ElInfo3d.cc 18.1 KB
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#include "ElInfo3d.h"
#include "BasisFunction.h"
#include "Element.h"
#include "Line.h"
#include "Triangle.h"
#include "Tetrahedron.h"
#include "FiniteElemSpace.h"
#include "Flag.h"
#include "MacroElement.h"
#include "Mesh.h"
#include "Global.h"
#include "FixVec.h"
#include "DOFVector.h"

namespace AMDiS {

  void ElInfo3d::fillMacroInfo(const MacroElement * mel)
  {
    FUNCNAME("ElInfo3d::fillMacroInfo");
    Element      *nb;
    MacroElement *mnb;
    Flag    fill_opp_coords;

    macroElement_  = const_cast<MacroElement*>( mel);
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    element_  = const_cast<Element*>( mel->getElement());
    parent_ = NULL;
    level_ = 0;
    el_type = const_cast<MacroElement*>(mel)->getElType();
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    int vertices = mesh_->getGeo(VERTEX);

    if (fillFlag_.isSet(Mesh::FILL_COORDS) || 
	fillFlag_.isSet(Mesh::FILL_DET) ||
	fillFlag_.isSet(Mesh::FILL_GRD_LAMBDA)) {
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      for (int i = 0; i < vertices; i++) {
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	coord_[i] = mel->coord[i];
      }
    }

    //   if(fillFlag_.isSet(Mesh::FILL_DET) || fillFlag_.isSet(Mesh::FILL_GRD_LAMBDA)) {
    //     det = calcGrdLambda(*Lambda);
    //   }

    int neighbours = mesh_->getGeo(NEIGH);

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    if (fillFlag_.isSet(Mesh::FILL_OPP_COORDS) || 
        fillFlag_.isSet(Mesh::FILL_NEIGH)) {
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      fill_opp_coords.setFlags(fillFlag_ & Mesh::FILL_OPP_COORDS);
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      for (int i = 0; i < neighbours; i++) {
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	if ((mnb = const_cast<MacroElement*>( mel->getNeighbour(i)))) {
	  neighbour_[i] = const_cast<Element*>( mel->getNeighbour(i)->getElement());
	  nb = const_cast<Element*>( neighbour_[i]);
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	  int k;
	  k = oppVertex_[i] = mel->getOppVertex(i);
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	  if (nb->getChild(0) && (k < 2)) {   /*make nb nearest element.*/
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	    if (k == 1) {
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	      neighbour_[i]      = const_cast<Element*>( nb->getChild(0));
	      nb = const_cast<Element*>( neighbour_[i]);
	    } else {
	      neighbour_[i]      = const_cast<Element*>( nb->getChild(1));
	      nb = const_cast<Element*>( neighbour_[i]);
	    }
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	    k = oppVertex_[i] = 3;
	    if (fill_opp_coords.isAnySet()) {
	      /* always edge between vertices 0 and 1 is bisected! */
	      if (mnb->getElement()->isNewCoordSet())
		oppCoord_[i] = *(mnb->getElement()->getNewCoord());
	      else
		oppCoord_[i] = (mnb->coord[0] + mnb->coord[1]) * 0.5;
	    }
	  } else {
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	    if  (fill_opp_coords.isAnySet()) {
	      oppCoord_[i] = mnb->coord[k];
	    }
	  }
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	} else {
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	  neighbour_[i] = NULL;
	}
      }
    }

    //int faces = mesh->getGeo(FACE);
    //int edges = mesh->getGeo(EDGE);

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    if (fillFlag_.isSet(Mesh::FILL_BOUND)) {
      for (int i = 0; i < element_->getGeo(BOUNDARY); i++) {
	boundary_[i] = mel->getBoundary(i);
      }
      
      for (int i = 0; i < element_->getGeo(PROJECTION); i++) {
	projection_[i] = mel->getProjection(i);
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      }
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    }
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    if (fillFlag_.isSet(Mesh::FILL_ORIENTATION)) {
      WorldVector<WorldVector<double> > a;
      double s;

