hfv1_geom.h

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/*
 * Copyright (c) 2010-2015:  G-CSC, Goethe University Frankfurt
 * Author: Andreas Vogel
 * 
 * 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__LIB_DISC__SPATIAL_DISC__DISC_HELPER__HANGING_FINITE_VOLUME_GEOMETRY__
#define __H__UG__LIB_DISC__SPATIAL_DISC__DISC_HELPER__HANGING_FINITE_VOLUME_GEOMETRY__
 
// extern libraries
#include <cmath>
#include <vector>
 
// other ug4 modules
#include "common/common.h"
 
// library intern includes
#include "lib_disc/reference_element/reference_element.h"
#include "lib_disc/local_finite_element/local_finite_element_provider.h"
#include "fv_util.h"
#include "fv1_geom.h"
 
namespace ug{
 
// Hanging node FV1 Geometry for Reference Element Type
 
 
template <  typename TElem, int TWorldDim>
class HFV1Geometry : public FVGeometryBase{
  private:
    typedef typename reference_element_traits<TElem>::reference_element_type ref_elem_type;
 
    static const size_t m_numNaturalSCV = ref_elem_type::numCorners;
 
    static const size_t m_numNaturalSCVF = ref_elem_type::numEdges;
 
  public:
    static const int dim = ref_elem_type::dim;
 
    static const int worldDim = TWorldDim;
 
    static const bool usesHangingNodes = true;
 
    static const bool staticLocalData = true;
 
  protected:
    struct MidID
    {
        MidID() : dim(0), id(0) {};
        MidID(size_t dim_, size_t id_) : dim(dim_), id(id_) {};
        size_t dim;
        size_t id;
    };
    struct MidID {…};
 
  public:
    class SCVF
    {
      public:
        static const int dim = ref_elem_type::dim;
 
        static const int worldDim = TWorldDim;
 
      private:
        friend class HFV1Geometry<TElem, TWorldDim>;
 
        static const size_t m_numIP = 1;
 
        static const size_t m_numCorners = hfv1_traits<ref_elem_type, TWorldDim>::NumCornersOfSCVF;
 
      public:
        SCVF() {};
 
        inline size_t from() const {return m_from;}
 
        inline size_t to() const {return m_to;}
 
        inline size_t num_ip() const {return m_numIP;}
 
        inline const MathVector<dim>& local_ip() const {return localIP;}
 
        inline const MathVector<worldDim>& global_ip() const {return globalIP;}
 
        inline const MathVector<worldDim>& normal() const {return Normal;} // includes area
 
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        inline size_t num_sh() const {return vShape.size();}
 
        inline number shape(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid ip index"); return vShape[sh];}
        inline number shape(size_t sh) const {…}
 
        inline const MathVector<dim>& local_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid ip index"); return localGrad[sh];}
        inline const MathVector<dim>& local_grad(size_t sh) const {…}
 
        inline const MathVector<dim>* local_grad_vector() const {return &localGrad[0];}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid ip index"); return globalGrad[sh];}
        inline const MathVector<worldDim>& global_grad(size_t sh) const {…}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return &globalGrad[0];}
 
        inline size_t num_corners() const {return m_numCorners;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vLocPos[co];}
        inline const MathVector<dim>& local_corner(size_t co) const {…}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vGloPos[co];}
        inline const MathVector<worldDim>& global_corner(size_t co) const {…}
 
      private:
        // This scvf separates the scv with the ids given in "from" and "to"
        // The computed normal points in direction from->to
        size_t m_from, m_to;
 
        // ordering is:
        // 2D: edgeMidPoint, CenterOfElement
        // 3D: edgeMidPoint, Side one, CenterOfElement, Side two
        MathVector<dim> m_vLocPos[m_numCorners]; // local corners of scvf
        MathVector<worldDim> m_vGloPos[m_numCorners]; // global corners of scvf
        MidID m_midId[m_numCorners]; // dimension and id of object, that's midpoint bounds the scvf
 
        // scvf part
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global intergration point
        MathVector<worldDim> Normal; // normal (incl. area)
 
        // shapes and derivatives
        std::vector<number> vShape; // shapes at ip
        std::vector<MathVector<dim> > localGrad; // local grad at ip
        std::vector<MathVector<worldDim> > globalGrad; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
    class SCVF {…};
 
    class SCV
    {
      private:
      //  let outer class access private members
        friend class HFV1Geometry<TElem, TWorldDim>;
 
        static const size_t m_numIP = 1;
 
        static const size_t m_maxNumCorners = hfv1_traits<ref_elem_type, TWorldDim>::MaxNumCornersOfSCV;
 
        typedef typename hfv1_traits<ref_elem_type, TWorldDim>::scv_type scv_type;
 
      public:
        SCV() : m_numCorners(m_maxNumCorners) {};
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return m_numIP;}
 
        inline const MathVector<dim>& local_ip() const {return m_vLocPos[0];}
 
        inline const MathVector<worldDim>& global_ip() const {return m_vGloPos[0];}
 
        inline number volume() const {return vol;}
 
        inline size_t num_corners() const {return m_numCorners;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vLocPos[co];}
        inline const MathVector<dim>& local_corner(size_t co) const {…}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vGloPos[co];}
        inline const MathVector<worldDim>& global_corner(size_t co) const {…}
 
      private:
        size_t nodeId; // node id of associated node
        size_t m_numCorners;
 
