http://trilinos.sandia.gov/packages/docs/r10.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_TRI_C2_FEMDef.hpp

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//                           Intrepid Package
//                 Copyright (2007) Sandia Corporation
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namespace Intrepid {
  
  
template<class Scalar, class ArrayScalar>
Basis_HGRAD_TRI_C2_FEM<Scalar,ArrayScalar>::Basis_HGRAD_TRI_C2_FEM()
  {
    this -> basisCardinality_  = 6;
    this -> basisDegree_       = 2;    
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
    this -> basisType_         = BASIS_FEM_DEFAULT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;
  }
  
  
  
template<class Scalar, class ArrayScalar>
void Basis_HGRAD_TRI_C2_FEM<Scalar, ArrayScalar>::initializeTags() {
  
  // Basis-dependent initializations
  int tagSize  = 4;        // size of DoF tag, i.e., number of fields in the tag
  int posScDim = 0;        // position in the tag, counting from 0, of the subcell dim 
  int posScOrd = 1;        // position in the tag, counting from 0, of the subcell ordinal
  int posDfOrd = 2;        // position in the tag, counting from 0, of DoF ordinal relative to the subcell
  
  // An array with local DoF tags assigned to the basis functions, in the order of their local enumeration 
  int tags[]  = { 0, 0, 0, 1,
                  0, 1, 0, 1,
                  0, 2, 0, 1,
                  1, 0, 0, 1,
                  1, 1, 0, 1,
                  1, 2, 0, 1};
  
  // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
  Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
                              this -> ordinalToTag_,
                              tags,
                              this -> basisCardinality_,
                              tagSize,
                              posScDim,
                              posScOrd,
                              posDfOrd);
}  



template<class Scalar, class ArrayScalar> 
void Basis_HGRAD_TRI_C2_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar &        outputValues,
                                                            const ArrayScalar &  inputPoints,
                                                            const EOperator      operatorType) const {
  
  // Verify arguments
#ifdef HAVE_INTREPID_DEBUG
  Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues,
                                                      inputPoints,
                                                      operatorType,
                                                      this -> getBaseCellTopology(),
                                                      this -> getCardinality() );
#endif
  
  // Number of evaluation points = dim 0 of inputPoints
  int dim0 = inputPoints.dimension(0);  
  
  // Temporaries: (x,y) coordinates of the evaluation point
  Scalar x = 0.0;                                    
  Scalar y = 0.0;   
  
  switch (operatorType) {
    
    case OPERATOR_VALUE:
      for (int i0 = 0; i0 < dim0; i0++) {
        x = inputPoints(i0, 0);
        y = inputPoints(i0, 1);
          
        // outputValues is a rank-2 array with dimensions (basisCardinality_, dim0)
        outputValues(0, i0) = (x + y - 1.0)*(2.0*x + 2.0*y - 1.0);
        outputValues(1, i0) = x*(2.0*x - 1.0);
        outputValues(2, i0) = y*(2.0*y - 1.0);
        outputValues(3, i0) = -4.0*x*(x + y - 1.0);
        outputValues(4, i0) =  4.0*x*y;
        outputValues(5, i0) = -4.0*y*(x + y - 1.0);
        
      }
      break;

    case OPERATOR_GRAD:
    case OPERATOR_D1:
      for (int i0 = 0; i0 < dim0; i0++) {
        x = inputPoints(i0, 0);
        y = inputPoints(i0, 1);

        // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
        outputValues(0, i0, 0) =  4.0*x + 4.0*y - 3.0;
        outputValues(0, i0, 1) =  4.0*x + 4.0*y - 3.0;

        outputValues(1, i0, 0) =  4.0*x - 1.0;
        outputValues(1, i0, 1) =  0.0;

        outputValues(2, i0, 0) =  0.0;
        outputValues(2, i0, 1) =  4.0*y - 1.0;
        
        outputValues(3, i0, 0) = -4.0*(2.0*x + y - 1.0);
        outputValues(3, i0, 1) = -4.0*x;

        outputValues(4, i0, 0) =  4.0*y;
        outputValues(4, i0, 1) =  4.0*x;

        outputValues(5, i0, 0) = -4.0*y;
        outputValues(5, i0, 1) = -4.0*(x + 2.0*y - 1.0);
      }
      break;

    case OPERATOR_CURL:
      for (int i0 = 0; i0 < dim0; i0++) {
        x = inputPoints(i0, 0);
        y = inputPoints(i0, 1);
        
