Operator.cc 58.1 KB
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#include "Operator.h"
#include "ElInfo.h"
#include "Assembler.h"
#include "FixVec.h"
#include "DOFVector.h"
#include "ElementMatrix.h"
#include "ElementVector.h"
#include "Quadrature.h"
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#include "OpenMP.h"
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namespace AMDiS {

  const Flag OperatorTerm::PW_CONST = 1;
  const Flag OperatorTerm::SYMMETRIC = 2;

  const Flag Operator::MATRIX_OPERATOR = 1;
  const Flag Operator::VECTOR_OPERATOR = 2;


  int Operator::getQuadratureDegree(int order, FirstOrderType firstOrderType) 
  {
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    std::vector<OperatorTerm*>* terms = NULL;
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    int myRank = omp_get_thread_num();
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    switch(order) {
    case 0:
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      terms = &zeroOrder[myRank];
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      break;
    case 1:
      if (firstOrderType == GRD_PHI)
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	terms = &firstOrderGrdPhi[myRank];
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      else 
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	terms = &firstOrderGrdPsi[myRank];
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      break;
    case 2:
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      terms = &secondOrder[myRank];
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      break;
    }

    const BasisFunction *psi = rowFESpace->getBasisFcts();
    const BasisFunction *phi = colFESpace->getBasisFcts();

    int psiDegree = psi->getDegree();
    int phiDegree = phi->getDegree();
    int maxTermDegree = 0;

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    for (int i = 0; i < static_cast<int>( terms->size()); i++) {
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      OperatorTerm *term = (*terms)[i];
      maxTermDegree = max(maxTermDegree, term->degree);
    }
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    return psiDegree + phiDegree - order + maxTermDegree;
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  }


  void OperatorTerm::setSymmetric(bool symm)
  {
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    if (symm) {
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      properties.setFlag(SYMMETRIC);
    } else {
      properties.unsetFlag(SYMMETRIC);   
    }
  }

  bool OperatorTerm::isSymmetric()
  {
    return properties.isSet(SYMMETRIC);
  }

  void OperatorTerm::lalt(const DimVec<WorldVector<double> >& Lambda,
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			  const WorldMatrix<double>& matrix,
			  DimMat<double>& LALt,
			  bool symm,
			  double factor)
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  {
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    int i, j, k, l;
    static const int dimOfWorld = Global::getGeo(WORLD);
    int dim = LALt.getNumRows() - 1;
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    double val = 0.0;

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    if (symm) {
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      for (i = 0; i <= dim; i++) {
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	val = 0.0;
	for (k = 0; k < dimOfWorld; k++)
	  for (l = 0; l < dimOfWorld; l++)
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	    val += Lambda[i][k] * matrix[k][l] * Lambda[i][l];
	val *= factor;
	LALt[i][i] += val;
	for (j = i+1; j <= dim; j++) {
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	  val = 0.0;
	  for (k = 0; k < dimOfWorld; k++)
	    for (l = 0; l < dimOfWorld; l++)
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	      val += Lambda[i][k] * matrix[k][l] * Lambda[j][l];
	  val *= factor;
	  LALt[i][j] += val;
	  LALt[j][i] += val;
	}
      }    
    } else {	
      for (i = 0; i <= dim; i++) {
	for (j = 0; j <= dim; j++) {
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	  val = 0.0;
	  for (k = 0; k < dimOfWorld; k++)
	    for (l = 0; l < dimOfWorld; l++) 
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	      val += Lambda[i][k] * matrix[k][l] * Lambda[j][l];
	  val *= factor;
	  LALt[i][j] += val;
	}
      }    
    }      
  }

  void OperatorTerm::lalt_kl(const DimVec<WorldVector<double> >& Lambda,
			     int k, int l,
			     DimMat<double>&            LALt,
			     double                     factor)
  {
    int i, j;
    int dim = LALt.getNumRows() - 1;

    for (i = 0; i <= dim; i++)
      for (j = 0; j <= dim; j++)
	LALt[i][j] += factor * Lambda[i][k] * Lambda[j][l];
  }

  void OperatorTerm::l1lt(const DimVec<WorldVector<double> >& Lambda,
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			  DimMat<double>& LALt,
			  double factor)
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  {
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    static const int dimOfWorld = Global::getGeo(WORLD);
    int dim = LALt.getNumRows() - 1;
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    double val = 0.0;

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    for (int i = 0; i <= dim; i++) {
      val = 0.0;
      for (int k = 0; k < dimOfWorld; k++)
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	val += Lambda[i][k] * Lambda[i][k];
      val *= factor;
      LALt[i][i] += val;
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      for (int j = i + 1; j <= dim; j++) {
	val = 0.0;
	for (int k = 0; k < dimOfWorld; k++)
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	  val += Lambda[i][k] * Lambda[j][k];
	val *= factor;
	LALt[i][j] += val;
	LALt[j][i] += val;
      }    
    }      
  }

  void OperatorTerm::lb(const DimVec<WorldVector<double> >& Lambda,
			const WorldVector<double>&         b,
			DimVec<double>&            Lb,
			double                     factor)
  {
    int                  i, j;
    int                  dim        = Lb.getSize() - 1;
    static const int     dimOfWorld = Global::getGeo(WORLD);

    double val = 0.0;

