fv1_geom.h

Go to the documentation of this file.

/*
 * 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__FV1_GEOMETRY__
#define __H__UG__LIB_DISC__SPATIAL_DISC__DISC_HELPER__FV1_GEOMETRY__
 
// extern libraries
#include <cmath>
#include <map>
#include <vector>
 
// other ug4 modules
#include "common/common.h"
 
// library intern includes
#include "lib_grid/tools/subset_handler_interface.h"
#include "lib_disc/reference_element/reference_element.h"
#include "lib_disc/reference_element/reference_element_traits.h"
#include "lib_disc/reference_element/reference_mapping.h"
#include "lib_disc/reference_element/reference_mapping_provider.h"
#include "lib_disc/local_finite_element/local_finite_element_provider.h"
#include "lib_disc/local_finite_element/lagrange/lagrangep1.h"
#include "lib_disc/quadrature/gauss/gauss_quad.h"
#include "fv_util.h"
#include "fv_geom_base.h"
 
namespace ug{
 
// FV1 Geometry for Reference Element Type
 
// forward declaration
template <  typename TElem, int TWorldDim, bool TCondensed> class FV1Geometry_gen;
 
 
template <typename TElem, int TWorldDim>
class FV1Geometry : public FV1Geometry_gen<TElem, TWorldDim, false> {};
 
 
template <typename TElem, int TWorldDim>
class FV1CondensedGeometry : public FV1Geometry_gen<TElem, TWorldDim, true> {};
 
 
template <typename TElem, int TWorldDim, bool TCondensed>
class FV1Geometry_gen : public FVGeometryBase
{
  public:
    typedef TElem elem_type;
 
    typedef typename reference_element_traits<TElem>::reference_element_type ref_elem_type;
 
    typedef fv1_traits<ref_elem_type, TWorldDim> traits;
 
  public:
    static const int dim = ref_elem_type::dim;
 
    static const int worldDim = TWorldDim;
 
    static const bool usesHangingNodes = false;
 
    static const bool staticLocalData = true;
    
    static const bool condensed_scvf_ips = TCondensed;
 
  public:
    static const int order = 1;
 
    static const size_t numSCV = traits::numSCV;
 
    typedef typename traits::scv_type scv_type;
 
    static const size_t numSCVF = traits::numSCVF;
 
    typedef LagrangeP1<ref_elem_type> local_shape_fct_set_type;
 
    static const size_t nsh = local_shape_fct_set_type::nsh;
 
    static const size_t nip = 1;
 
  public:
 
    class SCVF
    {
      public:
        static const size_t numCo = traits::NumCornersOfSCVF;
 
      public:
        SCVF() {}
 
        inline size_t from() const {return From;}
 
        inline size_t to() const {return To;}
 
        inline const MathVector<worldDim>& normal() const {return Normal;}
 
        inline size_t num_ip() const {return nip;}
 
        inline const MathVector<dim>& local_ip() const {return localIP;}
 
        inline const MathVector<worldDim>& global_ip() const {return globalIP;}
 
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        inline size_t num_sh() const {return nsh;}
 
        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 vLocalGrad[sh];}
 
        inline const MathVector<dim>* local_grad_vector() const {return vLocalGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return vGlobalGrad[sh];}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return vGlobalGrad;}
 
        inline size_t num_corners() const {return numCo;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vLocPos[co];}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vGloPos[co];}
 
      private:
      //  let outer class access private members
        friend class FV1Geometry_gen<TElem, TWorldDim, TCondensed>;
 
      // This scvf separates the scv with the ids given in "from" and "to"
      // The computed normal points in direction from->to
        size_t From, To;
 
      //  The normal on the SCVF pointing (from -> to)
        MathVector<worldDim> Normal; // normal (incl. area)
 
      // ordering is:
      // 1D: edgeMidPoint
      // 2D: edgeMidPoint, CenterOfElement
      // 3D: edgeMidPoint, Side #1, CenterOfElement, Side #2
        MathVector<dim> vLocPos[numCo]; // local corners of scvf
        MathVector<worldDim> vGloPos[numCo]; // global corners of scvf
        MidID vMidID[numCo]; // dimension and id of object, that's midpoint bounds the scvf
 
