ElInfo2d.cc

#include "ElInfo2d.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 ElInfo2d::fillMacroInfo(const MacroElement * mel)
  {
    FUNCNAME("ElInfo::fillMacroInfo()");
 
    macroElement_ = const_cast<MacroElement*>(mel);
    element_  = const_cast<Element*>(mel->getElement());
    parent_  = NULL;
    level_ = 0;

    if (fillFlag_.isSet(Mesh::FILL_COORDS) || 
	fillFlag_.isSet(Mesh::FILL_DET)    ||
	fillFlag_.isSet(Mesh::FILL_GRD_LAMBDA)) {

      int vertices = mesh_->getGeo(VERTEX);
      for (int i = 0; i < vertices; i++) {
	coord_[i] = mel->coord[i];
      }
    }

    int neighbours = mesh_->getGeo(NEIGH);

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

      bool fill_opp_coords = (fillFlag_.isSet(Mesh::FILL_OPP_COORDS));
    
      for (int i = 0; i < neighbours; i++) {
	MacroElement *macroNeighbour = mel->getNeighbour(i);

	if (macroNeighbour) {
	  neighbour_[i] = macroNeighbour->getElement();
	  
	  Element *nb = const_cast<Element*>(neighbour_[i]);

	  int edgeNo = oppVertex_[i] = mel->getOppVertex(i);
	  if (nb->getFirstChild() && (edgeNo != 2)) {   // make nb nearest el.
	    if (edgeNo == 0) {
	      nb = neighbour_[i] = nb->getSecondChild();
	    } else {
	      nb = neighbour_[i] = nb->getFirstChild();
	    }

	    oppVertex_[i] = 2;

	    if (fill_opp_coords) {
	      if (nb->getNewCoord(-1)) {
		oppCoord_[i] = *(nb->getNewCoord());
	      } else {
		oppCoord_[i] = (macroNeighbour->coord[0] + macroNeighbour->coord[1]) * 0.5;
	      }	    	      
	      
	      switch (i) {
	      case 0:
		if (*(macroNeighbour->getElement()->getDOF(2)) == *(element_->getDOF(2))) {
		  neighbourCoord_[i][0] = macroNeighbour->coord[2];
		  neighbourCoord_[i][1] = macroNeighbour->coord[0];
		} else if (*(macroNeighbour->getElement()->getDOF(2)) == *(element_->getDOF(1))) {
		  neighbourCoord_[i][0] = macroNeighbour->coord[1];
		  neighbourCoord_[i][1] = macroNeighbour->coord[2];
		} else {
		  ERROR_EXIT("should not happen!\n");
		}
	
		neighbourCoord_[i][2] = oppCoord_[i];
		break;
		
	      case 1:
		if (*(macroNeighbour->getElement()->getDOF(2)) == *(element_->getDOF(2))) {
		  neighbourCoord_[i][0] = macroNeighbour->coord[1];
		  neighbourCoord_[i][1] = macroNeighbour->coord[2];
		} else if (*(macroNeighbour->getElement()->getDOF(2)) == *(element_->getDOF(0))) {
		  neighbourCoord_[i][0] = macroNeighbour->coord[2];
		  neighbourCoord_[i][1] = macroNeighbour->coord[0];
		} else {
		  ERROR_EXIT("should not happen!\n");
		}
		
		neighbourCoord_[i][2] = oppCoord_[i];
		break;
		
	      default:
		ERROR_EXIT("should not happen!\n");
		break;
	      }
	    }
	  } else {
	    if (fill_opp_coords) {
	      oppCoord_[i] = macroNeighbour->coord[edgeNo];

	      neighbourCoord_[i] = macroNeighbour->coord;	      
	    }
	  }
	} else {
	  neighbour_[i] = NULL;
        }
      }
    }
    
    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);
      }
    }
  }


  /****************************************************************************/
  /*   fill ElInfo structure for one child of an element   		    */
  /****************************************************************************/

  void ElInfo2d::fillElInfo(int ichild, const ElInfo *elinfo_old)
  {
    FUNCNAME("ElInfo::fillElInfo()");

    Element *elem = elinfo_old->element_;
    Element *nb;