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      for (int i = 0; i < 3; i++) {
	a[i] = mel->coord[i + 1];
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	a[i] -= mel->coord[0];
      }

      s = (a[0][1] * a[1][2] - a[0][2] * a[1][1]) * a[2][0]
	+ (a[0][2] * a[1][0] - a[0][0] * a[1][2]) * a[2][1]
	+ (a[0][0] * a[1][1] - a[0][1] * a[1][0]) * a[2][2];

      if (s >= 0)
	orientation = 1;
      else
	orientation = -1;
    }
  }

  double ElInfo3d::calcGrdLambda(DimVec<WorldVector<double> >& grd_lam) const
  {
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    FUNCNAME("ElInfo3d::calcGrdLambda()");

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    TEST_EXIT_DBG(Global::getGeo(WORLD) == 3)
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      ("dim != dim_of_world ! use parametric elements!\n");

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    WorldVector<double> e1, e2, e3;
    WorldVector<double> v0;
    double det, adet;
    double a11, a12, a13, a21, a22, a23, a31, a32, a33;
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    testFlag(Mesh::FILL_COORDS);

    v0 = coord_[0];
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    for (int i = 0; i < 3; i++) {
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      e1[i] = coord_[1][i] - v0[i];
      e2[i] = coord_[2][i] - v0[i];
      e3[i] = coord_[3][i] - v0[i];
    }

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    det =   e1[0] * (e2[1] * e3[2] - e2[2] * e3[1])
          - e1[1] * (e2[0] * e3[2] - e2[2] * e3[0])
          + e1[2] * (e2[0] * e3[1] - e2[1] * e3[0]);
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    adet = abs(det);

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    if (adet < 1.0E-25) {
      MSG("abs(det) = %f\n",adet);
      for (int i = 0; i < 4; i++)
	for (int j = 0; j < 3; j++)
	  grd_lam[i][j] = 0.0;
    } else {
      det = 1.0 / det;
      a11 = (e2[1] * e3[2] - e2[2] * e3[1]) * det;    /* (a_ij) = A^{-T} */
      a12 = (e2[2] * e3[0] - e2[0] * e3[2]) * det;
      a13 = (e2[0] * e3[1] - e2[1] * e3[0]) * det;
      a21 = (e1[2] * e3[1] - e1[1] * e3[2]) * det;
      a22 = (e1[0] * e3[2] - e1[2] * e3[0]) * det;
      a23 = (e1[1] * e3[0] - e1[0] * e3[1]) * det;
      a31 = (e1[1] * e2[2] - e1[2] * e2[1]) * det;
      a32 = (e1[2] * e2[0] - e1[0] * e2[2]) * det;
      a33 = (e1[0] * e2[1] - e1[1] * e2[0]) * det;

      grd_lam[1][0] = a11;
      grd_lam[1][1] = a12;
      grd_lam[1][2] = a13;
      grd_lam[2][0] = a21;
      grd_lam[2][1] = a22;
      grd_lam[2][2] = a23;
      grd_lam[3][0] = a31;
      grd_lam[3][1] = a32;
      grd_lam[3][2] = a33;

      grd_lam[0][0] = -grd_lam[1][0] -grd_lam[2][0] -grd_lam[3][0];
      grd_lam[0][1] = -grd_lam[1][1] -grd_lam[2][1] -grd_lam[3][1];
      grd_lam[0][2] = -grd_lam[1][2] -grd_lam[2][2] -grd_lam[3][2];
    }
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    return adet;
  }

  const int ElInfo3d::worldToCoord(const WorldVector<double>& xy,
				   DimVec<double>* lambda) const
  {
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    FUNCNAME("ElInfo::worldToCoord()");

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    DimVec<WorldVector<double> > edge(mesh_->getDim(), NO_INIT);
    WorldVector<double> x;
    double  x0, det, det0, det1, det2;
  
    static DimVec<double> vec(mesh_->getDim(), NO_INIT);

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    TEST_EXIT_DBG(lambda)("lambda must not be NULL\n");
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    int dim = mesh_->getDim();
    int dimOfWorld = Global::getGeo(WORLD);

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    TEST_EXIT_DBG(dim == dimOfWorld)("dim!=dimOfWorld not yet implemented\n");
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    /*  wir haben das gleichungssystem zu loesen: */
    /*       ( q1x q2x q3x)  (lambda1)     (qx)      */
    /*       ( q1y q2y q3y)  (lambda2)  =  (qy)      */
    /*       ( q1z q2z q3z)  (lambda3)     (qz)      */
    /*      mit qi=pi-p3, q=xy-p3                 */