      // scvf part
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global integration point
 
      // shapes and derivatives
        number vShape[nsh]; // shapes at ip
        MathVector<dim> vLocalGrad[nsh]; // local grad at ip
        MathVector<worldDim> vGlobalGrad[nsh]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
 
    class SCV
    {
      public:
        static const size_t numCo = traits::NumCornersOfSCV;
 
      public:
        SCV() {};
 
        inline number volume() const {return Vol;}
 
        inline size_t num_corners() const {return numCo;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vLocPos[co];}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vGloPos[co];}
 
        inline const MathVector<dim>* local_corners() const
          {return &vLocPos[0];}
 
        inline const MathVector<worldDim>* global_corners() const
          {return &vGloPos[0];}
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return nip;}
 
        inline const MathVector<dim>& local_ip() const {return vLocPos[0];}
 
        inline const MathVector<worldDim>& global_ip() const {return vGloPos[0];}
 
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        inline size_t num_sh() const {return nsh;}
 
        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 vLocalGrad[sh];}
 
        inline const MathVector<dim>* local_grad_vector() const {return vLocalGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return vGlobalGrad[sh];}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return vGlobalGrad;}
 
      private:
      //  let outer class access private members
        friend class FV1Geometry_gen<TElem, TWorldDim, TCondensed>;
 
      //  node id of associated node
        size_t nodeId;
 
      //  volume of scv
        number Vol;
 
      //  local and global positions of this element
        MathVector<dim> vLocPos[numCo]; // local position of node
        MathVector<worldDim> vGloPos[numCo]; // global position of node
        MidID midId[numCo]; // dimension and id of object, that's midpoint bounds the scv
 
      // shapes and derivatives
        number vShape[nsh]; // shapes at ip
        MathVector<dim> vLocalGrad[nsh]; // local grad at ip
        MathVector<worldDim> vGlobalGrad[nsh]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
 
    class BF
    {
      public:
        static const size_t numCo = traits::NumCornersOfBF;
 
      public:
        BF() {}
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return nip;}
 
        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 number volume() const {return Vol;}
 
        inline const MathMatrix<worldDim, dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        inline size_t num_sh() const {return nsh;}
 
        inline number shape(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); 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 vLocalGrad[sh];}
 
        inline const MathVector<dim>* local_grad_vector() const {return vLocalGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return vGlobalGrad[sh];}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return vGlobalGrad;}
 
        inline size_t num_corners() const {return numCo;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vLocPos[co];}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vGloPos[co];}
 
      private:
        friend class FV1Geometry_gen<TElem, TWorldDim, TCondensed>;
 
      //  id of scv this bf belongs to
        size_t nodeId;
 
      // ordering is:
      // 1D: edgeMidPoint
      // 2D: edgeMidPoint, CenterOfElement
      // 3D: edgeMidPoint, Side one, CenterOfElement, Side two
        MathVector<dim> vLocPos[numCo]; // local corners of bf
        MathVector<worldDim> vGloPos[numCo]; // global corners of bf
        MidID vMidID[numCo]; // dimension and id of object, that's midpoint bounds the bf
 
      //  scvf part
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global integration point
        MathVector<worldDim> Normal; // normal (incl. area)
        number Vol; // volume of bf
 
      //  shapes and derivatives
        number vShape[nsh]; // shapes at ip
        MathVector<dim> vLocalGrad[nsh]; // local grad at ip
        MathVector<worldDim> vGlobalGrad[nsh]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
 
  public:
    FV1Geometry_gen();
 
    void update_local_data();
 
    void update(GridObject* elem, const MathVector<worldDim>* vCornerCoords,
                const ISubsetHandler* ish = NULL);
 
    void update_boundary_faces(GridObject* elem,
                               const MathVector<worldDim>* vCornerCoords,
                               const ISubsetHandler* ish = NULL);
 
    TElem* elem() const {return m_pElem;}
    
    const MathVector<worldDim>* corners() const {return m_vvGloMid[0];}
 
    size_t num_scvf() const {return numSCVF;};
 
    const SCVF& scvf(size_t i) const
      {UG_ASSERT(i < num_scvf(), "Invalid Index."); return m_vSCVF[i];}
 
