Lagrange.cc 179 KB
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#include "Mesh.h"
#include "Element.h"
#include "Lagrange.h"
#include "DOFAdmin.h"
#include "RCNeighbourList.h"
#include "DOFVector.h"
#include "Traverse.h"
#include "Line.h"
#include "Triangle.h"
#include "Tetrahedron.h"
#include "Parametric.h"

#include <stdio.h>
#include <algorithm>
#include <list>

namespace AMDiS {

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  std::vector<DimVec<double>* > Lagrange::baryDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  DimVec<int>* Lagrange::ndofDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  int Lagrange::nBasFctsDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  std::vector<BasFctType*> Lagrange::phiDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  std::vector<GrdBasFctType*> Lagrange::grdPhiDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  std::vector<D2BasFctType*> Lagrange::D2PhiDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
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  std::list<Lagrange*> Lagrange::allBasFcts;
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  Lagrange::Lagrange(int dim, int degree)
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    : BasisFunction(std::string("Lagrange"), dim, degree)
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  {
    // set name
    char dummy[3];
    sprintf(dummy, "%d", dim);
    name.append(dummy);
    name.append(" ");
    sprintf(dummy, "%d", degree);  
    name.append(dummy);

    // set nDOF
    setNDOF();

    // set barycentric coordinates
    setBary();

    // set function pointer
    setFunctionPointer();

  }

  Lagrange::~Lagrange()
  {
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    std::cout << "DELETE LAGRANGE" << std::endl;
    std::cout << "BARY ADR = " << bary << std::endl;
    for (int i = 0; i < static_cast<int>(bary->size()); i++) {
      if ((*bary)[i]) {
	std::cout << "DEL ADR = " << (*bary)[i] << std::endl;
	DELETE (*bary)[i];
	(*bary)[i] = NULL;
      }
    }
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  }

  Lagrange* Lagrange::getLagrange(int dim, int degree)
  {
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    std::list<Lagrange*>::iterator it;
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    for (it = allBasFcts.begin(); it != allBasFcts.end(); it++) {
      if (((*it)->dim == dim) && ((*it)->degree == degree)) {
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	return (*it);
      } 
    }

    Lagrange* newLagrange = NEW Lagrange(dim, degree);
    allBasFcts.push_back(newLagrange);
    return newLagrange;
  }

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  void Lagrange::clear()
  {    
    std::list<Lagrange*>::iterator it;
    for (it = allBasFcts.begin(); it != allBasFcts.end(); it++) {
      DELETE *it;
    }
  }

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  void Lagrange::setFunctionPointer()
  {
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    if (static_cast<int>(phiDimDegree[dim][degree].size()) == 0) {
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      // for all positions
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      for (int i = 0; i < dim+1; i++) {
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	// no vertex dofs for degree 0 ?
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	if (degree == 0 && i != dim) 
	  continue;
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	// for all vertices/edges/...
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	for (int j = 0; j < Global::getGeo(INDEX_OF_DIM(i, dim),dim); j++) {
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	  // for all dofs at this position
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	  for (int k = 0; k < (*nDOF)[INDEX_OF_DIM(i, dim)]; k++) {
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	    // basis function
	    phiDimDegree[dim][degree].push_back(NEW Phi(this, 
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							INDEX_OF_DIM(i ,dim),j, k));
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	    // gradients
	    grdPhiDimDegree[dim][degree].push_back(NEW GrdPhi(this, 
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							      INDEX_OF_DIM(i, dim),
							      j, k));
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	    // D2-Matrices
	    D2PhiDimDegree[dim][degree].push_back(NEW D2Phi(this, 
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							    INDEX_OF_DIM(i, dim),
							    j, k));
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	  }
	}
      }
    }
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    phi = &phiDimDegree[dim][degree];
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    grdPhi = &grdPhiDimDegree[dim][degree];
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    d2Phi = &D2PhiDimDegree[dim][degree];
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    switch(degree) {
    case 0:
      refineInter_fct = refineInter0;
      coarseRestr_fct = coarseRestr0;
      coarseInter_fct = coarseInter0;  // not yet implemented
      break;
    case 1:
      refineInter_fct = refineInter1;
      coarseRestr_fct = coarseRestr1;
      coarseInter_fct = NULL;  // not yet implemented
      break;
    case 2:
      switch(dim) {
      case 1:
	refineInter_fct = refineInter2_1d;
	coarseRestr_fct = NULL; // not yet implemented
	coarseInter_fct = coarseInter2_1d;
	break;
      case 2: 
	refineInter_fct = refineInter2_2d;
	coarseRestr_fct = coarseRestr2_2d;
	coarseInter_fct = coarseInter2_2d;
	break;
      case 3:
	refineInter_fct = refineInter2_3d;
	coarseRestr_fct = coarseRestr2_3d;
	coarseInter_fct = coarseInter2_3d;
	break;
      default: ERROR_EXIT("invalid dim\n");
      }
      break;
    case 3:
      switch(dim) {
      case 1:
	refineInter_fct = refineInter3_1d;
	coarseRestr_fct = coarseRestr3_1d;
	coarseInter_fct = coarseInter3_1d;
	break;
      case 2: 
	refineInter_fct = refineInter3_2d;
	coarseRestr_fct = coarseRestr3_2d;
	coarseInter_fct = coarseInter3_2d;
	break;
      case 3:
	refineInter_fct = refineInter3_3d;
	coarseRestr_fct = coarseRestr3_3d;
	coarseInter_fct = coarseInter3_3d;
	break;
      default: ERROR_EXIT("invalid dim\n");
      }
      break;
    case 4:
      switch(dim) {
      case 1: 
	refineInter_fct = refineInter4_1d;
	coarseRestr_fct = coarseRestr4_1d;
	coarseInter_fct = coarseInter4_1d;
	break;
      case 2:
	refineInter_fct = refineInter4_2d;
	coarseRestr_fct = coarseRestr4_2d;
	coarseInter_fct = coarseInter4_2d;
	break;
      case 3:
	refineInter_fct = refineInter4_3d;
	coarseRestr_fct = coarseRestr4_3d;
	coarseInter_fct = coarseInter4_3d;
	break;
      default: ERROR_EXIT("invalid dim\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