        // The ordering is: Corner, ...
        MathVector<dim> m_vLocPos[m_maxNumCorners]; // local position of node
        MathVector<worldDim> m_vGloPos[m_maxNumCorners]; // global position of node
        MidID m_midId[m_maxNumCorners]; // dimension and id of object, that's midpoint bounds the scv
        number vol;
    };
    class SCV {…};
 
 
  public:
    HFV1Geometry();
 
    void update(GridObject* pElem, const MathVector<worldDim>* vCornerCoords,
                       const ISubsetHandler* ish = NULL);
 
  //  debug output
    void print();
 
    GridObject* elem() const {return m_pElem;}
 
  public:
    inline size_t num_scvf() const {return m_vSCVF.size();}
 
    inline const SCVF& scvf(size_t i) const
      {UG_ASSERT(i < num_scvf(), "Invalid Index."); return m_vSCVF[i];}
    inline const SCVF& scvf(size_t i) const {…}
 
    size_t num_scv() const {return m_vSCV.size();}
 
    inline const SCV& scv(size_t i) const
      {UG_ASSERT(i < num_scv(), "Invalid Index."); return m_vSCV[i];}
    inline const SCV& scv(size_t i) const {…}
 
    inline size_t num_sh() const
    {
      return m_numSh;
    };
    inline size_t num_sh() const {…}
 
  public:
    size_t num_scvf_ips() const {return m_vGlobSCVFIP.size();}
 
    const MathVector<worldDim>* scvf_global_ips() const {return &m_vGlobSCVFIP[0];}
 
    const MathVector<dim>* scvf_local_ips() const {return &m_vLocSCVFIP[0];}
 
    size_t num_scv_ips() const {return m_vGlobSCVIP.size();}
 
    const MathVector<worldDim>* scv_global_ips() const {return &m_vGlobSCVIP[0];}
 
    const MathVector<dim>* scv_local_ips() const {return &m_vLocSCVIP[0];}
 
    const MathVector<dim>& local_node_position(size_t nodeID) const
    {
      UG_ASSERT(nodeID < m_locMid[0].size(), "Invalid node id.");
      return m_locMid[0][nodeID];
    }
    const MathVector<dim>& local_node_position(size_t nodeID) const {…}
 
    const MathVector<worldDim>& global_node_position(size_t nodeID) const
    {
      UG_ASSERT(nodeID < m_gloMid[0].size(), "Invalid node id.");
      return m_gloMid[0][nodeID];
    }
    const MathVector<worldDim>& global_node_position(size_t nodeID) const {…}
 
  protected:
    std::vector<MathVector<worldDim> > m_vGlobSCVFIP;
    std::vector<MathVector<dim> > m_vLocSCVFIP;
    std::vector<MathVector<worldDim> > m_vGlobSCVIP;
    std::vector<MathVector<dim> > m_vLocSCVIP;
 
  protected:
    void copy_local_corners(SCVF& scvf)
    {
      for(size_t i = 0; i < scvf.num_corners(); ++i)
      {
        const size_t dim = scvf.m_midId[i].dim;
        const size_t id = scvf.m_midId[i].id;
        scvf.m_vLocPos[i] = m_locMid[dim][id];
      }
    }
    void copy_local_corners(SCVF& scvf) {…}
 
    void copy_global_corners(SCVF& scvf)
    {
      for(size_t i = 0; i < scvf.num_corners(); ++i)
      {
        const size_t dim = scvf.m_midId[i].dim;
        const size_t id = scvf.m_midId[i].id;
        scvf.m_vGloPos[i] = m_gloMid[dim][id];
      }
    }
    void copy_global_corners(SCVF& scvf) {…}
 
    void copy_local_corners(SCV& scv)
    {
      for(size_t i = 0; i < scv.num_corners(); ++i)
      {
        const size_t dim_ = scv.m_midId[i].dim;
        const size_t id = scv.m_midId[i].id;
        UG_ASSERT(dim_ <= (size_t)dim, "Dimension wrong");
        UG_ASSERT(id < m_locMid[dim_].size(), "id " << id << " in dim="
                  <<dim_<<" wrong. (size is "<< m_locMid[dim_].size()<<")\n");
        scv.m_vLocPos[i] = m_locMid[dim_][id];
      }
    }
    void copy_local_corners(SCV& scv) {…}
 
    void copy_global_corners(SCV& scv)
    {
      for(size_t i = 0; i < scv.num_corners(); ++i)
      {
        const size_t dim_ = scv.m_midId[i].dim;
        const size_t id = scv.m_midId[i].id;
        UG_ASSERT(dim_ <= (size_t)dim, "Dimension wrong");
        UG_ASSERT(id < m_gloMid[dim_].size(), "id " << id << " in dim="
                  <<dim_<<" wrong. (size is "<< m_gloMid[dim_].size()<<")\n");
        scv.m_vGloPos[i] = m_gloMid[dim_][id];
      }
    }
    void copy_global_corners(SCV& scv) {…}
 