    // do not use this method to obtain the number of shape functions,
    // since this is NOT the same for pyramids; use num_sh() instead.
    size_t num_scv() const {return numSCV;}
 
    const SCV& scv(size_t i) const
      {UG_ASSERT(i < num_scv(), "Invalid Index."); return m_vSCV[i];}
 
    size_t num_sh() const {return nsh;};
 
    ReferenceObjectID roid() const {return ref_elem_type::REFERENCE_OBJECT_ID;}
 
 
  public:
    size_t num_scvf_ips() const {return numSCVF;}
 
    const MathVector<dim>* scvf_local_ips() const {return m_vLocSCVF_IP;}
 
    const MathVector<worldDim>* scvf_global_ips() const {return m_vGlobSCVF_IP;}
 
    size_t num_scv_ips() const {return numSCV;}
 
    const MathVector<dim>* scv_local_ips() const {
      if(ref_elem_type::REFERENCE_OBJECT_ID == ROID_PYRAMID || ref_elem_type::REFERENCE_OBJECT_ID == ROID_OCTAHEDRON)
        return &(m_vLocSCV_IP[0]);
      else
        return &(m_vvLocMid[0][0]);
    }
 
    const MathVector<worldDim>* scv_global_ips() const {
      if(ref_elem_type::REFERENCE_OBJECT_ID == ROID_PYRAMID || ref_elem_type::REFERENCE_OBJECT_ID == ROID_OCTAHEDRON)
        return &(m_vGlobSCV_IP[0]);
      else
        return &(m_vvGloMid[0][0]);
    }
 
    const MathVector<dim>& local_node_position(size_t nodeID) const
    {
      UG_ASSERT(nodeID < (size_t) ref_elem_type::numCorners, "Invalid node id.");
      return m_vvLocMid[0][nodeID];
    }
 
    const MathVector<worldDim>& global_node_position(size_t nodeID) const
    {
      UG_ASSERT(nodeID < (size_t) ref_elem_type::numCorners, "Invalid node id.");
      return m_vvGloMid[0][nodeID];
    }
 
    const MathVector<dim>* coe_local() const {return &(m_vvLocMid[dim][0]);}
    
    const MathVector<worldDim>* coe_global() const {return &(m_vvGloMid[dim][0]);}
 
  protected:
  //  global and local ips on SCVF
    MathVector<worldDim> m_vGlobSCVF_IP[numSCVF];
    MathVector<dim> m_vLocSCVF_IP[numSCVF];
 
  //  global and local ips on SCV (only needed for Pyramid and Octahedron)
    MathVector<worldDim> m_vGlobSCV_IP[numSCV];
    MathVector<dim> m_vLocSCV_IP[numSCV];
 
  public:
    inline void add_boundary_subset(int subsetIndex) {m_mapVectorBF[subsetIndex];}
 
    inline void remove_boundary_subset(int subsetIndex) {m_mapVectorBF.erase(subsetIndex);}
 
    inline void clear_boundary_subsets() {m_mapVectorBF.clear();}
 
    inline size_t num_boundary_subsets() {return m_mapVectorBF.size();}
 
    inline size_t num_bf() const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      size_t num = 0;
      for ( it=m_mapVectorBF.begin() ; it != m_mapVectorBF.end(); it++ )
        num += (*it).second.size();
      return num;
    }
 
    inline size_t num_bf(int si) const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      it = m_mapVectorBF.find(si);
      if(it == m_mapVectorBF.end()) return 0;
      else return (*it).second.size();
    }
 
    inline const BF& bf(int si, size_t i) const
    {
      UG_ASSERT(i < num_bf(si), "Invalid index.");
      typename std::map<int, std::vector<BF> >::const_iterator it;
      it = m_mapVectorBF.find(si);
      if(it == m_mapVectorBF.end()) UG_THROW("FVGeom: No bnd face for subset"<<si);
      return (*it).second[i];
    }
 
    inline const std::vector<BF>& bf(int si) const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      it = m_mapVectorBF.find(si);
      if(it == m_mapVectorBF.end()) return m_vEmptyVectorBF;
      return (*it).second;
    }
 
    void reset_curr_elem() {m_pElem = NULL;}
 
  protected:
    std::map<int, std::vector<BF> > m_mapVectorBF;
    std::vector<BF> m_vEmptyVectorBF;
 
  private:
    TElem* m_pElem;
 