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    for (i = 0; i <= dim; i++) {
      for (val = j = 0; j < dimOfWorld; j++)
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	val += Lambda[i][j] * b[j];
      val *= factor;
      Lb[i] += val;
    }    
  }

  Operator::Operator(Flag operatorType,
		     const FiniteElemSpace *rowFESpace_,
		     const FiniteElemSpace *colFESpace_)
    : rowFESpace(rowFESpace_), 
      colFESpace(colFESpace_ ? colFESpace_ : rowFESpace_),
      type(operatorType), 
      fillFlag(Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | 
	       Mesh::FILL_DET | Mesh::FILL_GRD_LAMBDA),
      uhOld(NULL),
      optimized(true)
  {
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    int maxThreads = omp_get_max_threads();

    assembler.resize(maxThreads);
    secondOrder.resize(maxThreads);
    firstOrderGrdPsi.resize(maxThreads);
    firstOrderGrdPhi.resize(maxThreads);
    zeroOrder.resize(maxThreads);

    for (int i = 0; i < maxThreads; i++) {
      assembler[i] = NULL;
      secondOrder[i].resize(0);
      firstOrderGrdPsi[i].resize(0);
      firstOrderGrdPhi[i].resize(0);
      zeroOrder[i].resize(0);
    }

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    nRow = rowFESpace->getBasisFcts()->getNumber();
    nCol = colFESpace->getBasisFcts()->getNumber();
  };

  void Operator::setUhOld(const DOFVectorBase<double> *uhOld_)
  {
    uhOld = uhOld_;
  }

  void Operator::getElementMatrix(const ElInfo *elInfo, 
				  ElementMatrix *userMat, 
				  double factor)
  {
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    int myRank = omp_get_thread_num();

    if (!assembler[myRank]) {
      initAssembler(myRank, NULL, NULL, NULL, NULL);
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    }

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    assembler[myRank]->calculateElementMatrix(elInfo, userMat, factor);
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  }

  void Operator::getElementVector(const ElInfo *elInfo, 
				  ElementVector *userVec, 
				  double factor)
  {
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    int myRank = omp_get_thread_num();

    if (!assembler[myRank]) {
      initAssembler(myRank, NULL, NULL, NULL, NULL);
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    }

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    assembler[myRank]->calculateElementVector(elInfo, userVec, factor);
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  }

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  void Operator::initAssembler(int rank,
			       Quadrature *quad2,
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			       Quadrature *quad1GrdPsi,
			       Quadrature *quad1GrdPhi,
			       Quadrature *quad0) 
  {
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    if (!assembler[rank])
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      if (optimized) {
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	assembler[rank] = 
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	  NEW OptimizedAssembler(this,
				 quad2, quad1GrdPsi, quad1GrdPhi, quad0,
				 rowFESpace, colFESpace);
      } else {
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	assembler[rank] = 
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	  NEW StandardAssembler(this,
				quad2, quad1GrdPsi, quad1GrdPhi, quad0,
				rowFESpace, colFESpace);
      }
  }


  void MatrixFct_SOT::initElement(const ElInfo* elInfo, 
				  SubAssembler* subAssembler,
				  Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
  }
 
  void VecAtQP_SOT::initElement(const ElInfo* elInfo, 
				SubAssembler* subAssembler,
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				Quadrature* quad) 
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  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
  }
 
  void CoordsAtQP_SOT::initElement(const ElInfo* elInfo, 
				   SubAssembler* subAssembler,
				   Quadrature *quad) 
  {
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }

  void MatrixGradient_SOT::initElement(const ElInfo* elInfo, 
				       SubAssembler* subAssembler,
				       Quadrature *quad) 
  {
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
  }

  void FctGradient_SOT::initElement(const ElInfo* elInfo, 
				    SubAssembler* subAssembler,
				    Quadrature *quad) 
  {
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
  }

  void VecAndGradientAtQP_SOT::initElement(const ElInfo* elInfo, 
					   SubAssembler* subAssembler,
					   Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
  }

  void VecAndCoordsAtQP_SOT::initElement(const ElInfo* elInfo, 
					 SubAssembler* subAssembler,
					 Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }
 
  void MatrixGradientAndCoords_SOT::initElement(const ElInfo* elInfo, 
						SubAssembler* subAssembler,
						Quadrature *quad) 
  {
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);  
  }

  void VecGradCoordsAtQP_SOT::initElement(const ElInfo* elInfo, 
					  SubAssembler* subAssembler,
					  Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);  
  }

  void VecAtQP_FOT::initElement(const ElInfo* elInfo, 
				SubAssembler* subAssembler,
				Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
  }

  void CoordsAtQP_FOT::initElement(const ElInfo* elInfo, 
				   SubAssembler* subAssembler,
				   Quadrature *quad) 
  {
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }

  void VecCoordsAtQP_FOT::initElement(const ElInfo* elInfo, 
				      SubAssembler* subAssembler,
				      Quadrature *quad) 
  {
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }

  void VectorGradient_FOT::initElement(const ElInfo* elInfo, 
				       SubAssembler* subAssembler,
				       Quadrature *quad) 
  {
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
  }

  void VectorFct_FOT::initElement(const ElInfo* elInfo, 
				  SubAssembler* subAssembler,
				  Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
  }
 
  void VecFctAtQP_FOT::initElement(const ElInfo* elInfo, 
				   SubAssembler* subAssembler,
				   Quadrature *quad) 
  {
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }

