Intrepid_HCURL_QUAD_In_FEMDef.hpp

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namespace Intrepid {

  template<class Scalar, class ArrayScalar>
  Basis_HCURL_QUAD_In_FEM<Scalar,ArrayScalar>::Basis_HCURL_QUAD_In_FEM( int order ,
                                                                      const ArrayScalar & ptsClosed ,
                                                                      const ArrayScalar & ptsOpen):
    closedBasis_( order , ptsClosed ),
    openBasis_( order-1 , ptsOpen ) ,
    closedPts_( ptsClosed ),
    openPts_( ptsOpen )
  {
    this -> basisDegree_       = order;
    this -> basisCardinality_  = 2 * closedBasis_.getCardinality() * openBasis_.getCardinality(); 
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;

    Array<Array<RCP<Basis<Scalar,ArrayScalar > > > > bases(2);
    bases[0].resize(2); bases[1].resize(2);
    bases[0][0] = rcp( &openBasis_ , false );
    bases[0][1] = rcp( &closedBasis_ , false );
    bases[1][0] = rcp( &closedBasis_ , false );
    bases[1][1] = rcp( &openBasis_ , false );
    this->setBases( bases );


  }

  template<class Scalar, class ArrayScalar>
  Basis_HCURL_QUAD_In_FEM<Scalar,ArrayScalar>::Basis_HCURL_QUAD_In_FEM( int order , const EPointType &pointType ):
    closedBasis_( order , pointType==POINTTYPE_SPECTRAL?POINTTYPE_SPECTRAL:POINTTYPE_EQUISPACED ),
    openBasis_( order-1 , pointType==POINTTYPE_SPECTRAL?POINTTYPE_SPECTRAL_OPEN:POINTTYPE_EQUISPACED ) ,
    closedPts_( order+1 , 1 ),
    openPts_( order , 1 )
  {
    this -> basisDegree_       = order;
    this -> basisCardinality_  = 2 * closedBasis_.getCardinality() * openBasis_.getCardinality(); 
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;

    PointTools::getLattice<Scalar,FieldContainer<Scalar> >( closedPts_ ,
                                                            shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >()) ,
                                                            order ,
                                                            0 ,
                                                            pointType==POINTTYPE_SPECTRAL?POINTTYPE_WARPBLEND:POINTTYPE_EQUISPACED );

    if (pointType == POINTTYPE_SPECTRAL)
      {
        PointTools::getGaussPoints<Scalar,FieldContainer<Scalar> >( openPts_ ,
                                                                    order - 1 );
      }
    else
      {
        PointTools::getLattice<Scalar,FieldContainer<Scalar> >( openPts_ ,
                                                                shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >()) ,
                                                                order + 1,
                                                                1 ,
                                                                POINTTYPE_EQUISPACED );
      }

    Array<Array<RCP<Basis<Scalar,ArrayScalar > > > > bases(2);
    bases[0].resize(2); bases[1].resize(2);
    bases[0][0] = rcp( &openBasis_ , false );
    bases[0][1] = rcp( &closedBasis_ , false );
    bases[1][0] = rcp( &closedBasis_ , false );
    bases[1][1] = rcp( &openBasis_ , false );
    this->setBases( bases );

  }
  
  template<class Scalar, class ArrayScalar>
  void Basis_HCURL_QUAD_In_FEM<Scalar, ArrayScalar>::initializeTags() {
    
    // Basis-dependent intializations
    int tagSize  = 4;        // size of DoF 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
    
    std::vector<int> tags( tagSize * this->getCardinality() );
    
    const std::vector<std::vector<int> >& closedDofTags = closedBasis_.getAllDofTags();
    const std::vector<std::vector<int> >& openDofTags = openBasis_.getAllDofTags();

    std::map<int,std::map<int,int> > total_dof_per_entity;
    std::map<int,std::map<int,int> > current_dof_per_entity;

    for (int i=0;i<4;i++) {
      total_dof_per_entity[0][i] = 0;
      current_dof_per_entity[0][i] = 0;
    }
    for (int i=0;i<4;i++) {
      total_dof_per_entity[1][i] = 0;
      current_dof_per_entity[1][i] = 0;
    }
    total_dof_per_entity[2][0] = 0;
    current_dof_per_entity[2][0] = 0;

    // tally dof on each facet.  none on vertex
    for (int i=0;i<4;i++) {
      total_dof_per_entity[1][i] = openBasis_.getCardinality();
    }

    total_dof_per_entity[2][0] = this->getCardinality() - 4 * openBasis_.getCardinality();

    int tagcur = 0;
    // loop over the x-face tangent basis functions, which are (phi(x)psi(y),0)
    // for psi in the closed basis and phi in the open
    for (int j=0;j<closedBasis_.getCardinality();j++) 
      {
        const int cdim = closedDofTags[j][0];
        const int cent = closedDofTags[j][1];
        for (int i=0;i<openBasis_.getCardinality();i++) 
          {
            const int odim = openDofTags[i][0];
            const int oent = openDofTags[i][1];
            int dofdim;
            int dofent;
            ProductTopology::lineProduct2d(odim,oent,cdim,cent,dofdim,dofent);
            tags[4*tagcur] = dofdim;
            tags[4*tagcur+1] = dofent;
            tags[4*tagcur+2] = current_dof_per_entity[dofdim][dofent];
            current_dof_per_entity[dofdim][dofent]++;
            tags[4*tagcur+3] = total_dof_per_entity[dofdim][dofent];
            tagcur++;
          }
      }
    