  void Lagrange::setNDOF()
  {
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    if (static_cast<int>(baryDimDegree[dim][degree].size()) == 0) {
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      ndofDimDegree[dim][degree] = NEW DimVec<int>(dim, DEFAULT_VALUE, 0);

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      if (degree != 0) {
	(*ndofDimDegree[dim][degree])[VERTEX] = 1;
      } else {
	(*ndofDimDegree[dim][degree])[VERTEX] = 0;
      }
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      for (int i = 1; i < dim + 1; i++) {
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	nBasFcts = getNumberOfDOFs(i, degree);
	(*ndofDimDegree[dim][degree])[INDEX_OF_DIM(i, dim)] = nBasFcts;
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	for (int j = 0; j < i; j++) {
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	  (*ndofDimDegree[dim][degree])[INDEX_OF_DIM(i, dim)] -= 
	    Global::getGeo(INDEX_OF_DIM(j, dim), i) * 
	    (*ndofDimDegree[dim][degree])[INDEX_OF_DIM(j, dim)];
	}
      }
      nBasFctsDimDegree[dim][degree] = nBasFcts;
    }
    nBasFcts = nBasFctsDimDegree[dim][degree];
    nDOF = ndofDimDegree[dim][degree];
  } 

  DimVec<double> *Lagrange::getCoords(int i) const
  {
    return (*bary)[i];
  }

  void Lagrange::setVertices(int dim, int degree, 
			     GeoIndex position, int positionIndex, int nodeIndex, 
			     int** vertices)
  {
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    TEST_EXIT_DBG((*vertices) == NULL)("vertices != NULL\n");
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    int dimOfPosition = DIM_OF_INDEX(position, dim);

    *vertices = GET_MEMORY(int, dimOfPosition + 1);

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    if ((degree == 4) && (dimOfPosition==1)) {
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      (*vertices)[(nodeIndex != 2) ? 0 : 1] = 
	Global::getReferenceElement(dim)->getVertexOfPosition(position,
							      positionIndex,
							      0);
      (*vertices)[(nodeIndex != 2) ? 1 : 0] = 
	Global::getReferenceElement(dim)->getVertexOfPosition(position,
							      positionIndex, 
							      1);
    } else if ((degree==4) && (dimOfPosition==2)) {
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      for (int i = 0; i < dimOfPosition + 1; i++) {
	(*vertices)[(i+dimOfPosition*nodeIndex) % (dimOfPosition + 1)] = 
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	  Global::getReferenceElement(dim)->getVertexOfPosition(position,
								positionIndex,
								i);
      }    
    } else {
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      for (int i = 0; i < dimOfPosition + 1; i++) {
	(*vertices)[(i+nodeIndex) % (dimOfPosition + 1)] = 
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	  Global::getReferenceElement(dim)->getVertexOfPosition(position,
								positionIndex,
								i);
      }
    }
  }

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  Lagrange::Phi::Phi(Lagrange* owner, 
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		     GeoIndex position, 
		     int positionIndex, 
		     int nodeIndex)
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    : vertices(NULL)
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  {
    FUNCNAME("Lagrange::Phi::Phi")
      // get relevant vertices
      Lagrange::setVertices(owner->getDim(), 
			    owner->getDegree(), 
			    position, 
			    positionIndex, 
			    nodeIndex, 
			    &vertices);
  
