {…}
    
  ~VariableBoxFilter(){
    domain_type& domain = *m_uInfo->domain().get();
    domain.grid()->template detach_from<side_type>(m_aSideVolume);
    domain.grid()->template detach_from<vertex_type>(m_aVertexVolume);
  }
  ~VariableBoxFilter() {…}
    
private:
  template <typename VType>
  void collectSides(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& acUHat,
            PeriodicAttachmentAccessor<side_type,Attachment<number> >& acVolume,
            std::vector< MathVector<dim> >& coord,
            VType values[DimFV1Geometry<dim>::maxNumSCV],
            number volumes[DimFV1Geometry<dim>::maxNumSCV],
            std::vector<side_type*>& sides
          );
    
  //  volume attachment
  ANumber m_aSideVolume;
  aSideNumber m_acSideVolume;
  ANumber m_aVertexVolume;
  aVertexNumber m_acVertexVolume;
    
  position_accessor_type m_posAcc;
    
  // grid function
  SmartPtr<TGridFunction> m_uInfo;
    
  // filter width
  SmartPtr<TGridFunction> m_width;
  
  number m_maxwidth;
  
  std::vector<WallObject<TGridFunction> > m_walls;
  
  using base_type::assignVal;
  using base_type::copyWallData;
};
class VariableBoxFilter {…};
  
 
 
// Box filter with local filter volume given by vertex-centered FV (fv1 geometry)
template <typename TGridFunction>
class FV1BoxFilter
  : public FilterImplBaseClass<FV1BoxFilter<TGridFunction>,TGridFunction>
{
public:
  // base type
  typedef FilterImplBaseClass<FV1BoxFilter<TGridFunction>,TGridFunction> base_type;
 
  // dimension
  static const size_t dim = TGridFunction::dim;
 
  // element type
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
 
  //  domain type
  typedef typename TGridFunction::domain_type domain_type;
 
  // side type
  typedef typename elem_type::side side_type;
 
  // vertex type
  typedef Vertex vertex_type;
 
  //  grid type
  typedef typename domain_type::grid_type grid_type;
 
  //  position accessor type
  typedef typename domain_type::position_accessor_type position_accessor_type;
 
  // element iterator
  typedef typename TGridFunction::template dim_traits<dim>::const_iterator ElemIterator;
 
  // side iterator
  typedef typename TGridFunction::template traits<side_type>::const_iterator SideIterator;
 
  // vertex iterator
  typedef typename TGridFunction::template traits<vertex_type>::const_iterator VertexIterator;
 
  typedef PeriodicAttachmentAccessor<side_type,ANumber > aSideNumber;
  typedef PeriodicAttachmentAccessor<vertex_type,ANumber > aVertexNumber;
 
  // filter for crouzeix-raviart type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,
             SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaU);
 
  // filter for fv1 type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
             SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaU);
 
  // filter for crouzeix-raviart grid function with output in node attachment
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
         SmartPtr<TGridFunction> u)
            {
              UG_THROW("not implemented");
            };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
 
  // return filter width
  inline number width(vertex_type* vrt){ return pow(m_acVertexVolume[vrt],(number)1.0/dim); }
 
  inline number width(side_type* side){ return pow(m_acSideVolume[side],(number)1.0/dim); }
  
  void compute_filterwidth(){
    if (m_uInfo->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      compute_filterwidth_fvcr();
    } else {
      compute_filterwidth_fv1();
    }
  }
  void compute_filterwidth() {…}
  
  void compute_filterwidth_fv1();
  
  void compute_filterwidth_fvcr();
  
  void add_wall(WallObject<TGridFunction> w){
    m_walls.push_back(w);
  }
  void add_wall(WallObject<TGridFunction> w) {…}
 
  // constructor
  FV1BoxFilter(SmartPtr<TGridFunction> u){
    m_uInfo = u;
    domain_type& domain = *u->domain().get();
    if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      domain.grid()->template attach_to<side_type>(m_aSideVolume);
      m_acSideVolume.access(*domain.grid(),m_aSideVolume);
    } else {
      domain.grid()->template attach_to<vertex_type>(m_aVertexVolume);
      m_acSideVolume.access(*domain.grid(),m_aVertexVolume);
    }
  }
  FV1BoxFilter(SmartPtr<TGridFunction> u) {…}
 