        // CURL(u) = (u_y, -u_x), is rotated GRAD
        outputValues(0, i0, 1) =-(4.0*x + 4.0*y - 3.0);
        outputValues(0, i0, 0) =  4.0*x + 4.0*y - 3.0;
        
        outputValues(1, i0, 1) =-(4.0*x - 1.0);
        outputValues(1, i0, 0) =  0.0;
        
        outputValues(2, i0, 1) =  0.0;
        outputValues(2, i0, 0) =  4.0*y - 1.0;
        
        outputValues(3, i0, 1) =  4.0*(2.0*x + y - 1.0);
        outputValues(3, i0, 0) = -4.0*x;
        
        outputValues(4, i0, 1) = -4.0*y;
        outputValues(4, i0, 0) =  4.0*x;
        
        outputValues(5, i0, 1) =  4.0*y;
        outputValues(5, i0, 0) = -4.0*(x + 2.0*y - 1.0);
      }
      break;

    case OPERATOR_DIV:
      TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument,
                          ">>> ERROR (Basis_HGRAD_TRI_C2_FEM): DIV is invalid operator for rank-0 (scalar) fields in 2D.");
      break;

    case OPERATOR_D2:
      for (int i0 = 0; i0 < dim0; i0++) {
        // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
        // D2 -> (2,0) -> dx^2. 
        outputValues(0, i0, 0) = 4.0;
        outputValues(1, i0, 0) = 4.0;
        outputValues(2, i0, 0) = 0.0;
        outputValues(3, i0, 0) =-8.0;
        outputValues(4, i0, 0) = 0.0;
        outputValues(5, i0, 0) = 0.0;
        
        // D2 -> (1,1) -> dx dy
        outputValues(0, i0, 1) = 4.0;
        outputValues(1, i0, 1) = 0.0;
        outputValues(2, i0, 1) = 0.0;
        outputValues(3, i0, 1) =-4.0;
        outputValues(4, i0, 1) = 4.0;
        outputValues(5, i0, 1) =-4.0;
        
        // D2 -> (0,2) -> dy^2
        outputValues(0, i0, 2) = 4.0;
        outputValues(1, i0, 2) = 0.0;
        outputValues(2, i0, 2) = 4.0;
        outputValues(3, i0, 2) = 0.0;
        outputValues(4, i0, 2) = 0.0;
        outputValues(5, i0, 2) =-8.0;
      }// for i0
      break;
      
    case OPERATOR_D3:
    case OPERATOR_D4:
    case OPERATOR_D5:
    case OPERATOR_D6:
    case OPERATOR_D7:
    case OPERATOR_D8:
    case OPERATOR_D9:
    case OPERATOR_D10:
      {
        // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
        int DkCardinality = Intrepid::getDkCardinality(operatorType, 
                                                       this -> basisCellTopology_.getDimension() );
        for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) {
          for (int i0 = 0; i0 < dim0; i0++) {
            for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){
              outputValues(dofOrd, i0, dkOrd) = 0.0;
            }
          }
        }
      }
      break;

    default:
      TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
                          ">>> ERROR (Basis_HGRAD_TRI_C2_FEM): Invalid operator type");
  }
}
  

  
template<class Scalar, class ArrayScalar>
void Basis_HGRAD_TRI_C2_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar&           outputValues,
                                                            const ArrayScalar &    inputPoints,
                                                            const ArrayScalar &    cellVertices,
                                                            const EOperator        operatorType) const {
  TEST_FOR_EXCEPTION( (true), std::logic_error,
                      ">>> ERROR (Basis_HGRAD_TRI_C2_FEM): FEM Basis calling an FVD member function");
}


}// namespace Intrepid

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