    // now we have to do it for the other basis functions, which are
    // (psi(x)phi(y)) for psi in the closed basis and phi in the open
    for (int j=0;j<openBasis_.getCardinality();j++) 
      {
        const int odim = openDofTags[j][0];
        const int oent = openDofTags[j][1];
        for (int i=0;i<closedBasis_.getCardinality();i++) 
          {
            const int cdim = closedDofTags[i][0];
            const int cent = closedDofTags[i][1];
            int dofdim;
            int dofent;
            ProductTopology::lineProduct2d(cdim,cent,odim,oent,dofdim,dofent);
            tags[4*tagcur] = dofdim;
            tags[4*tagcur+1] = dofent;
            tags[4*tagcur+2] = current_dof_per_entity[dofdim][dofent];
            current_dof_per_entity[dofdim][dofent]++;
            tags[4*tagcur+3] = total_dof_per_entity[dofdim][dofent];
            tagcur++;
          }
      }

    // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
    Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
                                this -> ordinalToTag_,
                                &(tags[0]),
                                this -> basisCardinality_,
                                tagSize,
                                posScDim,
                                posScOrd,
                                posDfOrd);
  }


  template<class Scalar, class ArrayScalar>
  void Basis_HCURL_QUAD_In_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar &        outputValues,
                                                              const ArrayScalar &  inputPoints,
                                                              const EOperator      operatorType) const {
    
    // Verify arguments
#ifdef HAVE_INTREPID_DEBUG
    Intrepid::getValues_HCURL_Args<Scalar, ArrayScalar>(outputValues,
                                                       inputPoints,
                                                       operatorType,
                                                       this -> getBaseCellTopology(),
                                                       this -> getCardinality() );
#endif
    
    // Number of evaluation points = dim 0 of inputPoints
    int dim0 = inputPoints.dimension(0);
    
    // separate out points
    FieldContainer<Scalar> xPoints(dim0,1);
    FieldContainer<Scalar> yPoints(dim0,1);
    
    for (int i=0;i<dim0;i++) {
      xPoints(i,0) = inputPoints(i,0);
      yPoints(i,0) = inputPoints(i,1);
    }
    
    switch (operatorType) {
    case OPERATOR_VALUE:
      {
        FieldContainer<Scalar> closedBasisValsXPts( closedBasis_.getCardinality() , dim0 );
        FieldContainer<Scalar> closedBasisValsYPts( closedBasis_.getCardinality() , dim0 );
        FieldContainer<Scalar> openBasisValsXPts( openBasis_.getCardinality() , dim0 );
        FieldContainer<Scalar> openBasisValsYPts( openBasis_.getCardinality() , dim0 );
        
        closedBasis_.getValues( closedBasisValsXPts , xPoints , OPERATOR_VALUE );
        closedBasis_.getValues( closedBasisValsYPts , yPoints , OPERATOR_VALUE );
        openBasis_.getValues( openBasisValsXPts , xPoints , OPERATOR_VALUE );
        openBasis_.getValues( openBasisValsYPts , yPoints , OPERATOR_VALUE );
        
        int bfcur = 0;
        // x component bfs are (open(x) closed(y),0)
        for (int j=0;j<closedBasis_.getCardinality();j++) 
          {
            for (int i=0;i<openBasis_.getCardinality();i++) 
              {
                for (int l=0;l<dim0;l++) 
                  {
                    outputValues(bfcur,l,0) = closedBasisValsYPts(j,l) * openBasisValsXPts(i,l);
                    outputValues(bfcur,l,1) = 0.0;
                  }
                bfcur++;
              }
          }
        
        // y component bfs are (0,closed(x) open(y))
        for (int j=0;j<openBasis_.getCardinality();j++) 
          {
            for (int i=0;i<closedBasis_.getCardinality();i++) 
              {
                for (int l=0;l<dim0;l++) 
                  {
                    outputValues(bfcur,l,0) = 0.0;
                    outputValues(bfcur,l,1) = openBasisValsYPts(j,l) * closedBasisValsXPts(i,l);
                  }
                bfcur++;
              }
          }
      }
      break;
    case OPERATOR_CURL:
      {
        FieldContainer<Scalar> closedBasisDerivsXPts( closedBasis_.getCardinality() , dim0 , 1 );
        FieldContainer<Scalar> closedBasisDerivsYPts( closedBasis_.getCardinality() , dim0 , 1 );
        FieldContainer<Scalar> openBasisValsXPts( openBasis_.getCardinality() , dim0 );
        FieldContainer<Scalar> openBasisValsYPts( openBasis_.getCardinality() , dim0 );
        
        closedBasis_.getValues( closedBasisDerivsXPts , xPoints , OPERATOR_D1 );
        closedBasis_.getValues( closedBasisDerivsYPts , yPoints , OPERATOR_D1 );
        openBasis_.getValues( openBasisValsXPts , xPoints , OPERATOR_VALUE );
        openBasis_.getValues( openBasisValsYPts , yPoints , OPERATOR_VALUE );
        
        int bfcur = 0;
        