    // set function pointer
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    switch (owner->getDegree()) {
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    case 0:
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      switch (position) {
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      case CENTER:
	func = phi0c;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 1:
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      switch (position) {
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      case VERTEX:
	func = phi1v;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 2:
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      switch (position) {
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      case VERTEX:
	func = phi2v;
	break;
      case EDGE:
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	TEST_EXIT_DBG(owner->getDim() > 1)("no edge in 1d\n");
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	func = phi2e;
	break;
      case CENTER:
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	TEST_EXIT_DBG(owner->getDim() == 1)("no center dofs for dim != 1\n");
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	func = phi2e;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 3:
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      switch (position) {
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      case VERTEX:
	func = phi3v;
	break;
      case EDGE:
	func = phi3e;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = phi3f;
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  func = phi3e;
	  break;
	case 2:
	  func = phi3f;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 4:
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      switch (position) {
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      case VERTEX:
	func = phi4v;
	break;
      case EDGE:
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	if (nodeIndex == 1)
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	  func = phi4e1;
	else 
	  func = phi4e0;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = phi4f;      
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  if(nodeIndex == 1)
	    func = phi4e1;
	  else 
	    func = phi4e0;
	  break;
	case 2:
	  func = phi4f;
	  break;
	case 3:
	  func = phi4c;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

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  Lagrange::Phi::~Phi() { 
    DELETE [] vertices; 
  }
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  Lagrange::GrdPhi::GrdPhi(Lagrange* owner, 
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			   GeoIndex position, 
			   int positionIndex, 
			   int nodeIndex)
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    : vertices(NULL)
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  {
    // get relevant vertices
    Lagrange::setVertices(owner->getDim(), 
			  owner->getDegree(), 
			  position, 
			  positionIndex, 
			  nodeIndex, 
			  &vertices);

    // set function pointer
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    switch (owner->getDegree()) {
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    case 0:
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      switch (position) {
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      case CENTER:
	func = grdPhi0c;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 1:
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      switch (position) {
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      case VERTEX:
	func = grdPhi1v;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 2:
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      switch (position) {
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      case VERTEX:
	func = grdPhi2v;
	break;
      case EDGE:
	func = grdPhi2e;
	break;
      case CENTER:
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	TEST_EXIT_DBG(owner->getDim() == 1)("no center dofs for dim != 1\n");
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	func = grdPhi2e;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 3:
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      switch (position) {
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      case VERTEX:
	func = grdPhi3v;
	break;
      case EDGE:
	func = grdPhi3e;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = grdPhi3f;
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  func = grdPhi3e;
	  break;
	case 2:
	  func = grdPhi3f;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 4:
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      switch (position) {
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      case VERTEX:
	func = grdPhi4v;
	break;
      case EDGE:
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	if (nodeIndex == 1)
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	  func = grdPhi4e1;
	else 
	  func = grdPhi4e0;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = grdPhi4f;      
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
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	  if (nodeIndex == 1)
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	    func = grdPhi4e1;
	  else 
	    func = grdPhi4e0;
	  break;
	case 2:
	  func = grdPhi4f;
	  break;
	case 3:
	  func = grdPhi4c;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

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  Lagrange::GrdPhi::~GrdPhi() { 
    DELETE [] vertices; 
  }
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  Lagrange::D2Phi::D2Phi(Lagrange* owner, 
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			 GeoIndex position, 
			 int positionIndex, 
			 int nodeIndex)
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    : vertices(NULL)
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  {
    // get relevant vertices
    Lagrange::setVertices(owner->getDim(), 
			  owner->getDegree(), 
			  position, 
			  positionIndex, 
			  nodeIndex, 
			  &vertices);

    // set function pointer
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    switch (owner->getDegree()) {
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    case 0:
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      switch (position) {
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      case CENTER:
	func = D2Phi0c;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 1:
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      switch (position) {
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      case VERTEX:
	func = D2Phi1v;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 2:
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      switch (position) {
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      case VERTEX:
	func = D2Phi2v;
	break;
      case EDGE:
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	TEST_EXIT_DBG(owner->getDim() > 1)("no edge in 1d\n");
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	func = D2Phi2e;
	break;
      case CENTER:
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	TEST_EXIT_DBG(owner->getDim() == 1)("no center dofs for dim != 1\n");
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	func = D2Phi2e;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 3:
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      switch (position) {
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      case VERTEX:
	func = D2Phi3v;
	break;
      case EDGE:
	func = D2Phi3e;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = D2Phi3f;
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  func = D2Phi3e;
	  break;
	case 2:
	  func = D2Phi3f;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 4:
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      switch (position) {
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      case VERTEX:
	func = D2Phi4v;
	break;
      case EDGE:
	if(nodeIndex == 1)
	  func = D2Phi4e1;
	else 
	  func = D2Phi4e0;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = D2Phi4f;      
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
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	  if (nodeIndex == 1)
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	    func = D2Phi4e1;
	  else 
	    func = D2Phi4e0;
	  break;
	case 2:
	  func = D2Phi4f;
	  break;
	case 3:
	  func = D2Phi4c;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