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    for (int j = 0; j < dimOfWorld; j++) {
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      x0 = coord_[dim][j];
      x[j] = xy[j] - x0;
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      for (int i = 0; i < dim; i++)
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	edge[i][j] = coord_[i][j] - x0;
    }

    det =  edge[0][0] * edge[1][1] * edge[2][2]
      + edge[0][1] * edge[1][2] * edge[2][0]
      + edge[0][2] * edge[1][0] * edge[2][1]
      - edge[0][2] * edge[1][1] * edge[2][0]
      - edge[0][0] * edge[1][2] * edge[2][1]
      - edge[0][1] * edge[1][0] * edge[2][2];
    det0 =       x[0] * edge[1][1] * edge[2][2]
      +       x[1] * edge[1][2] * edge[2][0]
      +       x[2] * edge[1][0] * edge[2][1]
      -       x[2] * edge[1][1] * edge[2][0]
      -       x[0] * edge[1][2] * edge[2][1]
      -       x[1] * edge[1][0] * edge[2][2];
    det1 = edge[0][0] *       x[1] * edge[2][2]
      + edge[0][1] *       x[2] * edge[2][0]
      + edge[0][2] *       x[0] * edge[2][1]
      - edge[0][2] *       x[1] * edge[2][0]
      - edge[0][0] *       x[2] * edge[2][1]
      - edge[0][1] *       x[0] * edge[2][2];
    det2 = edge[0][0] * edge[1][1] *       x[2]
      + edge[0][1] * edge[1][2] *       x[0]
      + edge[0][2] * edge[1][0] *       x[1]
      - edge[0][2] * edge[1][1] *       x[0]
      - edge[0][0] * edge[1][2] *       x[1]
      - edge[0][1] * edge[1][0] *       x[2];
  
    if (abs(det) < DBL_TOL) {
      ERROR("det = %le; abort\n", det);
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      for (int i = 0; i <= dim; i++) {
	(*lambda)[i] = 1.0 / dim;
      }

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      return 0;
    }

    (*lambda)[0] = det0 / det;
    (*lambda)[1] = det1 / det;
    (*lambda)[2] = det2 / det;
    (*lambda)[3] = 1.0 - (*lambda)[0] - (*lambda)[1] - (*lambda)[2];
  
    int k = -1;
    double lmin = 0.0;
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    for (int i = 0; i <= dim; i++) {
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      if ((*lambda)[i] < -1.E-5) {
	if ((*lambda)[i] < lmin) {
	  k = i;
	  lmin = (*lambda)[i];
	}
      }
    }

    return k;
  }


  /****************************************************************************/
  /*   update EL_INFO structure after refinement (of some neighbours)	    */
  /****************************************************************************/

  void ElInfo3d::update()
  {
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    FUNCNAME("ElInfo::update()");
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    int neighbours = mesh_->getGeo(NEIGH);
    int vertices = mesh_->getGeo(VERTEX);
    int dow = Global::getGeo(WORLD);
  
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    if (fillFlag_.isSet(Mesh::FILL_NEIGH) || fillFlag_.isSet(Mesh::FILL_OPP_COORDS)) {
      Tetrahedron *nb;
      Flag fill_opp_coords = fillFlag_ & Mesh::FILL_OPP_COORDS;
      
      for (int ineigh = 0; ineigh < neighbours; ineigh++) {
	if ((nb = dynamic_cast<Tetrahedron*>(const_cast<Element*>(neighbour_[ineigh])))) {
	  int ov = oppVertex_[ineigh];
	  if (ov < 2 && nb->getFirstChild()) {
	    if (fill_opp_coords != Flag(0)) {
	      int k = -1;
	      for (int j = 0; j < vertices; j++)
		if (element_->getDOF(j) == nb->getDOF(1 - ov)) 
		  k = j;
	      
	      if (k == -1) {
		for (int j = 0; j < vertices; j++) {
		  if (mesh_->associated(element_->getDOF(j, 0), nb->getDOF(1 - ov, 0))) {
		    k = j;
		  }
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		}
	      }
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	      TEST_EXIT_DBG(k >= 0)("neighbour dof not found\n");
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	      if (nb->isNewCoordSet())
		oppCoord_[ineigh] = *(nb->getNewCoord());
	      else
		for (int j = 0; j < dow; j++)
		  oppCoord_[ineigh][j] = (oppCoord_[ineigh][j] + coord_[k][j]) / 2;
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	    }
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	    neighbour_[ineigh] = dynamic_cast<Tetrahedron*>(const_cast<Element*>(nb->getChild(1-ov)));
	    oppVertex_[ineigh] = 3;
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	  }
	}
      }
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    }
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  }


  double ElInfo3d::getNormal(int face, WorldVector<double> &normal) const
  {
    FUNCNAME("ElInfo3d::getNormal");
    double det = 0.0;
    WorldVector<double> e0, e1, e2;

    int dow = Global::getGeo(WORLD);