    Flag fill_flag = elinfo_old->fillFlag_;

    TEST_EXIT_DBG(elem->getFirstChild())("no children?\n");
    element_ = const_cast<Element*>((ichild == 0) ? 
				    elem->getFirstChild() : 
				    elem->getSecondChild());
    TEST_EXIT_DBG(element_)("missing child %d?\n", ichild);

    macroElement_  = elinfo_old->macroElement_;
    fillFlag_ = fill_flag;
    parent_ = elem;
    level_ = elinfo_old->level_ + 1;

    int dow = Global::getGeo(WORLD);

    if (fillFlag_.isSet(Mesh::FILL_COORDS) || 
	fillFlag_.isSet(Mesh::FILL_DET)    ||
	fillFlag_.isSet(Mesh::FILL_GRD_LAMBDA)) {
      
      if (elem->getNewCoord(-1)) {
	coord_[2] = *(elem->getNewCoord());
      } else {
	coord_[2].setMidpoint(elinfo_old->coord_[0], elinfo_old->coord_[1]);
      }
      
      if (ichild == 0) {
	coord_[0] = elinfo_old->coord_[2];
	coord_[1] = elinfo_old->coord_[0];
      } else {
	coord_[0] = elinfo_old->coord_[1];
	coord_[1] = elinfo_old->coord_[2];
      }
    }

    bool fill_opp_coords = (fill_flag.isSet(Mesh::FILL_OPP_COORDS));

    if (fill_flag.isSet(Mesh::FILL_NEIGH) || fill_opp_coords) {     
      if (ichild == 0) {
	// Calculation of the neighbour 2, its oppCoords and the
	// cooresponding oppVertex.

	neighbour_[2] = elinfo_old->neighbour_[1];
	oppVertex_[2] = elinfo_old->oppVertex_[1];
	
	if (neighbour_[2] && fill_opp_coords) {
	  oppCoord_[2] = elinfo_old->oppCoord_[1];
	  neighbourCoord_[2] = elinfo_old->neighbourCoord_[1];
	}
	
	
	// Calculation of the neighbour 1, its oppCoords and the
	// cooresponding oppVertex.
	
	if (elem->getFirstChild()  &&  
	    elem->getSecondChild()->getFirstChild()  &&  
	    elem->getSecondChild()->getFirstChild()) {
	  
	  neighbour_[1] = elem->getSecondChild()->getSecondChild();
	  oppVertex_[1] = 2;
	  
	  if (fill_opp_coords) {
	    if (elem->getSecondChild()->getNewCoord(-1)) {
	      oppCoord_[1] = *(elem->getSecondChild()->getNewCoord());
	    } else {      
	      oppCoord_[1].setMidpoint(elinfo_old->coord_[1], 
				       elinfo_old->coord_[2]);
	    }

	    neighbourCoord_[1][0] = coord_[0];
	    neighbourCoord_[1][1] = coord_[2];
	    neighbourCoord_[1][2] = oppCoord_[1];  
	  }
	} else {
	  neighbour_[1] = elem->getSecondChild();
	  oppVertex_[1] = 0;

	  if (fill_opp_coords) {
	    oppCoord_[1] = elinfo_old->coord_[1];

	    neighbourCoord_[1][0] = elinfo_old->coord_[1];
	    neighbourCoord_[1][1] = elinfo_old->coord_[2];
	    neighbourCoord_[1][2] = coord_[2];
	  }
	}


	// Calculation of the neighbour 0, its oppCoords and the
	// cooresponding oppVertex.
	
	nb = elinfo_old->neighbour_[2];
	if (nb) {
	  TEST(elinfo_old->oppVertex_[2] == 2)("invalid neighbour\n"); 
	  TEST_EXIT_DBG(nb->getFirstChild())("missing first child?\n");
	  TEST_EXIT_DBG(nb->getSecondChild())("missing second child?\n");
	 
	  nb = nb->getSecondChild();

	  if (nb->getFirstChild()) {
	    oppVertex_[0] = 2;

	    if (fill_opp_coords) {
	      if (nb->getNewCoord(-1)) {
		oppCoord_[0] = *(nb->getNewCoord());
	      } else {
		oppCoord_[0].setMidpoint(elinfo_old->neighbourCoord_[2][1],
					 elinfo_old->neighbourCoord_[2][2]);
	      }