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  Lagrange::D2Phi::~D2Phi() { 
    DELETE [] vertices; 
  }
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  void Lagrange::createCoords(int* coordInd, 
			      int numCoords, 
			      int dimIndex, 
			      int rest, 
			      DimVec<double>* vec)
  {
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    if (vec == NULL) {
      vec = NEW DimVec<double>(dim, DEFAULT_VALUE, 0.0);
    }
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    if (dimIndex == numCoords - 1) {
      (*vec)[coordInd[dimIndex]] = double(rest) / degree;
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      DimVec<double>* newCoords = NEW DimVec<double>(*vec);
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      std::cout << "BARY ADR = " << bary << std::endl;
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      bary->push_back(newCoords);
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      std::cout << "ADD ADR = " << newCoords << std::endl;
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    } else {
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      for (int i = rest - 1; i >= 1; i--) {
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	(*vec)[coordInd[dimIndex]] = double(i) / degree;
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	createCoords(coordInd, numCoords, dimIndex + 1, rest - i, vec);
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      }
    }
  }

  void Lagrange::setBary()
  {
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    bary = &baryDimDegree[dim][degree];
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    if (static_cast<int>(bary->size()) == 0) {
      for (int i = 0; i <= dim; i++) { // for all positions
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	int partsAtPos = Global::getGeo(INDEX_OF_DIM(i, dim), dim);
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	for (int j = 0; j < partsAtPos; j++) { // for all vertices/edges/faces/...
	  int *coordInd = GET_MEMORY(int, i + 1); // indices of relevant coords
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	  for (int k = 0; k < i + 1; k++) { 
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	    coordInd[k] = Global::getReferenceElement(dim)->
	      getVertexOfPosition(INDEX_OF_DIM(i,dim), j, k);
	  }
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	  createCoords(coordInd, i + 1, 0, degree);
	  FREE_MEMORY(coordInd, int, i + 1);
	  if(static_cast<int>(bary->size()) == nBasFcts) return;
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	}
      }
    }
  }

  int Lagrange::getNumberOfDOFs(int dim, int degree)
  {
    int result = 0;
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    for (int i = 0; i <= degree; i++) {
      result += fac(dim - 1 + i) / (fac(i) * fac(dim - 1));
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    }
    return result;
  }


  const DegreeOfFreedom *Lagrange::getDOFIndices(const Element *el, 
						 const DOFAdmin& admin,
						 DegreeOfFreedom *idof) const
  {
    WARNING("depricated: use getLocalIndices() instead\n");
    return getLocalIndices(el, &admin, idof);
  }

  int* Lagrange::orderOfPositionIndices(const Element* el, 
					GeoIndex position, 
					int positionIndex) const
  {
    static int sortedVertex = 0;
    static int sortedEdgeDeg2 = 0;
    static int sortedEdgeDeg3[2][2] = {{0, 1}, {1, 0}};
    static int sortedEdgeDeg4[2][3] = {{0, 1, 2}, {2, 1, 0}};
    static int sortedFaceDeg3 = 0;
    static int sortedFaceDeg4[7][3] = {{0,0,0}, {0,2,1}, {1,0,2}, {0,1,2},
				       {2,1,0}, {1,2,0}, {2,0,1}};
    static int sortedCenterDeg4 = 0;

    int dimOfPosition = DIM_OF_INDEX(position, dim);

    // vertex
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    if (dimOfPosition == 0) {
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      return &sortedVertex;
    }

    // edge
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    if ((dimOfPosition == 1) && (degree == 2)) {
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      return &sortedEdgeDeg2;
    }
      
    int vertex[3];
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    int** dof = const_cast<int**>(el->getDOF());
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    int verticesOfPosition = dimOfPosition + 1;

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    for (int i = 0; i < verticesOfPosition; i++) {
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      vertex[i] = Global::getReferenceElement(dim)->
	getVertexOfPosition(position, positionIndex, i);
    }

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    if (dimOfPosition == 1) {
      if (degree == 3) {
	if (dof[vertex[0]][0] < dof[vertex[1]][0]) {
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	  return sortedEdgeDeg3[0];
	} else {
	  return sortedEdgeDeg3[1];
	}
      } else { // degree == 4
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	if (dof[vertex[0]][0] < dof[vertex[1]][0]) {
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	  return sortedEdgeDeg4[0];
	} else {
	  return sortedEdgeDeg4[1];
	}
      }
    }