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    if (dow == 3) {
      int i0 = (face + 1) % 4;
      int i1 = (face + 2) % 4;
      int i2 = (face + 3) % 4;
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      for (int i = 0; i < dow; i++) {
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	e0[i] = coord_[i1][i] - coord_[i0][i];
	e1[i] = coord_[i2][i] - coord_[i0][i];
	e2[i] = coord_[face][i] - coord_[i0][i];
      }

      vectorProduct(e0, e1, normal);

      if ((e2*normal) < 0.0)
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	for (int i = 0; i < dow; i++)
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	  normal[i] = -normal[i];

      det = norm(&normal);
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      TEST_EXIT_DBG(det > 1.e-30)("det = 0 on face %d\n", face);
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      normal[0] /= det;
      normal[1] /= det;
      normal[2] /= det;
    } else {
      MSG("not implemented for DIM_OF_WORLD = %d in 3d\n", dow);
    }

    return(det);
  }




  void ElInfo3d::fillElInfo(int ichild, const ElInfo *elinfo_old)
  {
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    FUNCNAME("ElInfo3d::fillElInfo()");

    int el_type_local = 0;      /* el_type in {0,1,2} */
    int ochild = 0;             /* index of other child = 1-ichild */
    int *cv = NULL;             /* cv = child_vertex[el_type][ichild] */
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    const int (*cvg)[4] = NULL;     /* cvg = child_vertex[el_type] */
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    int *ce;                    /* ce = child_edge[el_type][ichild] */
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    Element *nb, *nbk;
    const FixVec<Element*, NEIGH> *neigh_old;
    Element *el_old = elinfo_old->element_;
    Flag fillFlag__local = elinfo_old->fillFlag_;
    DegreeOfFreedom *dof;
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    int ov = -1;
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    FixVec<Element*, NEIGH> *neigh_local;
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    Flag fill_opp_coords;
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    Mesh *mesh = elinfo_old->getMesh();

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    TEST_EXIT_DBG(el_old->getChild(0))("missing child?\n");  /* Kuni 22.08.96 */
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    element_ = const_cast<Element*>( el_old->getChild(ichild));
    macroElement_ = elinfo_old->macroElement_;
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    fillFlag_ = fillFlag__local;
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    parent_  = el_old;
    level_ = elinfo_old->level_ + 1;
    el_type = (( dynamic_cast<ElInfo3d*>(const_cast<ElInfo*>( elinfo_old)))->el_type + 1) % 3;
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    TEST_EXIT_DBG(element_)("missing child %d?\n", ichild);
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    if (fillFlag__local.isAnySet()) {
      el_type_local = ( dynamic_cast<ElInfo3d*>(const_cast<ElInfo*>( elinfo_old)))->getType();
      cvg = Tetrahedron::childVertex[el_type_local];
      cv = const_cast<int*>( cvg[ichild]);
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      ochild = 1 - ichild;
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    }

    int dow = Global::getGeo(WORLD);

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    if (fillFlag__local.isSet(Mesh::FILL_COORDS) || 
	fillFlag_.isSet(Mesh::FILL_DET) ||
	fillFlag_.isSet(Mesh::FILL_GRD_LAMBDA)) {
      for (int i = 0; i < 3; i++) {
	for (int j = 0; j < dow; j++) {
	  coord_[i][j] = elinfo_old->coord_[cv[i]][j];
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	}
      }
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      if (el_old->getNewCoord()) {
	coord_[3] = *(el_old->getNewCoord());
      } else {
	for (int j = 0; j < dow; j++) {
	  coord_[3][j] = (elinfo_old->coord_[0][j] + elinfo_old->coord_[1][j]) / 2;
	}
      }
    }
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    //   if(fillFlag_.isSet(Mesh::FILL_DET) || fillFlag_.isSet(Mesh::FILL_GRD_LAMBDA)) {
    //     det = calcGrdLambda(*Lambda);
    //   }