	      neighbourCoord_[0][0].setMidpoint(elinfo_old->neighbourCoord_[2][0],
						elinfo_old->neighbourCoord_[2][1]);
	      neighbourCoord_[0][1] = elinfo_old->neighbourCoord_[2][1];
	      neighbourCoord_[0][2] = oppCoord_[0];
	    }	   
 
	    nb = nb->getFirstChild();
	  } else {
	    oppVertex_[0] = 1;

	    if (fill_opp_coords) {
	      oppCoord_[0] = elinfo_old->oppCoord_[2];    

	      neighbourCoord_[0][0] = elinfo_old->neighbourCoord_[2][0];
	      neighbourCoord_[0][1] = elinfo_old->neighbourCoord_[2][2];
	      neighbourCoord_[0][2].setMidpoint(elinfo_old->neighbourCoord_[2][0],
						elinfo_old->neighbourCoord_[2][1]);
	    }
	  }
	}
	
	neighbour_[0] = nb;
      } else {   /* ichild == 1 */
	// Calculation of the neighbour 2, its oppCoords and the
	// cooresponding oppVertex.

	neighbour_[2] = elinfo_old->neighbour_[0];
	oppVertex_[2] = elinfo_old->oppVertex_[0];

	if (neighbour_[2] && fill_opp_coords) {
	  oppCoord_[2] = elinfo_old->oppCoord_[0];
	  neighbourCoord_[2] = elinfo_old->neighbourCoord_[0];
	}
	

	// Calculation of the neighbour 0, its oppCoords and the
	// cooresponding oppVertex.

	if (elem->getFirstChild()->getFirstChild()) {
	  neighbour_[0] = elem->getFirstChild()->getFirstChild();
	  oppVertex_[0] = 2;

	  if (fill_opp_coords) {
	    if (elem->getFirstChild()->getNewCoord(-1)) {
	      oppCoord_[0] = *(elem->getFirstChild()->getNewCoord());
	    } else {
	      oppCoord_[0].setMidpoint(elinfo_old->coord_[0], 
				       elinfo_old->coord_[2]);
	    }

	    neighbourCoord_[0][0] = coord_[2];
	    neighbourCoord_[0][1] = coord_[1];
	    neighbourCoord_[0][2] = oppCoord_[0];
	  }
	} else {
	  neighbour_[0] = elem->getFirstChild();
	  oppVertex_[0] = 1;

	  if (fill_opp_coords) {
	    oppCoord_[0] = elinfo_old->coord_[0];

	    neighbourCoord_[0][0] = elinfo_old->coord_[2];
	    neighbourCoord_[0][1] = elinfo_old->coord_[0];
	    neighbourCoord_[0][2] = coord_[2];
	  }
	}

	// Calculation of the neighbour 1, its oppCoords and the
	// cooresponding oppVertex.

	nb = elinfo_old->neighbour_[2];
	if (nb) {
	  TEST(elinfo_old->oppVertex_[2] == 2)("invalid neighbour\n"); 
	  TEST((nb = nb->getFirstChild()))("missing child?\n");

	  if (nb->getFirstChild()) {
	    oppVertex_[1] = 2;

	    if (fill_opp_coords) {
	      if (nb->getNewCoord(-1)) {
		oppCoord_[1] = *(nb->getNewCoord());
	      } else {
		oppCoord_[1].setMidpoint(elinfo_old->neighbourCoord_[2][0],
					 elinfo_old->neighbourCoord_[2][2]);
	      }

	      neighbourCoord_[1][0] = elinfo_old->neighbourCoord_[2][0];
	      neighbourCoord_[1][1].setMidpoint(elinfo_old->neighbourCoord_[2][0],
						elinfo_old->neighbourCoord_[2][1]);
	      neighbourCoord_[1][2] = oppCoord_[1];
	    }
	    nb = nb->getSecondChild();