  void VecAtQP_ZOT::initElement(const ElInfo* elInfo, 
				SubAssembler* subAssembler,
				Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
  }

  void MultVecAtQP_ZOT::initElement(const ElInfo* elInfo, 
				    SubAssembler* subAssembler,
				    Quadrature *quad) 
  {
    vecAtQPs1 = subAssembler->getVectorAtQPs(vec1, elInfo, quad);
    vecAtQPs2 = subAssembler->getVectorAtQPs(vec2, elInfo, quad);
  }

  void Vec2AtQP_ZOT::initElement(const ElInfo* elInfo, 
				 SubAssembler* subAssembler,
				 Quadrature *quad) 
  {
    vecAtQPs1 = subAssembler->getVectorAtQPs(vec1, elInfo, quad);
    vecAtQPs2 = subAssembler->getVectorAtQPs(vec2, elInfo, quad);
  }

  void VecAndCoordsAtQP_ZOT::initElement(const ElInfo* elInfo, 
					 SubAssembler* subAssembler,
					 Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }
 
  void FctGradientCoords_ZOT::initElement(const ElInfo* elInfo, 
					  SubAssembler* subAssembler,
					  Quadrature *quad) 
  {
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }
 
  void VecGradCoordsAtQP_ZOT::initElement(const ElInfo* elInfo, 
					  SubAssembler* subAssembler,
					  Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }
 
  void VecAndGradAtQP_ZOT::initElement(const ElInfo* elInfo, 
				       SubAssembler* subAssembler,
				       Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
  }
 
  void VecAndGradVecAtQP_ZOT::initElement(const ElInfo* elInfo, 
					  SubAssembler* subAssembler,
					  Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    gradAtQPs = subAssembler->getGradientsAtQPs(vecGrd, elInfo, quad);
  }

  void VecAndGradVec2AtQP_ZOT::initElement(const ElInfo* elInfo, 
					   SubAssembler* subAssembler,
					   Quadrature *quad) 
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
    grad1AtQPs = subAssembler->getGradientsAtQPs(vecGrd1, elInfo, quad);
    grad2AtQPs = subAssembler->getGradientsAtQPs(vecGrd2, elInfo, quad);
  }
 
  void FctGradient_ZOT::initElement(const ElInfo* elInfo, 
				    SubAssembler* subAssembler,
				    Quadrature *quad) 
  {
    gradAtQPs = subAssembler->getGradientsAtQPs(vec, elInfo, quad);
  }
 
  void CoordsAtQP_ZOT::initElement(const ElInfo* elInfo, 
				   SubAssembler* subAssembler,
				   Quadrature *quad) {
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }

  void MatrixFct_SOT::getLALt(const ElInfo *elInfo, int numPoints, DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lalt(Lambda, (*matrixFct)(vecAtQPs[iq]), *(LALt[iq]), symmetric, 1.0);
    }
  }

  void VecAtQP_SOT::getLALt(const ElInfo *elInfo, int numPoints, DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1lt(Lambda, *(LALt[iq]), (*f)(vecAtQPs[iq]));
    }
  }
  
  void CoordsAtQP_SOT::getLALt(const ElInfo *elInfo, int numPoints, DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1lt(Lambda, (*LALt[iq]), (*g)(coordsAtQPs[iq]));
    }
  }

  void MatrixGradient_SOT::getLALt(const ElInfo *elInfo, int numPoints, DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lalt(Lambda, (*f)(gradAtQPs[iq]), (*LALt[iq]), symmetric, 1.0);
    }
  }

  void FctGradient_SOT::getLALt(const ElInfo *elInfo, int numPoints, DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1lt(Lambda, *(LALt[iq]), (*f)(gradAtQPs[iq]));
    }
  }
  
  void VecAndGradientAtQP_SOT::getLALt(const ElInfo *elInfo, int numPoints,
				       DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1lt(Lambda, *(LALt[iq]), (*f)(vecAtQPs[iq], gradAtQPs[iq]));
    }
  }

  void VecAndCoordsAtQP_SOT::getLALt(const ElInfo *elInfo, int numPoints, DimMat<double> **LALt)
    const { const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1lt(Lambda, *(LALt[iq]), (*f)(vecAtQPs[iq], coordsAtQPs[iq]));
    }
  }
  
  void MatrixGradientAndCoords_SOT::getLALt(const ElInfo *elInfo, int numPoints,
					    DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lalt(Lambda, (*f)(gradAtQPs[iq], coordsAtQPs[iq]), (*LALt[iq]), symmetric, 1.0);
    }
  }

  void VecGradCoordsAtQP_SOT::getLALt(const ElInfo *elInfo, int numPoints,
				      DimMat<double> **LALt) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1lt(Lambda, *(LALt[iq]), (*f)(vecAtQPs[iq], gradAtQPs[iq], coordsAtQPs[iq]));
    }
  }

  void VecAtQP_FOT::getLb(const ElInfo *elInfo, int numPoints, VectorOfFixVecs<DimVec<double> >& Lb) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
      if (b)
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	lb(Lambda, *b, Lb[iq], (*f)(vecAtQPs[iq]));
      else
	l1(Lambda, Lb[iq], (*f)(vecAtQPs[iq]));
    }
  }

  void CoordsAtQP_FOT::getLb(const ElInfo *elInfo, int numPoints, VectorOfFixVecs<DimVec<double> >& Lb) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      l1(Lambda, Lb[iq], (*g)(coordsAtQPs[iq]));
    }
  }