  //  (most objects in 1 dim, i.e. number of edges, but +1 for 1D)
    static const int maxMid = numSCVF + 1;
 
    MathVector<dim> m_vvLocMid[dim+1][maxMid];
    MathVector<worldDim> m_vvGloMid[dim+1][maxMid];
 
    SCVF m_vSCVF[numSCVF];
 
    SCV m_vSCV[numSCV];
 
    ReferenceMapping<ref_elem_type, worldDim> m_mapping;
 
    const ref_elem_type& m_rRefElem;
 
    const local_shape_fct_set_type& m_rTrialSpace;
};
 
// Dim-dependent Finite Volume Geometry
 
 
template <int TDim, int TWorldDim = TDim>
class DimFV1Geometry : public FVGeometryBase
{
  public:
    typedef fv1_dim_traits<TDim, TWorldDim> traits;
 
  public:
    static const int dim = TDim;
 
    static const int worldDim = TWorldDim;
 
    static const bool usesHangingNodes = false;
 
    static const bool staticLocalData = false;
 
  public:
    static const int order = 1;
 
    static const size_t maxNumSCV = traits::maxNumSCV;
 
    typedef typename traits::scv_type scv_type;
 
    static const size_t maxNumSCVF = traits::maxNumSCVF;
 
    static const size_t maxNSH = traits::maxNSH;
 
    static const size_t nip = 1;
 
  public:
 
    class SCVF
    {
      public:
        static const size_t numCo = traits::NumCornersOfSCVF;
 
      public:
        SCVF() {}
 
        inline size_t from() const {return From;}
 
        inline size_t to() const {return To;}
 
        inline size_t num_ip() const {return nip;}
 
        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;}
 
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        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 vLocalGrad[sh];}
 
        inline const MathVector<dim>* local_grad_vector() const {return vLocalGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return vGlobalGrad[sh];}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return vGlobalGrad;}
 
        inline size_t num_corners() const {return numCo;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vLocPos[co];}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vGloPos[co];}
 
      private:
      //  let outer class access private members
        friend class DimFV1Geometry<dim, worldDim>;
 
      // This scvf separates the scv with the ids given in "from" and "to"
      // The computed normal points in direction from->to
        size_t From, To;
 
      //  The normal on the SCVF pointing (from -> to)
        MathVector<worldDim> Normal; // normal (incl. area)
 
      // ordering is:
      // 1D: edgeMidPoint
      // 2D: edgeMidPoint, CenterOfElement
      // 3D: edgeMidPoint, Side one, CenterOfElement, Side two
        MathVector<dim> vLocPos[numCo]; // local corners of scvf
        MathVector<worldDim> vGloPos[numCo]; // global corners of scvf
        MidID vMidID[numCo]; // dimension and id of object, that's midpoint bounds the scvf
 
      // scvf part
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global integration point
 
      // shapes and derivatives
        size_t numSH;
        number vShape[maxNSH]; // shapes at ip
        MathVector<dim> vLocalGrad[maxNSH]; // local grad at ip
        MathVector<worldDim> vGlobalGrad[maxNSH]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
 
    class SCV
    {
      public:
        static const size_t numCo = traits::NumCornersOfSCV;
 
      public:
        SCV() {};
 
        inline number volume() const {return Vol;}
 
        inline size_t num_corners() const {return numCo;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vLocPos[co];}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vGloPos[co];}
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return nip;}
 
        inline const MathVector<dim>& local_ip() const {return vLocPos[0];}
 
        inline const MathVector<worldDim>& global_ip() const {return vGloPos[0];}
 
        inline const MathMatrix<worldDim,dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        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 vLocalGrad[sh];}
 
        inline const MathVector<dim>* local_grad_vector() const {return vLocalGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return vGlobalGrad[sh];}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return vGlobalGrad;}
 
      private:
      //  let outer class access private members
        friend class DimFV1Geometry<dim, worldDim>;
 