  // destructor
  ~FV1BoxFilter(){
    domain_type& domain = *m_uInfo->domain().get();
    domain.grid()->template detach_from<side_type>(m_aSideVolume);
    domain.grid()->template detach_from<vertex_type>(m_aVertexVolume);
  }
  ~FV1BoxFilter() {…}
 
private:
  //  volume attachment
  ANumber m_aSideVolume;
  aSideNumber m_acSideVolume;
  ANumber m_aVertexVolume;
  aVertexNumber m_acVertexVolume;
 
  // grid function
  SmartPtr<TGridFunction> m_uInfo;
  
  std::vector<WallObject<TGridFunction> > m_walls;
  
  using base_type::assignVal;
  using base_type::copyWallData;
};
class FV1BoxFilter {…};
 
 
// Box filter with local filter volume given by vertex-centered FV (fv1 geometry)
template <typename TGridFunction>
class FVCRBoxFilter
  : public FilterImplBaseClass<FVCRBoxFilter<TGridFunction>,TGridFunction>
{
public:
  // base type
  typedef FilterImplBaseClass<FVCRBoxFilter<TGridFunction>,TGridFunction> base_type;
  
  // dimension
  static const size_t dim = TGridFunction::dim;
 
  // element type
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
 
  //  domain type
  typedef typename TGridFunction::domain_type domain_type;
 
  // side type
  typedef typename elem_type::side side_type;
 
  // vertex type
  typedef Vertex vertex_type;
 
  //  grid type
  typedef typename domain_type::grid_type grid_type;
 
  //  position accessor type
  typedef typename domain_type::position_accessor_type position_accessor_type;
 
  // element iterator
  typedef typename TGridFunction::template dim_traits<dim>::const_iterator ElemIterator;
 
  // side iterator
  typedef typename TGridFunction::template traits<side_type>::const_iterator SideIterator;
 
  // vertex iterator
  typedef typename TGridFunction::template traits<vertex_type>::const_iterator VertexIterator;
 
  typedef PeriodicAttachmentAccessor<side_type,ANumber > aSideNumber;
  typedef PeriodicAttachmentAccessor<vertex_type,ANumber > aVertexNumber;
 
  // filter for crouzeix-raviart type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,
             SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaU);
 
  // filter for fv1 type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
             SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaU)
              {
                UG_THROW("not implemented");
              };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
 
  // filter for crouzeix-raviart grid function with output in node attachment
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u)
            {
              UG_THROW("not implemented");
            };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
            
  void add_wall(WallObject<TGridFunction> w){
    m_walls.push_back(w);
  }
  void add_wall(WallObject<TGridFunction> w) {…}
 
  // return filter width
  inline number width(vertex_type* vrt){ UG_THROW("not implemented"); return 0; }
 
  inline number width(side_type* side){ return pow(m_acSideVolume[side],(number)1.0/dim); }
  
  void compute_filterwidth(){
    if (m_uInfo->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      compute_filterwidth_fvcr();
    } else {
      compute_filterwidth_fv1();
    }
  }
  void compute_filterwidth() {…}
  
  void compute_filterwidth_fv1(){
    UG_LOG("not implemented\n");
  }
  void compute_filterwidth_fv1() {…}
  
  void compute_filterwidth_fvcr();
 
  // constructors
  FVCRBoxFilter(SmartPtr<TGridFunction> u){
    m_uInfo = u;
    domain_type& domain = *u->domain().get();
    if (u->local_finite_element_id(0) != LFEID(LFEID::CROUZEIX_RAVIART, dim, 1))
      UG_THROW("Only implemented for Crouzeix-Raviart type functions.");
    domain.grid()->template attach_to<side_type>(m_aSideVolume);
    m_acSideVolume.access(*domain.grid(),m_aSideVolume);
  }
  FVCRBoxFilter(SmartPtr<TGridFunction> u) {…}
 
  ~FVCRBoxFilter(){
    domain_type& domain = *m_uInfo->domain().get();
    domain.grid()->template detach_from<side_type>(m_aSideVolume);
  }
  ~FVCRBoxFilter() {…}
 
  private:
  //  volume attachment
  ANumber m_aSideVolume;
  aSideNumber m_acSideVolume;
  //ANumber m_aVertexVolume;
  //aVertexNumber m_acVertexVolume;
 
  // grid function
  SmartPtr<TGridFunction> m_uInfo;
  
  std::vector<WallObject<TGridFunction> > m_walls;
  
  using base_type::assignVal;
  using base_type::copyWallData;
};
class FVCRBoxFilter {…};
  