    // i = number of side
    void compute_side_midpoints(size_t i,
                                MathVector<dim>& locSideMid,
                                MathVector<worldDim>& gloSideMid)
    {
      if(dim>1)
      {
        const size_t coID0 = m_rRefElem.id(2, i, 0, 0);
        locSideMid = m_locMid[0][coID0];
        gloSideMid = m_gloMid[0][coID0];
 
        // add corner coordinates of the corners of the geometric object
        for(size_t j = 1; j < m_rRefElem.num(2, i, 0); ++j)
        {
          const size_t coID = m_rRefElem.id(2, i, 0, j);
          locSideMid += m_locMid[0][coID];
          gloSideMid += m_gloMid[0][coID];
        }
 
        // scale for correct averaging
        locSideMid *= 1./(m_rRefElem.num(2, i, 0));
        gloSideMid *= 1./(m_rRefElem.num(2, i, 0));
      }
    }
    void compute_side_midpoints(size_t i, {…}
 
    // i, j, k, l = number nodes
    void compute_side_midpoints(size_t i, size_t j, size_t k, size_t l,
                  MathVector<dim>& locSideMid,
                  MathVector<worldDim>& gloSideMid)
    {
      VecAdd(locSideMid, m_locMid[0][i], m_locMid[0][j], m_locMid[0][k], m_locMid[0][l]);
      VecAdd(gloSideMid, m_gloMid[0][i], m_gloMid[0][j], m_gloMid[0][k], m_gloMid[0][l]);
 
      // scale for correct averaging
      locSideMid *= 0.25;
      gloSideMid *= 0.25;
    }
    void compute_side_midpoints(size_t i, size_t j, size_t k, size_t l, {…}
 
    // i, j, k = number nodes
    void compute_side_midpoints(size_t i, size_t j, size_t k,
                  MathVector<dim>& locSideMid, MathVector<worldDim>& gloSideMid)
    {
      VecAdd(locSideMid, m_locMid[0][i], m_locMid[0][j], m_locMid[0][k]);
      VecAdd(gloSideMid, m_gloMid[0][i], m_gloMid[0][j], m_gloMid[0][k]);
 
      // scale for correct averaging
      locSideMid *= 1./3.;
      gloSideMid *= 1./3.;
    }
    void compute_side_midpoints(size_t i, size_t j, size_t k, {…}
 
    // returns edgeID of child edge, that has corner co. i is the natural edge index
    size_t get_child_edge_of_corner(size_t i, size_t co)
        {
          for(size_t e = 0; e < m_vNatEdgeInfo[i].num_child_edges(); ++e)
          {
            const size_t childId = m_vNatEdgeInfo[i].child_edge(e);
            if(m_vNewEdgeInfo[childId].from() == co)
              return childId;
            if(m_vNewEdgeInfo[childId].to() == co)
              return childId;
          }
          return -1;
        }
    size_t get_child_edge_of_corner(size_t i, size_t co) {…}
 
  private:
    struct NewEdgeInfo
    {
      friend class HFV1Geometry<TElem, TWorldDim>;
    public:
      NewEdgeInfo() : m_from(-1), m_to(-1){}
            size_t from() const {return m_from;}
            size_t to() const {return m_to;}
    private:
      size_t m_from;
      size_t m_to;
    };
    struct NewEdgeInfo {…};
 
        struct NatEdgeInfo
        {
                friend class HFV1Geometry<TElem, TWorldDim>;
            public:
              NatEdgeInfo() : nodeId(-1), numChildEdges(0) {for(size_t i=0; i<2; ++i) childEdge[i] = -1;}
                bool is_hanging() const {return numChildEdges == 2;}
                size_t node_id() const {UG_ASSERT(is_hanging(), "Should only be called, if edge is hanging."); return nodeId;}
                size_t num_child_edges() const {return numChildEdges;}
                size_t child_edge(size_t i) const {UG_ASSERT(i < num_child_edges(), "Wrong id."); return childEdge[i];}
 
            private:
                size_t nodeId;
                size_t numChildEdges;
                size_t childEdge[2];
        };
        struct NatEdgeInfo {…};
 
    //  help array: maps NaturalEdge -> NodeOnEdge (-1 if no node on edge)
        std::vector<NatEdgeInfo> m_vNatEdgeInfo;
        std::vector<NewEdgeInfo> m_vNewEdgeInfo;
 
  private:
  //  pointer to current element
    GridObject* m_pElem;
 
    std::vector<MathVector<dim> > m_locMid[dim+1];
    std::vector<MathVector<worldDim> > m_gloMid[dim+1];
 