    // face
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    if (dimOfPosition == 2) {
      if (degree == 3) {
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	return &sortedFaceDeg3;
      } else {  // degree == 4!
	int no = 0;
	const Element *refElem = Global::getReferenceElement(dim);

	if (dof[refElem->getVertexOfPosition(position, positionIndex, 0)][0] <
	    dof[refElem->getVertexOfPosition(position, positionIndex, 1)][0]) 
	  no++;

	if (dof[refElem->getVertexOfPosition(position, positionIndex, 1)][0] <
	    dof[refElem->getVertexOfPosition(position, positionIndex, 2)][0])
	  no += 2;

	if (dof[refElem->getVertexOfPosition(position, positionIndex, 2)][0] <
	    dof[refElem->getVertexOfPosition(position, positionIndex, 0)][0])
	  no += 4;

	return sortedFaceDeg4[no];
      }
    }

    // center
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    if ((dimOfPosition == 3) && (degree == 4)) {
      return &sortedCenterDeg4;
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    } 

    ERROR_EXIT("should not be reached\n");
    return NULL;
  }

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  void Lagrange::getBound(const ElInfo* el_info, BoundaryType* bound) const
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  {
    el_info->testFlag(Mesh::FILL_BOUND);

    // boundaries
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    int index = 0;
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    int offset = 0;
    BoundaryType boundaryType;
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    for (int i = dim - 1; i > 0; i--)
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      offset += Global::getGeo(INDEX_OF_DIM(i, dim), dim);
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    for (int i = 0; i < dim; i++) {
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      int jto = offset + Global::getGeo(INDEX_OF_DIM(i, dim), dim);
      for (int j = offset; j < jto; j++) {
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	boundaryType = el_info->getBoundary(j);
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	int kto = (*nDOF)[INDEX_OF_DIM(i, dim)];
	for (int k = 0; k < kto; k++) {
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	  bound[index++] = boundaryType;
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	}
      }
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      offset -= Global::getGeo(INDEX_OF_DIM(i + 1, dim), dim);
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    }

    // interior nodes in the center
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    for (int i = 0; i < (*nDOF)[CENTER]; i++) {
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      bound[index++] = INTERIOR;
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    }

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    TEST_EXIT_DBG(index == nBasFcts)("found not enough boundarys\n");
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  }


  const double* Lagrange::interpol(const ElInfo *el_info, 
				   int no, const int *b_no, 
				   AbstractFunction<double, WorldVector<double> > *f, 
				   double *vec)
  {
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    FUNCNAME("Lagrange::interpol()");

    static double *inter = NULL;
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    static int inter_size = 0;

    double *rvec =  NULL;

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    if (vec) {
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      rvec = vec;
    } else {
      if(inter) FREE_MEMORY(inter, double, nBasFcts);
      inter = GET_MEMORY(double, nBasFcts);
      inter_size = nBasFcts;
      rvec = inter;
    } 

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    WorldVector<double> x;
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    el_info->testFlag(Mesh::FILL_COORDS);
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    if (b_no) {
      if (no <= 0  ||  no > getNumber()) {
	ERROR("something is wrong, doing nothing\n");
	rvec[0] = 0.0;
	return(const_cast<const double *>( rvec));
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      }
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      for (int i = 0; i < no; i++) {
	if (b_no[i] < Global::getGeo(VERTEX, dim)) {
	  rvec[i] = (*f)(el_info->getCoord(b_no[i]));
	} else {
	  el_info->coordToWorld(*(*bary)[b_no[i]], &x);
	  rvec[i] = (*f)(x);
	}
      }
    } else {
      int vertices = Global::getGeo(VERTEX, dim);
      for (int i = 0; i < vertices; i++)
	rvec[i] = (*f)(el_info->getCoord(i));
      for (int i = vertices; i < nBasFcts; i++) {
	el_info->coordToWorld(*(*bary)[i], &x);
	rvec[i] = (*f)(x);
      }
    }  
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    return(const_cast<const double *>( rvec));
  }

  const WorldVector<double>* 
  Lagrange::interpol(const ElInfo *el_info, int no, 
		     const int *b_no,
		     AbstractFunction<WorldVector<double>, WorldVector<double> > *f, 
		     WorldVector<double> *vec)
  {
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    FUNCNAME("*Lagrange::interpol_d()");

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    static WorldVector<double> *inter;
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    WorldVector<double> *rvec = 
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      vec ? vec : (inter?inter:inter= NEW WorldVector<double>[getNumber()]);
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    WorldVector<double> x;
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    el_info->testFlag(Mesh::FILL_COORDS);
  
    int vertices = Global::getGeo(VERTEX, dim);