      //  node id of associated node
        size_t nodeId;
 
      //  volume of scv
        number Vol;
 
      //  local and global positions of this element
        MathVector<dim> vLocPos[numCo]; // local position of node
        MathVector<worldDim> vGloPos[numCo]; // global position of node
        MidID vMidID[numCo]; // dimension and id of object, that's midpoint bounds the scv
 
      // shapes and derivatives
        size_t numSH;
        number vShape[maxNSH]; // shapes at ip
        MathVector<dim> vLocalGrad[maxNSH]; // local grad at ip
        MathVector<worldDim> vGlobalGrad[maxNSH]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
 
    class BF
    {
      public:
        static const size_t numCo = traits::NumCornersOfSCVF;
 
      public:
        BF() {}
 
        inline size_t node_id() const {return nodeId;}
 
        inline size_t num_ip() const {return nip;}
 
        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 number volume() const {return Vol;}
 
        inline const MathMatrix<worldDim, dim>& JTInv() const {return JtInv;}
 
        inline number detJ() const {return detj;}
 
        inline size_t num_sh() const {return numSH;}
 
        inline number shape(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); 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 vLocalGrad[sh];}
 
        inline const MathVector<dim>* local_grad_vector() const {return vLocalGrad;}
 
        inline const MathVector<worldDim>& global_grad(size_t sh) const
          {UG_ASSERT(sh < num_sh(), "Invalid index"); return vGlobalGrad[sh];}
 
        inline const MathVector<worldDim>* global_grad_vector() const {return vGlobalGrad;}
 
        inline size_t num_corners() const {return numCo;}
 
        inline const MathVector<dim>& local_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vLocPos[co];}
 
        inline const MathVector<worldDim>& global_corner(size_t co) const
          {UG_ASSERT(co < num_corners(), "Invalid index."); return vGloPos[co];}
 
      private:
        friend class DimFV1Geometry<dim, worldDim>;
 
      //  id of scv this bf belongs to
        size_t nodeId;
 
      // ordering is:
      // 1D: edgeMidPoint
      // 2D: edgeMidPoint, CenterOfElement
      // 3D: edgeMidPoint, Side one, CenterOfElement, Side two
        MathVector<dim> vLocPos[numCo]; // local corners of bf
        MathVector<worldDim> vGloPos[numCo]; // global corners of bf
        MidID vMidID[numCo]; // dimension and id of object, that's midpoint bounds the bf
 
      //  scvf part
        MathVector<dim> localIP; // local integration point
        MathVector<worldDim> globalIP; // global integration point
        MathVector<worldDim> Normal; // normal (incl. area)
        number Vol; // volume of bf
 
      //  shapes and derivatives
        size_t numSH;
        number vShape[maxNSH]; // shapes at ip
        MathVector<dim> vLocalGrad[maxNSH]; // local grad at ip
        MathVector<worldDim> vGlobalGrad[maxNSH]; // global grad at ip
        MathMatrix<worldDim,dim> JtInv; // Jacobian transposed at ip
        number detj; // Jacobian det at ip
    };
 
  public:
    DimFV1Geometry() : m_pElem(NULL), m_roid(ROID_UNKNOWN) {};
 
    void update(GridObject* elem, const MathVector<worldDim>* vCornerCoords,
                const ISubsetHandler* ish = NULL);
 
    void update_boundary_faces(GridObject* elem,
                               const MathVector<worldDim>* vCornerCoords,
                               const ISubsetHandler* ish = NULL);
 
    GridObject* elem() const {return m_pElem;}
    
    const MathVector<worldDim>* corners() const {return m_vvGloMid[0];}
 
    size_t num_scvf() const {return m_numSCVF;};
 
    const SCVF& scvf(size_t i) const
      {UG_ASSERT(i < num_scvf(), "Invalid Index."); return m_vSCVF[i];}
 