  //  SubControlVolumeFaces
    std::vector<SCVF> m_vSCVF;
 
  //  SubControlVolumes
    std::vector<SCV> m_vSCV;
 
  //  number of shape functions
    size_t m_numSh;
 
  //  Reference Mapping
    ReferenceMapping<ref_elem_type, worldDim> m_rMapping;
 
  //  Reference Element
    const ref_elem_type& m_rRefElem;
};
class HFV1Geometry : public FVGeometryBase {…};
 
template <  int TDim, int TWorldDim = TDim>
class DimHFV1Geometry : public FVGeometryBase{
  private:
    size_t m_numNaturalSCV;
 
    size_t m_numNaturalSCVF;
    
    static const size_t m_maxNSH = fv1_dim_traits<TDim, TWorldDim>::maxNSH;
 
  public:
    static const int dim = TDim;
 
    static const int worldDim = TWorldDim;
 
    static const bool usesHangingNodes = true;
 
    static const bool staticLocalData = true;
    
    typedef hdimfv1_traits<TDim> traits;
    
    typedef typename traits::elem_type_0 elem_type_0;
    typedef typename traits::elem_type_1 elem_type_1;
    typedef typename traits::elem_type_2 elem_type_2;
    typedef typename traits::elem_type_3 elem_type_3;
    typedef typename traits::elem_type_4 elem_type_4;
 
  protected:
    struct MidID
    {
        MidID() : dim(0), id(0) {};
        MidID(size_t dim_, size_t id_) : dim(dim_), id(id_) {};
        size_t dim;
        size_t id;
    };
    struct MidID {…};
 
  public:
    class SCVF
    {
      public:
        static const int dim = TDim;
 
        static const int worldDim = TWorldDim;
 
      private:
        friend class DimHFV1Geometry<TDim, TWorldDim>;
 
        static const size_t m_numIP = 1;
 
        static const size_t m_numCorners = traits::NumCornersOfSCVF;
 
      public:
        SCVF() {};
 
        inline size_t from() const {return m_from;}
 
        inline size_t to() const {return m_to;}
 
        inline size_t num_ip() const {return m_numIP;}
 
        inline const MathVector<dim>& local_ip() const {return localIP;}
 
        inline const MathVector<worldDim>& global_ip() const {return globalIP;}
 
        inline const MathVector<worldDim>& normal() const {return Normal;} // includes area
 
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        inline size_t num_sh() const {return vShape.size();}
 
        inline number shape(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid ip index"); return vShape[sh];}
        inline number shape(size_t sh) const {…}
 
        inline const MathVector<dim>& local_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid ip index"); return localGrad[sh];}
        inline const MathVector<dim>& local_grad(size_t sh) const {…}
 
        inline const MathVector<dim>* local_grad_vector() const {return &localGrad[0];}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid ip index"); return globalGrad[sh];}
        inline const MathVector<worldDim>& global_grad(size_t sh) const {…}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return &globalGrad[0];}
 
        inline size_t num_corners() const {return m_numCorners;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vLocPos[co];}
        inline const MathVector<dim>& local_corner(size_t co) const {…}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vGloPos[co];}
        inline const MathVector<worldDim>& global_corner(size_t co) const {…}
 
      private:
        // This scvf separates the scv with the ids given in "from" and "to"
        // The computed normal points in direction from->to
        size_t m_from, m_to;
 
        // ordering is:
        // 2D: edgeMidPoint, CenterOfElement
        // 3D: edgeMidPoint, Side one, CenterOfElement, Side two
        MathVector<dim> m_vLocPos[m_numCorners]; // local corners of scvf
        MathVector<worldDim> m_vGloPos[m_numCorners]; // global corners of scvf
        MidID m_midId[m_numCorners]; // dimension and id of object, that's midpoint bounds the scvf
 
        // scvf part
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global intergration point
        MathVector<worldDim> Normal; // normal (incl. area)
 
        // shapes and derivatives
        std::vector<number> vShape; // shapes at ip
        std::vector<MathVector<dim> > localGrad; // local grad at ip
        std::vector<MathVector<worldDim> > globalGrad; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
    class SCVF {…};
 
    class SCV
    {
      private:
      //  let outer class access private members
        friend class DimHFV1Geometry<TDim, TWorldDim>;
 
        static const size_t m_numIP = 1;
 
        static const size_t m_maxNumCorners = traits::MaxNumCornersOfSCV;
 
        typedef typename traits::scv_type scv_type;
 
      public:
        SCV() : m_numCorners(m_maxNumCorners) {};
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return m_numIP;}
 