  void VecCoordsAtQP_FOT::getLb(const ElInfo *elInfo, int numPoints,
				VectorOfFixVecs<DimVec<double> >& Lb) const
  {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
      lb(Lambda, b, Lb[iq], (*g)(coordsAtQPs[iq]));
    }
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  }

  void VectorGradient_FOT::getLb(const ElInfo *elInfo, int numPoints, VectorOfFixVecs<DimVec<double> >& Lb) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    if (f) {
      for (int iq = 0; iq < numPoints; iq++) {
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	lb(Lambda, (*f)(gradAtQPs[iq]), Lb[iq], 1.0);
      }
    } else {
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      for (int iq = 0; iq < numPoints; iq++) {
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	lb(Lambda, gradAtQPs[iq], Lb[iq], 1.0);
      }
    }
  }

  void VectorFct_FOT::getLb(const ElInfo *elInfo, int numPoints, VectorOfFixVecs<DimVec<double> >& Lb) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lb(Lambda, (*vecFct)(vecAtQPs[iq]), Lb[iq], 1.0);
    }
  }

  void VecFctAtQP_FOT::getLb(const ElInfo *elInfo, int numPoints, VectorOfFixVecs<DimVec<double> >& Lb) const {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lb(Lambda, (*g)(coordsAtQPs[iq]), Lb[iq], 1.0);
    }
  }

  void VecAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    if (f) {
      for (int iq = 0; iq < numPoints; iq++) {
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	C[iq] += (*f)(vecAtQPs[iq]);
      }
    } else {
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      for (int iq = 0; iq < numPoints; iq++) {
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	C[iq] += vecAtQPs[iq];
      }
    }
  }

  void VecAtQP_ZOT::eval(int numPoints,
			 const double              *uhAtQP,
			 const WorldVector<double> *grdUhAtQP,
			 const WorldMatrix<double> *D2UhAtQP,
			 double *result,
			 double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
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      result[iq] += fac * (*f)(vecAtQPs[iq]) * uhAtQP[iq];
    }
  }

  void MultVecAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f1)(vecAtQPs1[iq]) * (*f2)(vecAtQPs2[iq]);
    }
  }

  void MultVecAtQP_ZOT::eval(int numPoints,
			     const double              *uhAtQP,
			     const WorldVector<double> *grdUhAtQP,
			     const WorldMatrix<double> *D2UhAtQP,
			     double *result,
			     double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
      result[iq] += fac * (*f1)(vecAtQPs1[iq]) * 
	(*f2)(vecAtQPs2[iq]) * uhAtQP[iq];
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    }
  }

  void Vec2AtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(vecAtQPs1[iq], vecAtQPs2[iq]);
    }
  }

  void Vec2AtQP_ZOT::eval(int numPoints,
			  const double              *uhAtQP,
			  const WorldVector<double> *grdUhAtQP,
			  const WorldMatrix<double> *D2UhAtQP,
			  double *result,
			  double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
      result[iq] += fac * (*f)(vecAtQPs1[iq], vecAtQPs2[iq]) * 
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	uhAtQP[iq];
    }
  }

  void VecAndCoordsAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(vecAtQPs[iq], coordsAtQPs[iq]);
    }
  }

  void VecAndCoordsAtQP_ZOT::eval(int numPoints,
				  const double              *uhAtQP,
				  const WorldVector<double> *grdUhAtQP,
				  const WorldMatrix<double> *D2UhAtQP,
				  double *result,
				  double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
      result[iq] += fac * (*f)(vecAtQPs[iq], coordsAtQPs[iq]) * 
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	uhAtQP[iq];
    }
  }

 
  void FctGradientCoords_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(gradAtQPs[iq], coordsAtQPs[iq]);
    }
  }
 
  void FctGradientCoords_ZOT::eval(int numPoints,
				   const double              *uhAtQP,
				   const WorldVector<double> *grdUhAtQP,
				   const WorldMatrix<double> *D2UhAtQP,
				   double *result,
				   double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
      result[iq] += fac * (*f)(gradAtQPs[iq], coordsAtQPs[iq]) * 
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	uhAtQP[iq];
    }
  }

  void VecGradCoordsAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(vecAtQPs[iq], gradAtQPs[iq], coordsAtQPs[iq]);
    }
  }
 
  void VecGradCoordsAtQP_ZOT::eval(int numPoints,
				   const double              *uhAtQP,
				   const WorldVector<double> *grdUhAtQP,
				   const WorldMatrix<double> *D2UhAtQP,
				   double *result,
				   double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
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      result[iq] += 
	fac * 
	(*f)(vecAtQPs[iq], gradAtQPs[iq], coordsAtQPs[iq]) * 
	uhAtQP[iq];
    }
  }

  void VecAndGradAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(vecAtQPs[iq], gradAtQPs[iq]);
    }
  }
 
  void VecAndGradAtQP_ZOT::eval(int numPoints,
				const double              *uhAtQP,
				const WorldVector<double> *grdUhAtQP,
				const WorldMatrix<double> *D2UhAtQP,
				double *result,
				double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
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      result[iq] += 
	fac * 
	(*f)(vecAtQPs[iq], gradAtQPs[iq]) * 
	uhAtQP[iq];
    }
  }

  void VecAndGradVecAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const 
  { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(vecAtQPs[iq], gradAtQPs[iq]);
    }
  }
 