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    if (fillFlag__local.isSet(Mesh::FILL_NEIGH) || 
	fillFlag_.isSet(Mesh::FILL_OPP_COORDS)) {

      neigh_local = &neighbour_;
      neigh_old = &elinfo_old->neighbour_;
      fill_opp_coords.setFlags(fillFlag__local & Mesh::FILL_OPP_COORDS);
      
      /*----- nb[0] is other child --------------------------------------------*/
      
      /*    if (nb = el_old->child[ochild])   old version  */
      if (el_old->getChild(0)  &&  
	  (nb = const_cast<Element*>( el_old->getChild(ochild)))) {
	
	if (nb->getChild(0)) {         /* go down one level for direct neighbour */
	  if (fill_opp_coords.isAnySet()) {
	    if (nb->getNewCoord()) {
	      oppCoord_[0]= *(nb->getNewCoord());
	    } else {
	      int k = cvg[ochild][1];
	      for (int j = 0; j < dow; j++) {
		oppCoord_[0][j] = (elinfo_old->coord_[ochild][j] + elinfo_old->coord_[k][j]) / 2;
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	      }
	    }
	  }
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	  (*neigh_local)[0] = const_cast<Element*>( nb->getChild(1));
	  oppVertex_[0] = 3;
	} else {
	  if (fill_opp_coords.isAnySet()) {
	    for (int j = 0; j < dow; j++) {
	      oppCoord_[0][j] = elinfo_old->coord_[ochild][j];
	    }
	  }
	  (*neigh_local)[0] = nb;
	  oppVertex_[0] = 0;
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	}
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      } else {
	ERROR_EXIT("no other child");
	(*neigh_local)[0] = NULL;
      }
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      /*----- nb[1],nb[2] are childs of old neighbours nb_old[cv[i]] ----------*/
      
      for (int i = 1; i < 3; i++) {
	if ((nb = const_cast<Element*>( (*neigh_old)[cv[i]]))) {
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	  TEST_EXIT_DBG(nb->getChild(0))("nonconforming triangulation\n");
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	  int k;
	  for (k = 0; k < 2; k++) { /* look at both childs of old neighbour */
	    nbk = const_cast<Element*>( nb->getChild(k));
	    if (nbk->getDOF(0) == el_old->getDOF(ichild)) {
	      /* opp. vertex */
	      dof = const_cast<int*>(nb->getDOF(elinfo_old->oppVertex_[cv[i]])); 
	      
	      if (dof == nbk->getDOF(1)) {
		ov = 1;
		if (nbk->getChild(0)) {
		  if (fill_opp_coords.isAnySet()) {
		    if (nbk->getNewCoord()) {
		      oppCoord_[i] = *(nbk->getNewCoord());
		    } else {
		      for (int j = 0; j < dow; j++) {
			oppCoord_[i][j] = (elinfo_old->oppCoord_[cv[i]][j] + elinfo_old->coord_[ichild][j]) / 2;
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		      }
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		    }
		  }
		  (*neigh_local)[i] = nbk->getChild(0);
		  oppVertex_[i] = 3;
		  break;
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		}
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	      } else {
		if (dof != nbk->getDOF(2)) { 
		  ov = -1; 
		  break; 
		}
		ov = 2;
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	      }

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	      if (fill_opp_coords.isAnySet()) {
		for (int j = 0; j < dow; j++) {
		  oppCoord_[i][j] = elinfo_old->oppCoord_[cv[i]][j];
		}
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	      }
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	      (*neigh_local)[i] = nbk;
	      oppVertex_[i] = ov;
	      break;
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	    }
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	  } /* end for k */

	  // periodic ?
	  if (k == 2 || ov == -1) {
	    for (k = 0; k < 2; k++) {  /* look at both childs of old neighbour */
	      nbk = const_cast<Element*>( nb->getChild(k));
	      if (nbk->getDOF(0) == el_old->getDOF(ichild) ||
		  mesh->associated(nbk->getDOF(0, 0), el_old->getDOF(ichild, 0))) {
		/* opp. vertex */
		dof = const_cast<int*>(nb->getDOF(elinfo_old->oppVertex_[cv[i]])); 
		