        inline const MathVector<dim>& local_ip() const {return m_vLocPos[0];}
 
        inline const MathVector<worldDim>& global_ip() const {return m_vGloPos[0];}
 
        inline number volume() const {return vol;}
 
        inline size_t num_corners() const {return m_numCorners;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vLocPos[co];}
        inline const MathVector<dim>& local_corner(size_t co) const {…}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid corner index."); return m_vGloPos[co];}
        inline const MathVector<worldDim>& global_corner(size_t co) const {…}
          
        inline size_t num_sh() const {return numSH;}
 
        inline number shape(size_t sh) const {return vShape[sh];}
 
        inline const number* shape_vector() const {return vShape;}
 
        inline const MathVector<dim>& local_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return localGrad[sh];}
        inline const MathVector<dim>& local_grad(size_t sh) const {…}
 
        inline const MathVector<dim>* local_grad_vector() const {return localGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return globalGrad[sh];}
        inline const MathVector<worldDim>& global_grad(size_t sh) const {…}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return globalGrad;}
        
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
      private:
        size_t nodeId; // node id of associated node
        size_t m_numCorners;
 
      // The ordering is: Corner, ...
        MathVector<dim> m_vLocPos[m_maxNumCorners]; // local position of node
        MathVector<worldDim> m_vGloPos[m_maxNumCorners]; // global position of node
        MidID m_midId[m_maxNumCorners]; // dimension and id of object, that's midpoint bounds the scv
        number vol;
        
      // shapes and derivatives
        size_t numSH;
        number vShape[m_maxNSH]; // shapes at ip
        MathVector<dim> localGrad[m_maxNSH]; // local grad at ip
        MathVector<worldDim> globalGrad[m_maxNSH]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
    class SCV {…};
 
 
  public:
    DimHFV1Geometry() : m_pElem(NULL), m_roid(ROID_UNKNOWN) {};
    
    void update_local_data();
 
    void update(GridObject* pElem, const MathVector<worldDim>* vCornerCoords,
                       const ISubsetHandler* ish = NULL);
 
  //  debug output
  //  void print();
 
  public:
    inline size_t num_scvf() const {return m_vSCVF.size();}
 
    inline const SCVF& scvf(size_t i) const
      {UG_ASSERT(i < num_scvf(), "Invalid Index."); return m_vSCVF[i];}
    inline const SCVF& scvf(size_t i) const {…}
 
    size_t num_scv() const {return m_vSCV.size();}
 
    inline const SCV& scv(size_t i) const
      {UG_ASSERT(i < num_scv(), "Invalid Index."); return m_vSCV[i];}
    inline const SCV& scv(size_t i) const {…}
 
    inline size_t num_sh() const
    {
      return m_numSh;
    };
    inline size_t num_sh() const {…}
 
  public:
    size_t num_scvf_ips() const {return m_vGlobSCVFIP.size();}
 
    const MathVector<worldDim>* scvf_global_ips() const {return &m_vGlobSCVFIP[0];}
 
    const MathVector<dim>* scvf_local_ips() const {return &m_vLocSCVFIP[0];}
 
    size_t num_scv_ips() const {return m_vGlobSCVIP.size();}
 
    const MathVector<worldDim>* scv_global_ips() const {return &m_vGlobSCVIP[0];}
 
    const MathVector<dim>* scv_local_ips() const {return &m_vLocSCVIP[0];}
 
  protected:
    std::vector<MathVector<worldDim> > m_vGlobSCVFIP;
    std::vector<MathVector<dim> > m_vLocSCVFIP;
    std::vector<MathVector<worldDim> > m_vGlobSCVIP;
    std::vector<MathVector<dim> > m_vLocSCVIP;
 
  protected:
    void copy_local_corners(SCVF& scvf)
    {
      for(size_t i = 0; i < scvf.num_corners(); ++i)
      {
        const size_t dim = scvf.m_midId[i].dim;
        const size_t id = scvf.m_midId[i].id;
        scvf.m_vLocPos[i] = m_locMid[dim][id];
      }
    }
    void copy_local_corners(SCVF& scvf) {…}
 
    void copy_global_corners(SCVF& scvf)
    {
      for(size_t i = 0; i < scvf.num_corners(); ++i)
      {
        const size_t dim = scvf.m_midId[i].dim;
        const size_t id = scvf.m_midId[i].id;
        scvf.m_vGloPos[i] = m_gloMid[dim][id];
      }
    }
    void copy_global_corners(SCVF& scvf) {…}
 
    void copy_local_corners(SCV& scv)
    {
      for(size_t i = 0; i < scv.num_corners(); ++i)
      {
        const size_t dim_ = scv.m_midId[i].dim;
        const size_t id = scv.m_midId[i].id;
        UG_ASSERT(dim_ <= (size_t)dim, "Dimension wrong");
        UG_ASSERT(id < m_locMid[dim_].size(), "id " << id << " in dim="
                  <<dim_<<" wrong. (size is "<< m_locMid[dim_].size()<<")\n");
        scv.m_vLocPos[i] = m_locMid[dim_][id];
      }
    }
    void copy_local_corners(SCV& scv) {…}
 