    // do not use this method to obtain the number of shape functions,
    // since this is NOT the same for pyramids; use num_sh() instead.
    size_t num_scv() const {return m_numSCV;}
 
    const SCV& scv(size_t i) const
      {UG_ASSERT(i < num_scv(), "Invalid Index."); return m_vSCV[i];}
 
    size_t num_sh() const {return m_nsh;};
 
  public:
    size_t num_scvf_ips() const {return m_numSCVF;}
 
    const MathVector<dim>* scvf_local_ips() const {return m_vLocSCVF_IP;}
 
    const MathVector<worldDim>* scvf_global_ips() const {return m_vGlobSCVF_IP;}
 
    size_t num_scv_ips() const {return m_numSCV;}
 
    const MathVector<dim>* scv_local_ips() const {
      if(m_roid == ROID_PYRAMID || m_roid == ROID_OCTAHEDRON)
        return &(m_vLocSCV_IP[0]);
      else
        return &(m_vvLocMid[0][0]);
    }
 
    const MathVector<worldDim>* scv_global_ips() const {
      if(m_roid == ROID_PYRAMID || m_roid == ROID_OCTAHEDRON)
        return &(m_vGlobSCV_IP[0]);
      else
        return &(m_vvGloMid[0][0]);
    }
 
    const MathVector<dim>& local_node_position(size_t nodeID) const
    {
      UG_ASSERT(nodeID < (size_t) maxMid, "Invalid node id.");
      return m_vvLocMid[0][nodeID];
    }
 
    const MathVector<worldDim>& global_node_position(size_t nodeID) const
    {
      UG_ASSERT(nodeID < (size_t) maxMid, "Invalid node id.");
      return m_vvGloMid[0][nodeID];
    }
 
    const MathVector<dim>* coe_local() const {return &(m_vvLocMid[dim][0]);}
    
    const MathVector<worldDim>* coe_global() const {return &(m_vvGloMid[dim][0]);}
 
    ReferenceObjectID roid() const {return m_roid;}
 
    void update_local(ReferenceObjectID roid);
 
  protected:
  //  global and local ips on SCVF
    MathVector<worldDim> m_vGlobSCVF_IP[maxNumSCVF];
    MathVector<dim> m_vLocSCVF_IP[maxNumSCVF];
 
  //  global and local ips on SCV (only needed for Pyramid and Octahedron)
    MathVector<worldDim> m_vGlobSCV_IP[maxNumSCV];
    MathVector<dim> m_vLocSCV_IP[maxNumSCV];
 
  public:
    inline void add_boundary_subset(int subsetIndex) {m_mapVectorBF[subsetIndex];}
 
    inline void remove_boundary_subset(int subsetIndex) {m_mapVectorBF.erase(subsetIndex);}
 
    inline void clear_boundary_subsets() {m_mapVectorBF.clear();}
 
    inline size_t num_boundary_subsets() {return m_mapVectorBF.size();}
 
    inline size_t num_bf() const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      size_t num = 0;
      for ( it=m_mapVectorBF.begin() ; it != m_mapVectorBF.end(); it++ )
        num += (*it).second.size();
      return num;
    }
 
    inline size_t num_bf(int si) const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      it = m_mapVectorBF.find(si);
      if(it == m_mapVectorBF.end()) return 0;
      else return (*it).second.size();
    }
 
    inline const BF& bf(int si, size_t i) const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      it = m_mapVectorBF.find(si);
      if(it == m_mapVectorBF.end()) UG_THROW("DimFV1Geom: No BndSubset "<<si);
      return (*it).second[i];
    }
 
    inline const std::vector<BF>& bf(int si) const
    {
      typename std::map<int, std::vector<BF> >::const_iterator it;
      it = m_mapVectorBF.find(si);
      if(it == m_mapVectorBF.end()) return m_vEmptyVectorBF;
      return (*it).second;
    }
 
  protected:
    std::map<int, std::vector<BF> > m_mapVectorBF;
    std::vector<BF> m_vEmptyVectorBF;
 
  private:
    GridObject* m_pElem;
 
    ReferenceObjectID m_roid;
 
    size_t m_numSCV;
 
    size_t m_numSCVF;
 
    size_t m_nsh;
 
  //  (most objects in 1 dim, i.e. number of edges, but +1 for 1D)
    static const int maxMid = maxNumSCVF + 1;
 