// Box filter with local filter volume given by vertex-centered FV (fv1 geometry)
template <typename TGridFunction>
class ElementBoxFilter
: public FilterImplBaseClass<ElementBoxFilter<TGridFunction>,TGridFunction>
{
public:
  // base type
  typedef FilterImplBaseClass<ElementBoxFilter<TGridFunction>,TGridFunction> base_type;
  
  // dimension
  static const size_t dim = TGridFunction::dim;
    
  // element type
  typedef typename TGridFunction::template dim_traits<dim>::grid_base_object elem_type;
    
  //  domain type
  typedef typename TGridFunction::domain_type domain_type;
    
  // side type
  typedef typename elem_type::side side_type;
    
  // vertex type
  typedef Vertex vertex_type;
    
  //  grid type
  typedef typename domain_type::grid_type grid_type;
    
  //  position accessor type
  typedef typename domain_type::position_accessor_type position_accessor_type;
    
  // element iterator
  typedef typename TGridFunction::template dim_traits<dim>::const_iterator ElemIterator;
    
  // side iterator
  typedef typename TGridFunction::template traits<side_type>::const_iterator SideIterator;
    
  // vertex iterator
  typedef typename TGridFunction::template traits<vertex_type>::const_iterator VertexIterator;
    
  typedef PeriodicAttachmentAccessor<side_type,ANumber > aSideNumber;
  typedef PeriodicAttachmentAccessor<vertex_type,ANumber > aVertexNumber;
    
  // filter for crouzeix-raviart type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<side_type,Attachment<VType> >& aaU);
    
  // filter for fv1 type data
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u,PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaU);
    
  // filter for crouzeix-raviart grid function with output in node attachment
  template <typename VType>
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat,
            SmartPtr<TGridFunction> u)
  {
    UG_THROW("not implemented");
  };
  void apply_filter(PeriodicAttachmentAccessor<vertex_type,Attachment<VType> >& aaUHat, {…}
    
  // return filter width
  inline number width(vertex_type* vrt){ return pow(m_acVertexVolume[vrt],(number)1.0/dim); }
    
  inline number width(side_type* side){ return pow(m_acSideVolume[side],(number)1.0/dim); }
    
  void compute_filterwidth(){
    if (m_uInfo->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      compute_filterwidth_fvcr();
    } else {
      compute_filterwidth_fv1();
    }
  }
  void compute_filterwidth() {…}
  
  void compute_filterwidth_fv1();
  
  void compute_filterwidth_fvcr();
  
  void add_wall(WallObject<TGridFunction> w){
    m_walls.push_back(w);
  }
  void add_wall(WallObject<TGridFunction> w) {…}
  
  // constructors
  ElementBoxFilter(SmartPtr<TGridFunction> u){
    m_uInfo = u;
    domain_type& domain = *u->domain().get();
    if (u->local_finite_element_id(0) == LFEID(LFEID::CROUZEIX_RAVIART, dim, 1)){
      domain.grid()->template attach_to<side_type>(m_aSideVolume);
      m_acSideVolume.access(*domain.grid(),m_aSideVolume);
    } else {
      domain.grid()->template attach_to<side_type>(m_aVertexVolume);
      m_acSideVolume.access(*domain.grid(),m_aVertexVolume);
    }
  }
  ElementBoxFilter(SmartPtr<TGridFunction> u) {…}
 
  ~ElementBoxFilter(){
    domain_type& domain = *m_uInfo->domain().get();
    domain.grid()->template detach_from<side_type>(m_aSideVolume);
    domain.grid()->template detach_from<vertex_type>(m_aVertexVolume);
  }
  ~ElementBoxFilter() {…}
    
private:
  //  volume attachment
  ANumber m_aSideVolume;
  aSideNumber m_acSideVolume;
  ANumber m_aVertexVolume;
  aVertexNumber m_acVertexVolume;
    
  // grid function
  SmartPtr<TGridFunction> m_uInfo;
  
  std::vector<WallObject<TGridFunction> > m_walls;
  
  using base_type::assignVal;
  using base_type::copyWallData;
};
class ElementBoxFilter {…};
  
} // end namespace NavierStokes
} // end namespace ug
 
#include "filter_impl.h"
 
#endif /* __H__UG__LIB_DISC__NAVIER_STOKES__INCOMPRESSIBLE__FILTER__ */