    void copy_global_corners(SCV& scv)
    {
      for(size_t i = 0; i < scv.num_corners(); ++i)
      {
        const size_t dim_ = scv.m_midId[i].dim;
        const size_t id = scv.m_midId[i].id;
        UG_ASSERT(dim_ <= (size_t)dim, "Dimension wrong");
        UG_ASSERT(id < m_gloMid[dim_].size(), "id " << id << " in dim="
                  <<dim_<<" wrong. (size is "<< m_gloMid[dim_].size()<<")\n");
        scv.m_vGloPos[i] = m_gloMid[dim_][id];
      }
    }
    void copy_global_corners(SCV& scv) {…}
 
    // i = number of side
    void compute_side_midpoints(size_t i,
                                MathVector<dim>& locSideMid,
                                MathVector<worldDim>& gloSideMid)
    {
      if(dim>1)
      {
        const size_t coID0 = m_rRefElem.id(2, i, 0, 0);
        locSideMid = m_locMid[0][coID0];
        gloSideMid = m_gloMid[0][coID0];
 
        // add corner coordinates of the corners of the geometric object
        for(size_t j = 1; j < m_rRefElem.num(2, i, 0); ++j)
        {
          const size_t coID = m_rRefElem.id(2, i, 0, j);
          locSideMid += m_locMid[0][coID];
          gloSideMid += m_gloMid[0][coID];
        }
 
        // scale for correct averaging
        locSideMid *= 1./(m_rRefElem.num(2, i, 0));
        gloSideMid *= 1./(m_rRefElem.num(2, i, 0));
      }
    }
    void compute_side_midpoints(size_t i, {…}
 
    // i, j, k, l = number nodes
    void compute_side_midpoints(size_t i, size_t j, size_t k, size_t l,
                  MathVector<dim>& locSideMid,
                  MathVector<worldDim>& gloSideMid)
    {
      VecAdd(locSideMid, m_locMid[0][i], m_locMid[0][j], m_locMid[0][k], m_locMid[0][l]);
      VecAdd(gloSideMid, m_gloMid[0][i], m_gloMid[0][j], m_gloMid[0][k], m_gloMid[0][l]);
 
      // scale for correct averaging
      locSideMid *= 0.25;
      gloSideMid *= 0.25;
    }
    void compute_side_midpoints(size_t i, size_t j, size_t k, size_t l, {…}
 
    // i, j, k = number nodes
    void compute_side_midpoints(size_t i, size_t j, size_t k,
                  MathVector<dim>& locSideMid, MathVector<worldDim>& gloSideMid)
    {
      VecAdd(locSideMid, m_locMid[0][i], m_locMid[0][j], m_locMid[0][k]);
      VecAdd(gloSideMid, m_gloMid[0][i], m_gloMid[0][j], m_gloMid[0][k]);
 
      // scale for correct averaging
      locSideMid *= 1./3.;
      gloSideMid *= 1./3.;
    }
    void compute_side_midpoints(size_t i, size_t j, size_t k, {…}
 
    // returns edgeID of child edge, that has corner co. i is the natural edge index
    size_t get_child_edge_of_corner(size_t i, size_t co)
        {
          for(size_t e = 0; e < m_vNatEdgeInfo[i].num_child_edges(); ++e)
          {
            const size_t childId = m_vNatEdgeInfo[i].child_edge(e);
            if(m_vNewEdgeInfo[childId].from() == co)
              return childId;
            if(m_vNewEdgeInfo[childId].to() == co)
              return childId;
          }
          return -1;
        }
    size_t get_child_edge_of_corner(size_t i, size_t co) {…}
 
  private:
    struct NewEdgeInfo
    {
      friend class DimHFV1Geometry<TDim, TWorldDim>;
    public:
      NewEdgeInfo() : m_from(-1), m_to(-1){}
            size_t from() const {return m_from;}
            size_t to() const {return m_to;}
    private:
      size_t m_from;
      size_t m_to;
    };
    struct NewEdgeInfo {…};
 
        struct NatEdgeInfo
        {
                friend class DimHFV1Geometry<TDim, TWorldDim>;
            public:
              NatEdgeInfo() : nodeId(-1), numChildEdges(0) {for(size_t i=0; i<2; ++i) childEdge[i] = -1;}
                bool is_hanging() const {return numChildEdges == 2;}
                size_t node_id() const {UG_ASSERT(is_hanging(), "Should only be called, if edge is hanging."); return nodeId;}
                size_t num_child_edges() const {return numChildEdges;}
                size_t child_edge(size_t i) const {UG_ASSERT(i < num_child_edges(), "Wrong id."); return childEdge[i];}
 
            private:
                size_t nodeId;
                size_t numChildEdges;
                size_t childEdge[2];
        };
        struct NatEdgeInfo {…};
 