	  } else {
	    oppVertex_[1] = 0;

	    if (fill_opp_coords) {
	      oppCoord_[1] = elinfo_old->oppCoord_[2];

	      neighbourCoord_[1][0] = elinfo_old->neighbourCoord_[2][2];	      
	      neighbourCoord_[1][1] = elinfo_old->neighbourCoord_[2][0];
	      neighbourCoord_[1][2].setMidpoint(elinfo_old->neighbourCoord_[2][0],
						elinfo_old->neighbourCoord_[2][1]);
	    }
	  }
	}
	neighbour_[1] = nb;
      } // if (ichild == 0) {} else
    } // if (fill_flag.isSet(Mesh::FILL_NEIGH) || fillFlag_.isSet(Mesh::FILL_OPP_COORDS))
    

    if (fill_flag.isSet(Mesh::FILL_BOUND)) {
      if (elinfo_old->getBoundary(2)) {
	boundary_[5] = elinfo_old->getBoundary(2);
      } else {
	boundary_[5] = INTERIOR;
      }

      if (ichild == 0) {
	boundary_[3] = elinfo_old->getBoundary(5);
	boundary_[4] = elinfo_old->getBoundary(3);
	boundary_[0] = elinfo_old->getBoundary(2);
	boundary_[1] = INTERIOR;
	boundary_[2] = elinfo_old->getBoundary(1);
      } else {
	boundary_[3] = elinfo_old->getBoundary(4);
	boundary_[4] = elinfo_old->getBoundary(5);
	boundary_[0] = INTERIOR;
	boundary_[1] = elinfo_old->getBoundary(2);
	boundary_[2] = elinfo_old->getBoundary(0);
      }

      if (elinfo_old->getProjection(0) && 
	  elinfo_old->getProjection(0)->getType() == VOLUME_PROJECTION) {
	
	projection_[0] = elinfo_old->getProjection(0);
      } else { // boundary projection
	if (ichild == 0) {
	  projection_[0] = elinfo_old->getProjection(2);
	  projection_[1] = NULL;
	  projection_[2] = elinfo_old->getProjection(1);
	} else {
	  projection_[0] = NULL;
	  projection_[1] = elinfo_old->getProjection(2);
	  projection_[2] = elinfo_old->getProjection(0);
	}
      }
    }
  }

  double ElInfo2d::calcGrdLambda(DimVec<WorldVector<double> >& grd_lam) const
  {
    FUNCNAME("ElInfo2d::calcGrdLambda()");
  
    WorldVector<double> e1, e2;
    double adet = 0.0;
    const WorldVector<double> v0 = coord_[0];

    testFlag(Mesh::FILL_COORDS);
    int dow = Global::getGeo(WORLD);
    int dim = mesh_->getDim();

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

    if (dow == 2) {
      double sdet = e1[0] * e2[1] - e1[1] * e2[0];
      adet = abs(sdet);

      if (adet < 1.0E-25) {
	MSG("abs(det) = %f\n", adet);
	for (int i = 0; i <= dim; i++)
	  for (int j = 0; j < dow; j++)
	    grd_lam[i][j] = 0.0;
      } else {
	double det1 = 1.0 / sdet;
	double a11 =  e2[1] * det1;       /* (a_ij) = A^{-T} */
	double a21 = -e2[0] * det1;
	double a12 = -e1[1] * det1;
	double a22 =  e1[0] * det1;
	
	grd_lam[1][0] = a11;
	grd_lam[1][1] = a21;
	grd_lam[2][0] = a12;
	grd_lam[2][1] = a22;
	grd_lam[0][0] = - grd_lam[1][0] - grd_lam[2][0];
	grd_lam[0][1] = - grd_lam[1][1] - grd_lam[2][1];
      }
    } else {
      WorldVector<double> normal;
    
      vectorProduct(e1, e2, normal);

      adet = norm(&normal);

      if (adet < 1.0E-15) {
	MSG("abs(det) = %lf\n", adet);
	for (int i = 0; i <= dim; i++)
	  for (int j = 0; j < dow; j++)
	    grd_lam[i][j] = 0.0;
      } else {
	vectorProduct(e2, normal, grd_lam[1]);
	vectorProduct(normal, e1, grd_lam[2]);
      
	double adet2 = 1.0 / (adet * adet);

	for (int i = 0; i < dow; i++) {
	  grd_lam[1][i] *= adet2;
	  grd_lam[2][i] *= adet2;
	}

	grd_lam[0][0] = - grd_lam[1][0] - grd_lam[2][0];
	grd_lam[0][1] = - grd_lam[1][1] - grd_lam[2][1];
	grd_lam[0][2] = - grd_lam[1][2] - grd_lam[2][2];
      }
    }

    return adet;
  }

  const int ElInfo2d::worldToCoord(const WorldVector<double>& xy,
				   DimVec<double>* lambda) const
  {
    FUNCNAME("ElInfo::worldToCoord()");