    MathVector<dim> m_vvLocMid[dim+1][maxMid];
    MathVector<worldDim> m_vvGloMid[dim+1][maxMid];
 
    SCVF m_vSCVF[maxNumSCVF];
 
    SCV m_vSCV[maxNumSCV];
};
 
 
// FV1 Manifold Geometry
 
template <typename TElem, int TWorldDim>
class FV1ManifoldGeometry
{
  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 BoundaryFaces
    static const size_t m_numBF = ref_elem_type::numCorners;
    
  //  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 fv1_traits<ref_elem_type, dim>::scv_type bf_type;
 
  //  Hanging node flag: this Geometry does not support hanging nodes
    static const bool usesHangingNodes = false;
 
    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;
    };
    
  public: 
    class BF
    {
      private:
      //  let outer class access private members
        friend class FV1ManifoldGeometry<TElem, TWorldDim>;
 
      //  number of integration points
        static const size_t m_numIP = 1;
        
      //  max number of corners of bf
        static const size_t numCorners = fv1_traits<ref_elem_type, dim>::NumCornersOfSCV;
 
      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 vLocPos[0];}  // <-- always the vertex
 
        inline const MathVector<worldDim>& global_ip() const
        {return vGloPos[0];}  // <-- here too
 
        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 vLocPos[i];}
 
        inline const MathVector<worldDim>& global_corner(size_t i) const
          {UG_ASSERT(i < num_corners(), "Invalid index."); return vGloPos[i];}
        
        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];}
        
      private:
        size_t nodeId;                    // id of associated node
        
        // CORNERS: ordering is:
        // 1D: edgeMidPoint, CenterOfElement
        // 2D: edgeMidPoint, Side one, CenterOfElement, Side two
        MathVector<dim> vLocPos[numCorners];      // local position of node
        MathVector<worldDim> vGloPos[numCorners]; // global position of node
        MidID midId[numCorners];      // dimension and id of object, whose midpoint bounds the scv
        
        // IPs & shapes
        std::vector<number> vShape; // shapes at ip
        
        number vol;
    };
  
  protected:
    void copy_local_corners(BF& bf)
    {
      for (size_t i = 0; i < bf.num_corners(); ++i)
      {
        const size_t dim = bf.midId[i].dim;
        const size_t id = bf.midId[i].id;
        bf.vLocPos[i] = m_locMid[dim][id];
      }
    }
    
    void copy_global_corners(BF& bf)
    {
      for (size_t i = 0; i < bf.num_corners(); ++i)
      {
        const size_t dim = bf.midId[i].dim;
        const size_t id = bf.midId[i].id;
        bf.vGloPos[i] = m_gloMid[dim][id];
      }
    }
 
    std::vector<MathVector<dim> > m_vLocBFIP;
    std::vector<MathVector<worldDim> > m_vGlobBFIP;
    
    
  public:
    FV1ManifoldGeometry();
    
    void update(GridObject* elem, const MathVector<worldDim>* vCornerCoords,
                const ISubsetHandler* ish = NULL);
      
    GridObject* elem() const {return m_pElem;}
    
    const MathVector<worldDim>* corners() const {return m_gloMid[0];}
 
    inline size_t num_bf() const {return m_numBF;}
 
    inline const BF& bf(size_t i) const
      {UG_ASSERT(i < num_bf(), "Invalid Index."); return m_vBF[i];}
  
    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();}
 
  private:
  //  pointer to current element
    GridObject* m_pElem;
    
  //  local and global geom object midpoints for each dimension
    MathVector<dim> m_locMid[dim+1][m_numBF];
    MathVector<worldDim> m_gloMid[dim+1][m_numBF];
    
  //  BndFaces
    BF m_vBF[m_numBF];
    
  //  Reference Mapping
    ReferenceMapping<ref_elem_type, worldDim> m_rMapping;
 
  //  Reference Element
    const ref_elem_type& m_rRefElem;
};
 
}
 
#endif /* __H__UG__LIB_DISC__SPATIAL_DISC__DISC_HELPER__FV1_GEOMETRY__ */