    //  help array: maps NaturalEdge -> NodeOnEdge (-1 if no node on edge)
        std::vector<NatEdgeInfo> m_vNatEdgeInfo;
        std::vector<NewEdgeInfo> m_vNewEdgeInfo;
 
  private:
    GridObject* m_pElem;
    
    ReferenceObjectID m_roid;
 
    std::vector<MathVector<dim> > m_locMid[dim+1];
    std::vector<MathVector<worldDim> > m_gloMid[dim+1];
 
  //  SubControlVolumeFaces
    std::vector<SCVF> m_vSCVF;
 
  //  SubControlVolumes
    std::vector<SCV> m_vSCV;
 
  //  number of shape functions
    size_t m_numSh;
 
    DimReferenceElement<dim> m_rRefElem;
 
    DimReferenceMapping<dim, worldDim>* m_rMapping;
    
};
class DimHFV1Geometry : public FVGeometryBase {…};
 
 
// Hanging FV1 Manifold Geometry
 
template <typename TElem, int TWorldDim>
class HFV1ManifoldGeometry
{
  public:
  //  type of element
    typedef TElem elem_type;
 
  //  type of reference element
    typedef typename reference_element_traits<TElem>::reference_element_type ref_elem_type;
 
  public:
  //  order
    static const int order = 1;
 
  // number of natural bfs (eq. of SCV)
    static const size_t m_numNaturalBF = ref_elem_type::numCorners;
 
  // number of natural boundary face sides (eq. of SCVF)
    static const size_t m_numNaturalBFS = ref_elem_type::numEdges;
 
  //  dimension of reference element
    static const int dim = ref_elem_type::dim;
 
  //  dimension of world
    static const int worldDim = TWorldDim;
 
  //  type of BoundaryFaces
    typedef typename hfv1_traits<ref_elem_type, dim>::scv_type bf_type;
 
  //  Hanging node flag: this geometry supports hanging nodes
    static const bool usesHangingNodes = true;
 
    static const bool staticLocalData = true;
 
  protected:
    struct MidID
    {
        MidID() : dim(0), id(0) {};
        MidID(size_t dim_, size_t id_) : dim(dim_), id(id_) {};
        size_t dim;
        size_t id;
    };
    struct MidID {…};
 
  public:
    class BF
    {
      private:
      //  let outer class access private members
        friend class HFV1ManifoldGeometry<TElem, TWorldDim>;
 
      //  number of integration points
        static const size_t m_numIP = 1;
 
      //  max number of corners of bf
        static const size_t numCorners = hfv1_traits<ref_elem_type, dim>::MaxNumCornersOfSCV;
 
      public:
        BF() {};
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return m_numIP;}
 
        inline const MathVector<dim>& local_ip() const //{return localIP;}
        {return m_vLocPos[0];}  // <-- always the vertex
        inline const MathVector<dim>& local_ip() const //{return localIP;} {…}
 
        inline const MathVector<worldDim>& global_ip() const //{return globalIP;}
        {return m_vGloPos[0];}  // <-- here too
        inline const MathVector<worldDim>& global_ip() const //{return globalIP;} {…}
 
        inline number volume() const {return vol;}
 
        inline size_t num_corners() const {return numCorners;}
 
        inline const MathVector<dim>& local_corner(size_t i) const
          {UG_ASSERT(i < num_corners(), "Invalid index."); return m_vLocPos[i];}
        inline const MathVector<dim>& local_corner(size_t i) const {…}
 
        inline const MathVector<worldDim>& global_corner(size_t i) const
          {UG_ASSERT(i < num_corners(), "Invalid index."); return m_vGloPos[i];}
        inline const MathVector<worldDim>& global_corner(size_t i) const {…}
 
        inline size_t num_sh() const {return vShape.size();}
 
        inline number shape(size_t i, size_t ip) const
          {UG_ASSERT(ip < num_ip(), "Invalid index"); return vShape[i];}
        inline number shape(size_t i, size_t ip) const {…}
 
      private:
        size_t nodeId;                    // id of associated node
 
        // CORNERS: ordering is:
        // 1D: corner, centerOfElement
        // 2D: corner, side one, centerOfElement, side two
        MathVector<dim> m_vLocPos[numCorners];      // local position of node
        MathVector<worldDim> m_vGloPos[numCorners]; // global position of node
 