    TEST_EXIT_DBG(lambda)("lambda must not be NULL\n");

    DimVec<WorldVector<double> > edge(mesh_->getDim(), NO_INIT);
    WorldVector<double> x; 
    static DimVec<double> vec(mesh_->getDim(), NO_INIT);

    int dim = mesh_->getDim();
    int dimOfWorld = Global::getGeo(WORLD);

    for (int j = 0; j < dimOfWorld; j++) {
      double x0 = coord_[dim][j];
      x[j] = xy[j] - x0;
      for (int i = 0; i < dim; i++)
	edge[i][j] = coord_[i][j] - x0;
    }
  
    double det  = edge[0][0] * edge[1][1] - edge[0][1] * edge[1][0]; 
    double det0 =       x[0] * edge[1][1] -       x[1] * edge[1][0]; 
    double det1 = edge[0][0] * x[1]       - edge[0][1] * x[0]; 

    if (abs(det) < DBL_TOL) {
      ERROR("det = %le; abort\n", det);
      for (int i = 0; i <= dim; i++) 
	(*lambda)[i] = 1.0/dim;
      return 0;
    }

    (*lambda)[0] = det0 / det;
    (*lambda)[1] = det1 / det;
    (*lambda)[2] = 1.0 - (*lambda)[0] - (*lambda)[1];

    int k = -1;
    double lmin = 0.0;
    for (int i = 0; i <= dim; i++) {
      if ((*lambda)[i] < -1.E-5) {
	if ((*lambda)[i] < lmin) {
	  k = i;
	  lmin = (*lambda)[i];
	}
      }
    }

    return k;
  }


  double ElInfo2d::getNormal(int side, WorldVector<double> &normal) const
  {
    FUNCNAME("ElInfo::getNormal()");

    int i0 = (side + 1) % 3;
    int i1 = (side + 2) % 3;

    if (Global::getGeo(WORLD) == 2){
      normal[0] = coord_[i1][1] - coord_[i0][1];
      normal[1] = coord_[i0][0] - coord_[i1][0];
    } else { // dow == 3
      WorldVector<double> e0, e1,e2, elementNormal;

      e0 = coord_[i1]; 
      e0 -= coord_[i0];
      e1 = coord_[i1]; 
      e1 -= coord_[side];
      e2 = coord_[i0]; 
      e2 -= coord_[side];

      vectorProduct(e1, e2, elementNormal);
      vectorProduct(elementNormal, e0, normal);
    }

    double det = norm(&normal);

    TEST_EXIT_DBG(det > 1.e-30)("det = 0 on face %d\n", side);

    normal *= 1.0 / det;
    
    return(det);
  }


  /****************************************************************************/
  /*  calculate the normal of the element for dim of world = dim + 1          */
  /*  return the absulute value of the determinant from the                   */
  /*  transformation to the reference element                                 */
  /****************************************************************************/
  double ElInfo2d::getElementNormal( WorldVector<double> &elementNormal) const
  {
    FUNCNAME("ElInfo::getElementNormal()");

    TEST_EXIT_DBG(Global::getGeo(WORLD) == 3)(" element normal only well defined for  DIM_OF_WORLD = DIM + 1 !!");

    WorldVector<double> e0 = coord_[1] - coord_[0];
    WorldVector<double> e1 = coord_[2] - coord_[0];

    vectorProduct(e0, e1, elementNormal);

    double det = norm(&elementNormal);

    TEST_EXIT_DBG(det > 1.e-30)("det = 0");

    elementNormal *= 1.0 / det;
    
    return(det);
  }
}