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    if (b_no) {
      if (no <= 0  ||  no > getNumber()) {
	ERROR("something is wrong, doing nothing\n");
	for (int i = 0; i < dow; i++)
	  rvec[0][i] = 0.0;
	return(const_cast<const WorldVector<double> *>( rvec));
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      }
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      for (int i = 0; i < no; i++) {
	if (b_no[i] < Global::getGeo(VERTEX, dim)) {
	  rvec[i] = (*f)(el_info->getCoord(b_no[i]));
	} else {
	  el_info->coordToWorld(*(*bary)[b_no[i]], &x);
	  rvec[i] = (*f)(x);
	}
      }
    } else {
      for (int i = 0; i < vertices; i++)
	rvec[i] = (*f)(el_info->getCoord(i));
      for (int i = vertices; i < nBasFcts; i++) {
	el_info->coordToWorld(*(*bary)[i], &x);
	rvec[i] = (*f)(x);
      }
    }  
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    return(const_cast<const WorldVector<double> *>( rvec));
  }


  const DegreeOfFreedom *Lagrange::getLocalIndices(const Element* el,
						   const DOFAdmin *admin,
						   DegreeOfFreedom *indices) const
  {
    static DegreeOfFreedom *localVec = NULL;
    static int localVecSize = 0;

    const DegreeOfFreedom **dof = el->getDOF();
    const int *indi;
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    int nrDOFs, n0, node0, num = 0;
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    GeoIndex posIndex;

    DegreeOfFreedom* result;
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    if (indices) {
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      result = indices;
    } else {
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      if (localVec) 
	FREE_MEMORY(localVec, DegreeOfFreedom, localVecSize);
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      localVec = GET_MEMORY(DegreeOfFreedom, nBasFcts);
      localVecSize = nBasFcts;
      result = localVec;
    }
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    for (int pos = 0, j = 0; pos <= dim; pos++) {
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      posIndex = INDEX_OF_DIM(pos, dim);
      nrDOFs = admin->getNumberOfDOFs(posIndex);

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      if (nrDOFs) {
	n0 = admin->getNumberOfPreDOFs(posIndex);
	node0 = admin->getMesh()->getNode(posIndex);
	num = Global::getGeo(posIndex, dim);

	for (int i = 0; i < num; node0++, i++) {
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	  indi = orderOfPositionIndices(el, posIndex, i);

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	  for (int k = 0; k < nrDOFs; k++) {
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	    result[j++] = dof[node0][n0 + indi[k]];
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	  }
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	}
      }
    }
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    return result;
  }

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  void Lagrange::getLocalIndicesVec(const Element* el,
				    const DOFAdmin *admin,
				    Vector<DegreeOfFreedom> *indices) const
  {
    if (indices->getSize() < nBasFcts) {
      indices->resize(nBasFcts);
    }

    getLocalIndices(el, admin, &((*indices)[0]));
  }

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  void Lagrange::l2ScpFctBas(Quadrature *q,
			     AbstractFunction<WorldVector<double>, WorldVector<double> >* f,
			     DOFVector<WorldVector<double> >* fh)
  {
    ERROR_EXIT("not yet\n");
  }

  void Lagrange::l2ScpFctBas(Quadrature *q,
			     AbstractFunction<double, WorldVector<double> >* f,
			     DOFVector<double>* fh)
  {
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    FUNCNAME("Lagrange::l2ScpFctBas()");

    TraverseStack stack;
    double *wdetf_qp = NULL;
    double val, det;
    WorldVector<double> x;
    int iq, j;
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    const DegreeOfFreedom  *dof;
    const Parametric *parametric;

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    TEST_EXIT_DBG(fh)("no DOF_REAL_VEC fh\n");
    TEST_EXIT_DBG(fh->getFESpace())("no fe_space in DOF_REAL_VEC %s\n",
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				fh->getName().c_str());
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    TEST_EXIT_DBG(fh->getFESpace()->getBasisFcts() == this)("wrong basis fcts for fh\n");
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    Mesh* mesh = fh->getFESpace()->getMesh();
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    int n_phi = nBasFcts;
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    if (!q) {
      q = Quadrature::provideQuadrature(dim, 2 * degree - 2);
    }
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    const FastQuadrature *quad_fast = FastQuadrature::provideFastQuadrature(this, *q, INIT_PHI);
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    if ((parametric = mesh->getParametric())) {
      ERROR_EXIT("not yet implemented\n");
    } else {
      wdetf_qp = GET_MEMORY(double, q->getNumPoints());
    }
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    ElInfo *el_info = stack.traverseFirst(mesh, -1, Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS);
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    int numPoints = q->getNumPoints();
     
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    while (el_info) {
      dof = getLocalIndices(el_info->getElement(), (fh->getFESpace()->getAdmin()), NULL);      
      det = el_info->getDet();
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      for (iq = 0; iq < numPoints; iq++) {
	el_info->coordToWorld(q->getLambda(iq), &x);
	wdetf_qp[iq] = q->getWeight(iq)*det*((*f)(x));
      }
      
      for (j = 0; j < n_phi; j++) {
	for (val = iq = 0; iq < numPoints; iq++)
	  val += quad_fast->getPhi(iq,j)*wdetf_qp[iq];
	(*fh)[dof[j]] += val;
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      }

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      el_info = stack.traverseNext(el_info);
    }