        //IPs & shapes
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global integration point
        std::vector<number> vShape; // shapes at ip
 
        number vol;
    };
    class BF {…};
 
  protected:
    std::vector<MathVector<dim> > m_vLocBFIP;
    std::vector<MathVector<worldDim> > m_vGlobBFIP;
 
  public:
    HFV1ManifoldGeometry();
 
    void update(GridObject* elem, const MathVector<worldDim>* vCornerCoords,
                const ISubsetHandler* ish = NULL);
 
    void print();
/*
    const MathVector<worldDim>* corners() const {return m_gloMid[0];}
*/
    inline size_t num_bf() const {return m_vBF.size();}
 
    inline const BF& bf(size_t i) const
      {UG_ASSERT(i < num_bf(), "Invalid Index."); return m_vBF[i];}
    inline const BF& bf(size_t i) const {…}
 
    const MathVector<worldDim>* bf_global_ips() const {return &m_vGlobBFIP[0];}
 
    size_t num_bf_global_ips() const {return m_vGlobBFIP.size();}
 
    const MathVector<dim>* bf_local_ips() const {return &m_vLocBFIP[0];}
 
    size_t num_bf_local_ips() const {return m_vLocBFIP.size();}
 
  protected:
    void compute_side_midpoints(MathVector<dim>& locSideMid,
                   MathVector<worldDim>& gloSideMid)
    {
      locSideMid = m_locMid[0][0];
      gloSideMid = m_gloMid[0][0];
 
      // add corner coordinates of the corners of the geometric object
      for (size_t j = 1; j < m_numNaturalBF; ++j)
      {
        locSideMid += m_locMid[0][j];
        gloSideMid += m_gloMid[0][j];
      }
 
      // scale for correct averaging
      locSideMid /= m_numNaturalBF;
      gloSideMid /= m_numNaturalBF;
    }
    void compute_side_midpoints(MathVector<dim>& locSideMid, {…}
 
    // i, j, k, l = number nodes
    void compute_side_midpoints(size_t i, size_t j, size_t k, size_t l,
                  MathVector<dim>& locSideMid,
                  MathVector<worldDim>& gloSideMid)
    {
      VecAdd(locSideMid, m_locMid[0][i], m_locMid[0][j], m_locMid[0][k], m_locMid[0][l]);
      VecAdd(gloSideMid, m_gloMid[0][i], m_gloMid[0][j], m_gloMid[0][k], m_gloMid[0][l]);
 
      // scale for correct averaging
      locSideMid *= 0.25;
      gloSideMid *= 0.25;
    }
    void compute_side_midpoints(size_t i, size_t j, size_t k, size_t l, {…}
 
    // i, j, k = number nodes
    void compute_side_midpoints(size_t i, size_t j, size_t k,
                  MathVector<dim>& locSideMid, MathVector<worldDim>& gloSideMid)
    {
      VecAdd(locSideMid, m_locMid[0][i], m_locMid[0][j], m_locMid[0][k]);
      VecAdd(gloSideMid, m_gloMid[0][i], m_gloMid[0][j], m_gloMid[0][k]);
 
      // scale for correct averaging
      locSideMid *= 1./3.;
      gloSideMid *= 1./3.;
    }
    void compute_side_midpoints(size_t i, size_t j, size_t k, {…}
 
  private:
    struct NewEdgeInfo
    {
      friend class HFV1ManifoldGeometry<TElem, TWorldDim>;
 
      public:
        NewEdgeInfo() : m_from(-1), m_to(-1){}
        size_t from() const {return m_from;}
        size_t to() const {return m_to;}
      private:
        size_t m_from;
        size_t m_to;
    };
    struct NewEdgeInfo {…};
 
    struct NatEdgeInfo
    {
      friend class HFV1ManifoldGeometry<TElem, TWorldDim>;
      public:
        NatEdgeInfo() : nodeId(-1), numChildEdges(0) {for(size_t i=0; i<2; ++i) childEdge[i] = -1;}
        bool is_hanging() const {return numChildEdges == 2;}
        size_t node_id() const {UG_ASSERT(is_hanging(), "Should only be called, if edge is hanging."); return nodeId;}
        size_t num_child_edges() const {return numChildEdges;}
        size_t child_edge(size_t i) const {UG_ASSERT(i < num_child_edges(), "Wrong id."); return childEdge[i];}
 
      private:
        size_t nodeId;
        size_t numChildEdges;
        size_t childEdge[2];
    };
    struct NatEdgeInfo {…};
 
  //  help array: maps NaturalEdge -> NodeOnEdge (-1 if no node on edge)
    std::vector<NatEdgeInfo> m_vNatEdgeInfo;
    std::vector<NewEdgeInfo> m_vNewEdgeInfo;
 
  private:
  //  pointer to current element
    GridObject* m_pElem;
 
  //  local and global geom object midpoints for each dimension
    std::vector<MathVector<dim> > m_locMid[dim+1];
    std::vector<MathVector<worldDim> > m_gloMid[dim+1];
 
  //  BndFaces
    std::vector<BF> m_vBF;
 
  //  Reference Mapping
    ReferenceMapping<ref_elem_type, worldDim> m_rMapping;
 
  //  Reference Element
    const ref_elem_type& m_rRefElem;
};
class HFV1ManifoldGeometry {…};
 
 
}
 
#endif /* __H__UG__LIB_DISC__SPATIAL_DISC__DISC_HELPER__HANGING_FINITE_VOLUME_GEOMETRY__ */