		if (dof == nbk->getDOF(1) || 
		    mesh->associated(dof[0], nbk->getDOF(1, 0))) {
		  ov = 1;
		  if (nbk->getChild(0)) {
		    if (fill_opp_coords.isAnySet()) {
		      if (nbk->getNewCoord()) {
			oppCoord_[i] = *(nbk->getNewCoord());
		      } else {
			for (int j = 0; j < dow; j++) {
			  oppCoord_[i][j] = (elinfo_old->oppCoord_[cv[i]][j] + elinfo_old->coord_[ichild][j]) / 2;
			}
		      }
		    }
		    (*neigh_local)[i] = nbk->getChild(0);
		    oppVertex_[i] = 3;
		    break;
		  }
		} else {
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		  TEST_EXIT_DBG(dof == nbk->getDOF(2) || 
				mesh->associated(dof[0], nbk->getDOF(2, 0)))
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		    ("opp_vertex not found\n");
		  ov = 2;
		}
541

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		if (fill_opp_coords.isAnySet()) {
		  for (int j = 0; j < dow; j++) {
		    oppCoord_[i][j] = elinfo_old->oppCoord_[cv[i]][j];
		  }
		}
		(*neigh_local)[i] = nbk;
		oppVertex_[i] = ov;
		break;
	      }
	      
	    } /* end for k */
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	    TEST_EXIT_DBG(k < 2)("child not found with vertex\n");
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	  }
	} else {
	  (*neigh_local)[i] = NULL;
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	}
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      }  /* end for i */
      
      
      /*----- nb[3] is old neighbour neigh_old[ochild] ------------------------*/
      
      if (((*neigh_local)[3] = (*neigh_old)[ochild])) {
	oppVertex_[3] = elinfo_old->oppVertex_[ochild];

	if (fill_opp_coords.isAnySet()) {
	  for (int j = 0; j < dow; j++) {
	    oppCoord_[3][j] = elinfo_old->oppCoord_[ochild][j];
	  }
	}
      }
    }
573

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    if (fillFlag__local.isSet(Mesh::FILL_BOUND)) {
      for (int i = 0; i < 3; i++) {
	boundary_[10 + i] = elinfo_old->getBoundary(10 + cv[i]);
      }
      
      boundary_[13] = elinfo_old->getBoundary(4);
      
      boundary_[0] = INTERIOR;
      boundary_[1] = elinfo_old->getBoundary(cv[1]);
      boundary_[2] = elinfo_old->getBoundary(cv[2]);
      boundary_[3] = elinfo_old->getBoundary(ochild);
      
      ce = const_cast<int*>(Tetrahedron::childEdge[el_type_local][ichild]);
      for (int iedge = 0; iedge < 4; iedge++) {
	boundary_[mesh_->getGeo(FACE) + iedge] = 
	  elinfo_old->getBoundary(mesh_->getGeo(FACE)+ce[iedge]);
      }
      for (int iedge = 4; iedge < 6; iedge++) {
	int i = 5 - cv[iedge - 3];                /* old vertex opposite new edge */
	boundary_[mesh_->getGeo(FACE) + iedge] = elinfo_old->getBoundary(i);
      }
595

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      if (elinfo_old->getProjection(0) &&
	  elinfo_old->getProjection(0)->getType() == VOLUME_PROJECTION) {
	
	projection_[0] = elinfo_old->getProjection(0);      
      } else { // boundary projection
	projection_[0] = NULL;
	projection_[1] = elinfo_old->getProjection(cv[1]);
	projection_[2] = elinfo_old->getProjection(cv[2]);
	projection_[3] = elinfo_old->getProjection(ochild);
	
	for (int iedge = 0; iedge < 4; iedge++) {
	  projection_[mesh_->getGeo(FACE)+iedge] = 
	    elinfo_old->getProjection(mesh_->getGeo(FACE)+ce[iedge]);
609
	}
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	for (int iedge = 4; iedge < 6; iedge++) {
	  int i = 5 - cv[iedge - 3];                /* old vertex opposite new edge */
	  projection_[mesh_->getGeo(FACE) + iedge] = elinfo_old->getProjection(i);
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	}
      }
615
    }
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    if (fillFlag_.isSet(Mesh::FILL_ORIENTATION)) {
      orientation =
	( dynamic_cast<ElInfo3d*>(const_cast<ElInfo*>(elinfo_old)))->orientation 
	* Tetrahedron::childOrientation[el_type_local][ichild];
    }
  }

}