  void VecAndGradVecAtQP_ZOT::eval(int numPoints,
				   const double              *uhAtQP,
				   const WorldVector<double> *grdUhAtQP,
				   const WorldMatrix<double> *D2UhAtQP,
				   double *result,
				   double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
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      result[iq] += 
	fac * 
	(*f)(vecAtQPs[iq], gradAtQPs[iq]) * 
	uhAtQP[iq];
    }
  }

  void VecAndGradVec2AtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(vecAtQPs[iq], grad1AtQPs[iq], grad2AtQPs[iq]);
    }
  }
 
  void VecAndGradVec2AtQP_ZOT::eval(int numPoints,
				    const double              *uhAtQP,
				    const WorldVector<double> *grdUhAtQP,
				    const WorldMatrix<double> *D2UhAtQP,
				    double *result,
				    double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
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      result[iq] += 
	fac * 
	(*f)(vecAtQPs[iq], grad1AtQPs[iq], grad2AtQPs[iq]) * 
	uhAtQP[iq];
    }
  }

  void FctGradient_ZOT::getC(const ElInfo *, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
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      C[iq] += (*f)(gradAtQPs[iq]);
    }
  }
 
  void FctGradient_ZOT::eval(int numPoints,
			     const double              *uhAtQP,
			     const WorldVector<double> *grdUhAtQP,
			     const WorldMatrix<double> *D2UhAtQP,
			     double *result,
			     double fac) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
      result[iq] += fac * (*f)(gradAtQPs[iq]) * uhAtQP[iq];
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    }
  }

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  void CoordsAtQP_ZOT::getC(const ElInfo *elInfo, int numPoints, double *C) const { 
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    for (int iq = 0; iq < numPoints; iq++) {
      C[iq] += (*g)(coordsAtQPs[iq]);
    }
  }

  void CoordsAtQP_ZOT::eval(int numPoints,
			    const double              *uhAtQP,
			    const WorldVector<double> *grdUhAtQP,
			    const WorldMatrix<double> *D2UhAtQP,
			    double *result,
			    double fac) const
  {
    for (int iq = 0; iq < numPoints; iq++) {
      result[iq] += fac * (*g)(coordsAtQPs[iq]) * uhAtQP[iq];
    }
  }

  void MatrixFct_SOT::eval(int numPoints,
			   const double              *uhAtQP,
			   const WorldVector<double> *grdUhAtQP,
			   const WorldMatrix<double> *D2UhAtQP,
			   double *result,
			   double factor) const
  {
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    int dow = Global::getGeo(WORLD);
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    for (int iq = 0; iq < numPoints; iq++) {
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      double resultQP = 0.0;

      WorldMatrix<double> A = (*matrixFct)(vecAtQPs[iq]);

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      if (D2UhAtQP) {
	for (int i = 0; i < dow; i++) {
	  for (int j = 0; j < dow; j++) {
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	    resultQP += A[i][j] * D2UhAtQP[iq][j][i];
	  }
	}
      }

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      if (grdUhAtQP) {
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	resultQP += (*divFct)(A) * grdUhAtQP[iq];
      }

      result[iq] += resultQP * factor;
    }
  }

  void MatrixFct_SOT::weakEval(int numPoints,
			       const WorldVector<double> *grdUhAtQP,
			       WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
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      WorldMatrix<double> A;
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      for (int iq = 0; iq < numPoints; iq++) {
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	A = (*matrixFct)(vecAtQPs[iq]);
	result[iq] += A * grdUhAtQP[iq];
      }
    }
  }


  void Matrix_SOT::eval(int numPoints,
			const double              *uhAtQP,
			const WorldVector<double> *grdUhAtQP,
			const WorldMatrix<double> *D2UhAtQP,
			double *result,
			double factor) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double resultQP = 0.0;
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	for (int i = 0; i < dow; i++) {
	  for (int j = 0; j < dow; j++) {
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	    resultQP += matrix[i][j] * D2UhAtQP[iq][j][i];
	  }
	}
	result[iq] += resultQP * factor;
      }
    }
  }

  void Matrix_SOT::weakEval(int numPoints,
			    const WorldVector<double> *grdUhAtQP,
			    WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	result[iq] += matrix * grdUhAtQP[iq];
      }
    }
  }



  void MatrixGradient_SOT::eval(int numPoints,
				const double              *uhAtQP,
				const WorldVector<double> *grdUhAtQP,
				const WorldMatrix<double> *D2UhAtQP,
				double *result,
				double factor) const
  {
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    int dow = Global::getGeo(WORLD);
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    for (int iq = 0; iq < numPoints; iq++) {
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      double resultQP = 0.0;

      WorldMatrix<double> A = (*f)(gradAtQPs[iq]);

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      if (D2UhAtQP) {
	for (int i = 0; i < dow; i++) {
	  for (int j = 0; j < dow; j++) {
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	    resultQP += A[i][j] * D2UhAtQP[iq][j][i];
	  }
	}
      }

