fv1ib_geom.h

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/*
 * Copyright (c) 2014-2015:  G-CSC, Goethe University Frankfurt
 * Author: Susanne Höllbacher
 * 
 * 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 FV1IB_GEOM_H_
#define FV1IB_GEOM_H_
 
// 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
 
 
template <  typename TElem, int TWorldDim>
class FV1IBGeometry : 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;
 
public:
  static const int order = 1;
 
  static const size_t numSCV = (ref_elem_type::REFERENCE_OBJECT_ID != ROID_PYRAMID)
                ? ref_elem_type::numCorners : 8;
 
  typedef typename traits::scv_type scv_type;
 
  static const size_t numSCVF = (ref_elem_type::REFERENCE_OBJECT_ID != ROID_PYRAMID)
                ? ref_elem_type::numEdges : 12;
 
  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];}
 
    protected:
    //  let outer class access private members
      friend class FV1IBGeometry<TElem, TWorldDim>;
 
    // 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
      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 FV1IBGeometry<TElem, TWorldDim>;
 
    //  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::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 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 FV1IBGeometry<TElem, TWorldDim>;
 
    //  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:
    FV1IBGeometry();
 
    void adapt(GridObject* elem, const MathVector<TWorldDim>* vCornerCoords,
          const ISubsetHandler* ish = NULL);
 
    void adapt_normals(GridObject* elem, const MathVector<TWorldDim>* vCornerCoords,
          const ISubsetHandler* ish = NULL);
 
    void adapt_integration_points(GridObject* elem, const MathVector<TWorldDim>* vCornerCoords,
          const ISubsetHandler* ish = NULL);
 
    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);
 
    const MathVector<worldDim>* corners() const {return m_vvGloMid[0];}
 
    inline size_t num_scvf() const {return numSCVF;};
 
    inline 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.
    inline size_t num_scv() const {return numSCV;}
 
    inline const SCV& scv(size_t i) const
      {UG_ASSERT(i < num_scv(), "Invalid Index."); return m_vSCV[i];}
 
    inline size_t num_sh() const {return nsh;};
 
  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 {return &(m_vvLocMid[0][0]);}
 
    const MathVector<worldDim>* scv_global_ips() const {return &(m_vvGloMid[0][0]);}
 
 
  protected:
  //  global and local ips on SCVF
    MathVector<worldDim> m_vGlobSCVF_IP[numSCVF];
    MathVector<dim> m_vLocSCVF_IP[numSCVF];
 
  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;
    }
 
  protected:
    std::map<int, std::vector<BF> > m_mapVectorBF;
    std::vector<BF> m_vEmptyVectorBF;
 
  protected:
    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;
 
  public:
    MathVector<worldDim> vSCVF_PosOnEdge[numSCVF];  // global position of scvf on edges
    MathVector<worldDim> m_MidPoint;        // global position of the midpoint, connecting each entry of PosOnEdges to a scvf
 
 
};
 
// Dim-dependent Finite Volume Geometry
 
 
template <int TDim, int TWorldDim = TDim>
class DimFV1IBGeometry : 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 DimFV1IBGeometry<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 DimFV1IBGeometry<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 DimFV1IBGeometry<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:
    DimFV1IBGeometry() : m_pElem(NULL), m_roid(ROID_UNKNOWN) {};
 
    void adapt(GridObject* elem, const MathVector<TWorldDim>* vCornerCoords,
          const ISubsetHandler* ish = NULL);
 
    void adapt_normals(GridObject* elem, const MathVector<TWorldDim>* vCornerCoords,
          const ISubsetHandler* ish = NULL);
 
    void adapt_integration_points(GridObject* elem, const MathVector<TWorldDim>* vCornerCoords,
          const ISubsetHandler* ish = NULL);
 
    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);
 
    const MathVector<worldDim>* corners() const {return m_vvGloMid[0];}
 
    inline size_t num_scvf() const {return m_numSCVF;};
 
    inline 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.
    inline size_t num_scv() const {return m_numSCV;}
 
    inline const SCV& scv(size_t i) const
      {UG_ASSERT(i < num_scv(), "Invalid Index."); return m_vSCV[i];}
 
    inline 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 {return &(m_vvLocMid[0][0]);}
 
    const MathVector<worldDim>* scv_global_ips() const {return &(m_vvGloMid[0][0]);}
 
 
  protected:
  //  global and local ips on SCVF
    MathVector<worldDim> m_vGlobSCVF_IP[maxNumSCVF];
    MathVector<dim> m_vLocSCVF_IP[maxNumSCVF];
 
  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("DimFV1IBGeom: 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];
 
  public:
    MathVector<worldDim> vSCVF_PosOnEdge[maxNumSCVF];   // global position of scvf on edges
    MathVector<worldDim> m_MidPoint;        // global position of the midpoint, connecting each entry of PosOnEdges to a scvf
 
};
 
 
 
#include "fv1ib_geom_impl.h"
 
} // end ug namespace
 
#endif /* FV1IB_GEOM_H_ */