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    FREE_MEMORY(wdetf_qp, double, q->getNumPoints());

    return;
  }


  // ===== refineInter functions =====

  void  Lagrange::refineInter0(DOFIndexed<double> *drv, RCNeighbourList* list, int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter0()");
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    if (n < 1) 
      return;

    int n0 = drv->getFESpace()->getAdmin()->getNumberOfPreDOFs(CENTER);
    Element *el = list->getElement(0);
    int node = drv->getFESpace()->getMesh()->getNode(CENTER);
    DegreeOfFreedom dof0 = el->getDOF(node, n0);           /* Parent center */
    DegreeOfFreedom dof_new = el->getChild(0)->getDOF(node, n0);  /*      newest vertex is center */
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    (*drv)[dof_new] = (*drv)[dof0];
    dof_new = el->getChild(1)->getDOF(node, n0);  /*      newest vertex is center */
    (*drv)[dof_new] = (*drv)[dof0];
  }

  void  Lagrange::refineInter1(DOFIndexed<double> *drv, RCNeighbourList* list, int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter1_1d()");
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    if (n < 1) 
      return;
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    int dim = drv->getFESpace()->getMesh()->getDim();
    int n0 = drv->getFESpace()->getAdmin()->getNumberOfPreDOFs(VERTEX);
    Element *el = list->getElement(0);
    DegreeOfFreedom dof0 = el->getDOF(0, n0);           /* 1st endpoint of refinement edge */
    DegreeOfFreedom dof1 = el->getDOF(1, n0);           /* 2nd endpoint of refinement edge */
    DegreeOfFreedom dof_new = el->getChild(0)->getDOF(dim, n0);  /*      newest vertex is DIM */
    (*drv)[dof_new] = 0.5 * ((*drv)[dof0] + (*drv)[dof1]);
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  }

  void Lagrange::refineInter2_1d(DOFIndexed<double> *drv, RCNeighbourList* list, int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter2_1d()");
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    if (n < 1) 
      return;
    
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
    const DegreeOfFreedom *pdof = basFct->getLocalIndices(el, admin, NULL);
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    int node = drv->getFESpace()->getMesh()->getNode(VERTEX);        
    int n0 = admin->getNumberOfPreDOFs(VERTEX);
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    /****************************************************************************/
    /*  newest vertex of child[0] and child[1]                                  */
    /****************************************************************************/

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    DegreeOfFreedom cdof = el->getChild(0)->getDOF(node+1, n0);  /*      newest vertex is DIM */
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    (*drv)[cdof] = (*drv)[pdof[2]];

    node = drv->getFESpace()->getMesh()->getNode(CENTER);        
    n0 = admin->getNumberOfPreDOFs(CENTER);

    /****************************************************************************/
    /*  midpoint of edge on child[0] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(0)->getDOF(node, n0); 
    (*drv)[cdof] = 
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      0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] + 0.75 * (*drv)[pdof[2]];
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    /****************************************************************************/
    /*  midpoint of edge on child[1] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(1)->getDOF(node, n0); 
    (*drv)[cdof] = 
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      -0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]] + 0.75 * (*drv)[pdof[2]];
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    return;
  }

  void Lagrange::refineInter2_2d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter2_2d()");
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    if (n < 1) 
      return;
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    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
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    Element *el = list->getElement(0);
    const DegreeOfFreedom *pdof = basFct->getLocalIndices(el, admin, NULL);
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    int node = drv->getFESpace()->getMesh()->getNode(VERTEX);        
    int n0 = admin->getNumberOfPreDOFs(VERTEX);
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    /****************************************************************************/
    /*  newest vertex of child[0] and child[1]                                  */
    /****************************************************************************/

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    DegreeOfFreedom cdof = el->getChild(0)->getDOF(node+2, n0);  /*      newest vertex is DIM */
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    (*drv)[cdof] = (*drv)[pdof[5]];

    node = drv->getFESpace()->getMesh()->getNode(EDGE);        
    n0 = admin->getNumberOfPreDOFs(EDGE);

    /****************************************************************************/
    /*  midpoint of edge on child[0] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(0)->getDOF(node, n0); 
    (*drv)[cdof] = 
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      0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] + 0.75 * (*drv)[pdof[5]];
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    /****************************************************************************/
    /* node in the common edge of child[0] and child[1]                         */
    /****************************************************************************/

    cdof = el->getChild(0)->getDOF(node+1, n0); 
    (*drv)[cdof] =
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      -0.125 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[5]]
      + 0.5 * ((*drv)[pdof[3]] + (*drv)[pdof[4]]);
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    /****************************************************************************/
    /*  midpoint of edge on child[1] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(1)->getDOF(node+1, n0); 
    (*drv)[cdof] = 
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      -0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]]  + 0.75 * (*drv)[pdof[5]];

    if (n > 1) {
      /****************************************************************************/
      /*  adjust the value at the midpoint of the common edge of neigh's children */
      /****************************************************************************/
      el = list->getElement(1);
      pdof = basFct->getLocalIndices(el, admin, NULL);
      
      cdof = el->getChild(0)->getDOF(node+1, n0); 
      (*drv)[cdof] = 
	-0.125 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[5]]
	+ 0.5 * ((*drv)[pdof[3]] + (*drv)[pdof[4]]);
    }
1183
1184
1185
1186
1187
1188
  }

  void Lagrange::refineInter2_3d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
1189
    FUNCNAME("Lagrange::refineInter2_3d()");
1190