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      if (grdUhAtQP) {
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	resultQP += (*divFct)(A) * grdUhAtQP[iq];
      }

      result[iq] += resultQP * factor;
    }
  };

  void MatrixGradient_SOT::weakEval(int numPoints,
				    const WorldVector<double> *grdUhAtQP,
				    WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
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      WorldMatrix<double> A;
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      for (int iq = 0; iq < numPoints; iq++) {
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	A = (*f)(gradAtQPs[iq]);
	result[iq] += A * grdUhAtQP[iq];
      }
    }
  }

  void VecAtQP_SOT::eval(int numPoints,
			 const double              *uhAtQP,
			 const WorldVector<double> *grdUhAtQP,
			 const WorldMatrix<double> *D2UhAtQP,
			 double *result,
			 double fac) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq]);
	double resultQP = 0.0;
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	for (int i = 0; i < dow; i++) {
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	  resultQP += D2UhAtQP[iq][i][i];
	}
	result[iq] += fac * factor * resultQP;
      }
    }
  }

  void VecAtQP_SOT::weakEval(int numPoints,
			     const WorldVector<double> *grdUhAtQP,
			     WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq]);  
	axpy(factor, grdUhAtQP[iq], result[iq]);
      }
    }
  }

  void CoordsAtQP_SOT::eval(int numPoints,
			    const double              *uhAtQP,
			    const WorldVector<double> *grdUhAtQP,
			    const WorldMatrix<double> *D2UhAtQP,
			    double *result,
			    double f) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*g)(coordsAtQPs[iq]);
	double resultQP = 0.0;
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	for (int i = 0; i < dow; i++) {
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	  resultQP += D2UhAtQP[iq][i][i];
	}
	result[iq] += factor * f * resultQP;
      }
    }
  }

  void CoordsAtQP_SOT::weakEval(int numPoints,
				const WorldVector<double> *grdUhAtQP,
				WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*g)(coordsAtQPs[iq]);  
	axpy(factor, grdUhAtQP[iq], result[iq]);
      }
    }
  }

  void FctGradient_SOT::eval(int numPoints,
			     const double              *uhAtQP,
			     const WorldVector<double> *grdUhAtQP,
			     const WorldMatrix<double> *D2UhAtQP,
			     double *result,
			     double fac) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(gradAtQPs[iq]);
	double resultQP = 0.0;
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	for (int i = 0; i < dow; i++) {
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	  resultQP += D2UhAtQP[iq][i][i];
	}
	result[iq] += fac * factor * resultQP;
      }
    }
  }

  void FctGradient_SOT::weakEval(int numPoints,
				 const WorldVector<double> *grdUhAtQP,
				 WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {  
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(gradAtQPs[iq]);
	axpy(factor, grdUhAtQP[iq], result[iq]);
      }
    }
  }

  void VecAndGradientAtQP_SOT::eval(int numPoints,
				    const double              *uhAtQP,
				    const WorldVector<double> *grdUhAtQP,
				    const WorldMatrix<double> *D2UhAtQP,
				    double *result,
				    double fac) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq], gradAtQPs[iq]);
	double resultQP = 0.0;
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	  resultQP += D2UhAtQP[iq][i][i];
	}
	result[iq] += fac * factor * resultQP;
      }
    }
  }

  void VecAndGradientAtQP_SOT::weakEval(int numPoints,
					const WorldVector<double> *grdUhAtQP,
					WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {  
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq], gradAtQPs[iq]);
	axpy(factor, grdUhAtQP[iq], result[iq]);
      }
    }
  }



  void VecAndCoordsAtQP_SOT::eval(int numPoints,
				  const double              *uhAtQP,
				  const WorldVector<double> *grdUhAtQP,
				  const WorldMatrix<double> *D2UhAtQP,
				  double *result,
				  double fac) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq], coordsAtQPs[iq]);
	double resultQP = 0.0;
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	  resultQP += D2UhAtQP[iq][i][i];
	}
	result[iq] += fac * factor * resultQP;
      }
    }
  }

  void VecAndCoordsAtQP_SOT::weakEval(int numPoints,
				      const WorldVector<double> *grdUhAtQP,
				      WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq], coordsAtQPs[iq]);  
	axpy(factor, grdUhAtQP[iq], result[iq]);
      }
    }
  }

  void MatrixGradientAndCoords_SOT::eval(int numPoints,
					 const double              *uhAtQP,
					 const WorldVector<double> *grdUhAtQP,
					 const WorldMatrix<double> *D2UhAtQP,
					 double *result,
					 double factor) const
  {
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    for (int iq = 0; iq < numPoints; iq++) {
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      double resultQP = 0.0;

      WorldMatrix<double> A = (*f)(gradAtQPs[iq], coordsAtQPs[iq]);

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      if (D2UhAtQP) {
	for (int i = 0; i < dow; i++) {
	  for (int j = 0; j < dow; j++) {
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	    resultQP += A[i][j] * D2UhAtQP[iq][j][i];
	  }
	}
      }

      if(grdUhAtQP) {
	resultQP += (*divFct)(A) * grdUhAtQP[iq];
      }

      result[iq] += resultQP * factor;
    }
  };

  void MatrixGradientAndCoords_SOT::weakEval(int numPoints,
					     const WorldVector<double> *grdUhAtQP,
					     WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
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      WorldMatrix<double> A;
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      for (int iq = 0; iq < numPoints; iq++) {
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	A = (*f)(gradAtQPs[iq], coordsAtQPs[iq]);
	result[iq] += A * grdUhAtQP[iq];
      }
    }
  }