        // x component basis functions first
        for (int j=0;j<closedBasis_.getCardinality();j++) 
          {
            for (int i=0;i<openBasis_.getCardinality();i++) 
              {
                for (int l=0;l<dim0;l++) {
                  outputValues(bfcur,l) = -closedBasisDerivsYPts(j,l,0) * openBasisValsXPts(i,l);
                }
                bfcur++;
              }
          }
        
        // now y component basis functions
        for (int j=0;j<openBasis_.getCardinality();j++) 
          {
            for (int i=0;i<closedBasis_.getCardinality();i++) 
              {
                for (int l=0;l<dim0;l++) 
                  {
                    outputValues(bfcur,l) = closedBasisDerivsXPts(i,l,0) * openBasisValsYPts(j,l);
                  }
                bfcur++;
              }
          }
      }
      break;
    case OPERATOR_DIV:
      TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument,
                          ">>> ERROR (Basis_HCURL_QUAD_In_FEM): DIV is invalid operator for HCURL Basis Functions");
      break;
      
    case OPERATOR_GRAD:
      TEUCHOS_TEST_FOR_EXCEPTION( (operatorType == OPERATOR_GRAD), std::invalid_argument,
                          ">>> ERROR (Basis_HCURL_QUAD_In_FEM): GRAD is invalid operator for HCURL Basis Functions");
      break;
      
    case OPERATOR_D1:
    case OPERATOR_D2:
    case OPERATOR_D3:
    case OPERATOR_D4:
    case OPERATOR_D5:
    case OPERATOR_D6:
    case OPERATOR_D7:
    case OPERATOR_D8:
    case OPERATOR_D9:
    case OPERATOR_D10:
      TEUCHOS_TEST_FOR_EXCEPTION( ( (operatorType == OPERATOR_D1)    ||
                            (operatorType == OPERATOR_D2)    ||
                            (operatorType == OPERATOR_D3)    ||
                            (operatorType == OPERATOR_D4)    ||
                            (operatorType == OPERATOR_D5)    ||
                            (operatorType == OPERATOR_D6)    ||
                            (operatorType == OPERATOR_D7)    ||
                            (operatorType == OPERATOR_D8)    ||
                            (operatorType == OPERATOR_D9)    ||
                            (operatorType == OPERATOR_D10) ),
                          std::invalid_argument,
                          ">>> ERROR (Basis_HCURL_QUAD_In_FEM): Invalid operator type");
      break;
      
    default:
      TEUCHOS_TEST_FOR_EXCEPTION( ( (operatorType != OPERATOR_VALUE) &&
                            (operatorType != OPERATOR_GRAD)  &&
                            (operatorType != OPERATOR_CURL)  &&
                            (operatorType != OPERATOR_CURL)   &&
                            (operatorType != OPERATOR_D1)    &&
                            (operatorType != OPERATOR_D2)    &&
                            (operatorType != OPERATOR_D3)    &&
                            (operatorType != OPERATOR_D4)    &&
                            (operatorType != OPERATOR_D5)    &&
                            (operatorType != OPERATOR_D6)    &&
                            (operatorType != OPERATOR_D7)    &&
                            (operatorType != OPERATOR_D8)    &&
                            (operatorType != OPERATOR_D9)    &&
                            (operatorType != OPERATOR_D10) ),
                          std::invalid_argument,
                          ">>> ERROR (Basis_HCURL_QUAD_In_FEM): Invalid operator type");
    }
  }
  
  
  
  template<class Scalar, class ArrayScalar>
  void Basis_HCURL_QUAD_In_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar&           outputValues,
                                                              const ArrayScalar &    inputPoints,
                                                              const ArrayScalar &    cellVertices,
                                                              const EOperator        operatorType) const {
    TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
                        ">>> ERROR (Basis_HCURL_QUAD_In_FEM): FEM Basis calling an FVD member function");
  }

  template<class Scalar, class ArrayScalar>
  void Basis_HCURL_QUAD_In_FEM<Scalar,ArrayScalar>::getDofCoords(ArrayScalar & DofCoords) const
  {
    // x-component basis functions
    int cur = 0;

    for (int j=0;j<closedPts_.dimension(0);j++)
      {
        for (int i=0;i<openPts_.dimension(0);i++)
          {
            DofCoords(cur,0) = openPts_(i,0);
            DofCoords(cur,1) = closedPts_(j,0);
            cur++;
          }
      }

    // y-component basis functions
    for (int j=0;j<openPts_.dimension(0);j++)
      {
        for (int i=0;i<closedPts_.dimension(0);i++)
          {
            DofCoords(cur,0) = closedPts_(i,0);
            DofCoords(cur,1) = openPts_(j,0);
            cur++;
          }
      }

    return;
  }


  
}// namespace Intrepid