1191
1192
    if (n < 1) 
      return;
1193

1194
1195
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1196

1197
    DegreeOfFreedom pdof[10];
1198
1199
    basFct->getLocalIndices(el, admin, pdof);

1200
1201
    int node0 = drv->getFESpace()->getMesh()->getNode(EDGE);
    int n0 = admin->getNumberOfPreDOFs(EDGE);
1202
1203
1204
1205
1206

    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/

1207
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1208
1209
1210

    (*drv)[cdof[3]] = ((*drv)[pdof[4]]);
    (*drv)[cdof[6]] = 
1211
1212
      (0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] 
       + 0.75 * (*drv)[pdof[4]]);
1213
    (*drv)[cdof[8]] = 
1214
1215
      (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
       + 0.5 * ((*drv)[pdof[5]] + (*drv)[pdof[7]]));
1216
    (*drv)[cdof[9]] = 
1217
1218
      (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
       + 0.5 * ((*drv)[pdof[6]] + (*drv)[pdof[8]]));
1219
1220
1221
1222
1223

    /****************************************************************************/
    /*  values on child[1]                                                      */
    /****************************************************************************/
  
1224
    DegreeOfFreedom cdofi = el->getChild(1)->getDOF(node0 + 2, n0);
1225
    (*drv)[cdofi] = 
1226
1227
      (-0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]] 
       + 0.75 * (*drv)[pdof[4]]);
1228
1229
1230
1231
1232

    /****************************************************************************/
    /*   adjust neighbour values                                                */
    /****************************************************************************/
  
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
    for (int i = 1; i < n; i++) {
      el = list->getElement(i);
      basFct->getLocalIndices(el, admin, pdof);
      
      int lr_set = 0;
      if (list->getNeighbourElement(i, 0) && list->getNeighbourNr(i, 0) < i)
	lr_set = 1;
      
      if (list->getNeighbourElement(i, 1) && list->getNeighbourNr(i, 1) < i)
	lr_set += 2;
      
      TEST_EXIT(lr_set)("no values set on both neighbours\n");
      
      /****************************************************************************/
      /*  values on child[0]                                                      */
      /****************************************************************************/
      
      switch (lr_set) {
      case 1:
	cdofi = el->getChild(0)->getDOF(node0+4, n0);      
	(*drv)[cdofi] = 
	  (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
	   + 0.5 * ((*drv)[pdof[5]] + (*drv)[pdof[7]]));
	break;
      case 2:
	cdofi = el->getChild(0)->getDOF(node0+5, n0);      
	(*drv)[cdofi] = 
	  (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
	   + 0.5 * ((*drv)[pdof[6]] + (*drv)[pdof[8]]));
	
1263
      }
1264
    }
1265
1266
1267
1268
1269
1270
1271
    return;
  }

  void Lagrange::refineInter3_1d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
1272
    FUNCNAME("Lagrange::refineInter3_1d()");
1273

1274
1275
    if (n < 1) 
      return;
1276

1277
1278
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1279

1280
    DegreeOfFreedom *pdof = GET_MEMORY(DegreeOfFreedom, basFct->getNumber());
1281
1282
1283
1284
1285
    basFct->getLocalIndices(el, admin, pdof);
  
    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/
1286
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1287
1288

    (*drv)[cdof[2]] = 
1289
1290
      (-0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       + 0.5625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1291
    (*drv)[cdof[3]] = 
1292
1293
1294
1295
      (0.3125 * ((*drv)[pdof[0]] - (*drv)[pdof[8]]) + 0.0625 * (*drv)[pdof[1]]
       + 0.9375 * (*drv)[pdof[7]]);
    (*drv)[cdof[4]] = (*drv)[pdof[7]];
    (*drv)[cdof[5]] = (*drv)[pdof[9]];
1296
    (*drv)[cdof[6]] =  
1297
1298
1299
1300
      (0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]])
       - 0.25 * ((*drv)[pdof[3]] + (*drv)[pdof[6]])
       + 0.5 * ((*drv)[pdof[4]] + (*drv)[pdof[5]] + (*drv)[pdof[9]])
       - 0.0625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1301
    (*drv)[cdof[9]] = 
1302
1303
1304
      (0.0625 * (-(*drv)[pdof[0]] + (*drv)[pdof[1]]) - 0.125 * (*drv)[pdof[3]]
       + 0.375 * (*drv)[pdof[6]] + 0.1875 * ((*drv)[pdof[7]] - (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);