  void VecGradCoordsAtQP_SOT::eval(int numPoints,
				   const double              *uhAtQP,
				   const WorldVector<double> *grdUhAtQP,
				   const WorldMatrix<double> *D2UhAtQP,
				   double *result,
				   double fac) const
  {
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    int  dow = Global::getGeo(WORLD);
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq], gradAtQPs[iq], coordsAtQPs[iq]);
	double resultQP = 0.0;
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	  resultQP += D2UhAtQP[iq][i][i];
	}
	result[iq] += fac * factor * resultQP;
      }
    }
  }

  void VecGradCoordsAtQP_SOT::weakEval(int numPoints,
				       const WorldVector<double> *grdUhAtQP,
				       WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {  
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq], gradAtQPs[iq], coordsAtQPs[iq]);
	axpy(factor, grdUhAtQP[iq], result[iq]);
      }
    }
  }

  void VecAtQP_FOT::eval(int numPoints,
			 const double              *uhAtQP,
			 const WorldVector<double> *grdUhAtQP,
			 const WorldMatrix<double> *D2UhAtQP,
			 double *result,
			 double fac) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq]);
	double resultQP = 0.0;
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	  resultQP += grdUhAtQP[iq][i];
	}
	result[iq] += fac * factor * resultQP;
      } 
    }
  }

  void CoordsAtQP_FOT::eval(int numPoints,
			    const double              *uhAtQP,
			    const WorldVector<double> *grdUhAtQP,
			    const WorldMatrix<double> *D2UhAtQP,
			    double *result,
			    double f) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*g)(coordsAtQPs[iq]);
	double resultQP = 0.0;
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	  resultQP += grdUhAtQP[iq][i];
	}
	result[iq] += f * factor * resultQP;
      }
    }
  }

  void VecCoordsAtQP_FOT::eval(int numPoints,
			       const double              *uhAtQP,
			       const WorldVector<double> *grdUhAtQP,
			       const WorldMatrix<double> *D2UhAtQP,
			       double *result,
			       double f) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*g)(coordsAtQPs[iq]);
	double resultQP = 0.0;
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	  resultQP += grdUhAtQP[iq][i];
	}
	result[iq] += f * factor * resultQP;
      }
    }
  }

  void VectorGradient_FOT::eval(int numPoints,
				const double              *uhAtQP,
				const WorldVector<double> *grdUhAtQP,
				const WorldMatrix<double> *D2UhAtQP,
				double *result,
				double factor) const
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  { 
    if (grdUhAtQP) {
      if (f) {
	for (int iq = 0; iq < numPoints; iq++) {
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	  WorldVector<double> b = (*f)(gradAtQPs[iq]);
	  result[iq] += b * grdUhAtQP[iq] * factor;
	}
      } else {
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	for (int iq = 0; iq < numPoints; iq++) {
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	  result[iq] += gradAtQPs[iq] * grdUhAtQP[iq] * factor;
	}
      }
    }
  }

  void VectorFct_FOT::eval(int numPoints,
			   const double              *uhAtQP,
			   const WorldVector<double> *grdUhAtQP,
			   const WorldMatrix<double> *D2UhAtQP,
			   double *result,
			   double factor) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	WorldVector<double> b = (*vecFct)(vecAtQPs[iq]);
	result[iq] += b * grdUhAtQP[iq] * factor;
      }
    }
  }

  void VecFctAtQP_FOT::eval(int numPoints,
			    const double              *uhAtQP,
			    const WorldVector<double> *grdUhAtQP,
			    const WorldMatrix<double> *D2UhAtQP,
			    double *result,
			    double f) const
  {
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    int dow = Global::getGeo(WORLD);
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double resultQP = 0.0;
	const WorldVector<double> &b = (*g)(coordsAtQPs[iq]);
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	for (int i = 0; i < dow; i++) {
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	  resultQP += b[i] * grdUhAtQP[iq][i];
	}
	result[iq] += f * resultQP;
      }
    }
  }

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  Assembler *Operator::getAssembler(int rank) 
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  {
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    if (!assembler[rank]) {
      initAssembler(rank, NULL, NULL, NULL, NULL);
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    }

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    return assembler[rank];
  }

  void Operator::setAssembler(int rank, Assembler *a)
  {
    assembler[rank] = a; 
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  }

  void CoordsAtQP_IJ_SOT::initElement(const ElInfo* elInfo, 
				      SubAssembler* subAssembler,
				      Quadrature *quad)
  {
    coordsAtQPs = subAssembler->getCoordsAtQPs(elInfo, quad);
  }

  void CoordsAtQP_IJ_SOT::getLALt(const ElInfo *elInfo, 
				  int numPoints, 
				  DimMat<double> **LALt) const
  {
    const DimVec<WorldVector<double> > Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lalt_kl(Lambda, xi, xj, *(LALt[iq]), (*g)(coordsAtQPs[iq]));
    }
  }

  void CoordsAtQP_IJ_SOT::eval(int numPoints,
			       const double              *uhAtQP,
			       const WorldVector<double> *grdUhAtQP,
			       const WorldMatrix<double> *D2UhAtQP,
			       double *result,
			       double f) const
  {
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*g)(coordsAtQPs[iq]);
	result[iq] = D2UhAtQP[iq][xi][xj] * factor * f;
      }
    }
  }

  void CoordsAtQP_IJ_SOT::weakEval(int numPoints,
				   const WorldVector<double> *grdUhAtQP,
				   WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*g)(coordsAtQPs[iq]);  
	result[iq][xi] += grdUhAtQP[iq][xj] * factor;
      }
    }
  }

  void VecAtQP_IJ_SOT::initElement(const ElInfo* elInfo, 
				   SubAssembler* subAssembler,
				   Quadrature *quad)
  {
    vecAtQPs = subAssembler->getVectorAtQPs(vec, elInfo, quad);
  }
 
  void VecAtQP_IJ_SOT::getLALt(const ElInfo *elInfo, 
			       int numPoints, 
			       DimMat<double> **LALt) const
  {
    const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();
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    for (int iq = 0; iq < numPoints; iq++) {
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      lalt_kl(Lambda, xi, xj, *(LALt[iq]), (*f)(vecAtQPs[iq]));
    }
  }  

  void VecAtQP_IJ_SOT::eval(int numPoints,
			    const double              *uhAtQP,
			    const WorldVector<double> *grdUhAtQP,
			    const WorldMatrix<double> *D2UhAtQP,
			    double *result,
			    double fac) const
  {
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    if (D2UhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq]);
	result[iq] = D2UhAtQP[iq][xi][xj] * factor * fac;
      }
    }
  }

  void VecAtQP_IJ_SOT::weakEval(int numPoints,
				const WorldVector<double> *grdUhAtQP,
				WorldVector<double> *result) const
  {
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    if (grdUhAtQP) {
      for (int iq = 0; iq < numPoints; iq++) {
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	double factor = (*f)(vecAtQPs[iq]);  
	result[iq][xi] += grdUhAtQP[iq][xj] * factor;
      }
    }
  }

 
  void VecOfDOFVecsAtQP_ZOT::initElement(const ElInfo* elInfo, 
					 SubAssembler* subAssembler,
					 Quadrature *quad) 
  {
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    int size = static_cast<int>(vecs.size());
    for (int i = 0; i < size; i++) {
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      vecsAtQPs[i] = subAssembler->getVectorAtQPs(vecs[i], elInfo, quad);
    }
  }
 
  void VecOfDOFVecsAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const 
  { 
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    int size = static_cast<int>(vecs.size());
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    std::vector<double> arg(size);
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    for (int iq = 0; iq < numPoints; iq++) {
      for (int i = 0; i < size; i++) {
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	arg[i] = vecsAtQPs[i][iq];
      }
      C[iq] += (*f)(arg);
    }
  }

  void VecOfDOFVecsAtQP_ZOT::eval(int numPoints,
				  const double              *uhAtQP,
				  const WorldVector<double> *grdUhAtQP,
				  const WorldMatrix<double> *D2UhAtQP,
				  double *result,
				  double fac) const
  {
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    int size = static_cast<int>(vecs.size());
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    std::vector<double> arg(size);
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    for (int iq = 0; iq < numPoints; iq++) {
      for (int i = 0; i < size; i++) {
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	arg[i] = vecsAtQPs[i][iq];
      }
      result[iq] += fac * (*f)(arg) * uhAtQP[iq];
    }
  }

 
  void VecOfGradientsAtQP_ZOT::initElement(const ElInfo* elInfo, 
					   SubAssembler* subAssembler,
					   Quadrature *quad) 
  {
    int i ,size = static_cast<int>(vecs.size());
    for(i = 0; i < size; i++) {
      gradsAtQPs[i] = subAssembler->getGradientsAtQPs(vecs[i], elInfo, quad);
    }
  }
 
  void VecDivergence_ZOT::initElement(const ElInfo* elInfo, 
				      SubAssembler* subAssembler,
				      Quadrature *quad) 
  {
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    int size = static_cast<int>(vecs.size());
    for (int i = 0; i < size; i++) {
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      gradsAtQPs[i] = subAssembler->getGradientsAtQPs(vecs[i], elInfo, quad);
    }
  }
 

  void VecOfGradientsAtQP_ZOT::getC(const ElInfo *, int numPoints, double *C) const 
  { 
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    std::vector<WorldVector<double>*> arg(size);
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    for (int iq = 0; iq < numPoints; iq++) {
      for (int i = 0; i < size; i++) {
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	arg[i] = &(gradsAtQPs[i][iq]);
      }
      C[iq] += (*f)(arg);
    }
  }

  void VecOfGradientsAtQP_ZOT::eval(int numPoints,
				    const double              *uhAtQP,
				    const WorldVector<double> *grdUhAtQP,
				    const WorldMatrix<double> *D2UhAtQP,
				    double *result,
				    double fac) const
  {
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    int size = static_cast<int>(vecs.size());
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    std::vector<WorldVector<double>*> arg(size);
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    for (int iq = 0; iq < numPoints; iq++) {
      for (int i = 0; i < size; i++) {
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	arg[i] = &(gradsAtQPs[i][iq]);
      }
      result[iq] += fac * (*f)(arg) * uhAtQP[iq];
    }
  }

  void VecDivergence_ZOT::getC(const ElInfo *, int numPoints, double *C) const 
  { 
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    for (int iq = 0; iq < numPoints; iq++) {
      for (int i = 0; i < size; i++) {
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	C[iq] += gradsAtQPs[i][iq][i];
      }
    }
  }

  void VecDivergence_ZOT::eval(int numPoints,
			       const double              *uhAtQP,
			       const WorldVector<double> *grdUhAtQP,
			       const WorldMatrix<double> *D2UhAtQP,
			       double *result,
			       double fac) const
  {
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