SundanceGaussLobattoQuadrature.hpp

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/*
 * SundanceGaussLobattoQuadrature.hpp
 *
 *  Created on: Jan 20, 2011
 *      Author: benk
 */

#ifndef SUNDANCEGAUSSLOBATTOQUADRATURE_HPP_
#define SUNDANCEGAUSSLOBATTOQUADRATURE_HPP_

#include "SundanceDefs.hpp"
#include "PlayaTabs.hpp"
#include "SundanceQuadratureFamilyBase.hpp"

namespace Sundance {

class GaussLobattoQuadrature : public QuadratureFamilyBase {

public:

  /** In this case the */
  GaussLobattoQuadrature(int order);

  /** */
  virtual ~GaussLobattoQuadrature()
  {;}

  /** */
  virtual XMLObject toXML() const;

  /** Describable interface */
  virtual std::string description() const
  {
    return "GaussLobattoQuadrature[order=" + Teuchos::toString(order()) + "]";
  }

  /* handleable boilerplate */
  GET_RCP(QuadratureFamilyStub);

protected:
  /** compute a rule for the reference line cell */
  virtual void getLineRule(Array<Point>& quadPointsL,
      Array<double>& quadWeights) const;

  /** compute a rule for the reference triangle cell */
  virtual void getTriangleRule(Array<Point>& quadPoints,
      Array<double>& quadWeights) const;

  /** compute a rule for the reference quad cell */
  virtual void getQuadRule(Array<Point>& quadPoints,
      Array<double>& quadWeights) const;

  /** compute a rule for the reference tet cell */
  virtual void getTetRule(Array<Point>& quadPoints,
      Array<double>& quadWeights) const ;

  /** compute a rule for the reference brick cell */
  virtual void getBrickRule(Array<Point>& quadPoints,
      Array<double>& quadWeights) const;

  /**
   * Compute adapted weights according to curve
   *
   * @param cellType
   * @param cellDim
   * @param cellLID
   * @param facetIndex
   * @param mesh
   * @param globalCurve
   * @param quadPoints
   * @param quadWeights
   * @param changedWeights
   */
  virtual void getAdaptedWeights(const CellType& cellType, int cellDim,
      int cellLID, int facetIndex, const Mesh& mesh,
      const ParametrizedCurve& globalCurve,
      Array<Point>& quadPoints, Array<double>& quadWeights,
      bool &weightsChanged) const;

  /** Get the weights for one quad */
  virtual void getAdaptedQuadWeights(int cellLID, const Mesh& mesh,
      const ParametrizedCurve& globalCurve, Array<Point>& quadPoints,
      Array<double>& quadWeights, bool& weightsChanged) const;

  /** Get the weights for one quad knowing that the curve is a 2D polygon */
  virtual void getAdaptedQuadWeights_polygon(int cellLID, const Mesh& mesh,
      const ParametrizedCurve& globalCurve, Array<Point>& quadPoints,
      Array<double>& quadWeights, bool& weightsChanged) const;

  /** Get the weights for one quad knowing that the curve is a 3D surface */
  virtual void getAdaptedQuadWeights_surf(int cellLID, const Mesh& mesh,
      const ParametrizedCurve& globalCurve, Array<Point>& quadPoints,
      Array<double>& quadWeights, bool& weightsChanged) const;

private:

  /** get the triangle quadrature points for the adaptive integration*/
  void getTriangleQuadPoints(Array<Point>& pnt , Array<double>& weight ) const;

  /**
   * @param i , the i-th point
   * @param pnt 1D points where we interpolate
   * @param x the position where we evaluate */
  inline double evalLagrangePol(int i , Array<Point>& pnt , double x) const{
    int m = pnt.size();
    double p = 1.0;
    for (int j = 0 ; (j <= i-1)&&(j<m) ; j++){
     p = p *( x - pnt[j][0] )/(pnt[i][0] - pnt[j][0]);
    }
    for (int j = i+1 ; j < m ; j++){
     p = p *( x - pnt[j][0] )/(pnt[i][0] - pnt[j][0]);
    }
      return p;
  }

  /** this function applies quadrature to the Lagrange functions <br>
   * all the coordinates are in the reference coordinates */
  inline void makeInterpolantQuad( double px, double py, double ofx, double ofy,
                               int nr1DPoints , int nr2DPoints ,
                               Array<Point>& linePoints ,
                               Array<Point>& quadPoints ,
                               Array<double>& pointWeights ,
                               Array<double>& weightsOut ,
                               double areFakt ) const {
    int xi,yi;
    double xc,yc, intR , valTmp , valBasisX , valBasisY ;

        //SUNDANCE_MSG3(verb_, "px="<<px<<",py="<<py<<",ofx="<<ofx<<",ofy="<<ofy <<
        //    " , nr2DPoints:" << nr2DPoints << " , pointWeights.size():" <<
        //    pointWeights.size() << " , areFakt:" << areFakt);

    // if the area of integration is not significant then just return
    if ( fabs(ofx*ofy) < 1e-14 ) {
      //SUNDANCE_MSG3(verb_, "return");
      return;
    }

    for (int i = 0 ; i < nr2DPoints ; i++){
      // we should add the integration values, and we not set the values //weightsOut[i] = 0.0;
      yi = i % nr1DPoints; xi = i / nr1DPoints; intR = 0.0;
      // for each quadrature point
      for (int q = 0 ; q < pointWeights.size() ; q++){
        xc = px + quadPoints[q][0]*ofx;
        yc = py + quadPoints[q][1]*ofy;
        valBasisX = evalLagrangePol(xi , linePoints , xc);
        valBasisY = evalLagrangePol(yi , linePoints , yc);
        valTmp = pointWeights[q] * ( valBasisX *  valBasisY);
        intR = intR + valTmp;
        //SUNDANCE_MSG3(verb_, "i="<<i<< " , valBasisX=" << valBasisX  << " , valBasisY=" << valBasisY << " , valBasis="
        //    << valBasisX*valBasisY <<" , val=" << valTmp*::fabs(ofx*ofy/areFakt) );
        //SUNDANCE_MSG3(verb_, "i="<<i<<",xi="<<xi<<",yi="<<yi<<",q="<<q<<",xc="<<xc<<",yc="<<yc<<
        //    ",pointWeights[q]=" << pointWeights[q]);
      }
      intR = intR * ::fabs(ofx*ofy/areFakt);
      weightsOut[i] = weightsOut[i] + intR;
    }
  }


  /** this function applies quadrature to the Lagrange functions <br>
   * all the coordinates are in the reference coordinates */
  inline void makeInterpolantBrick(int nr1DPoints , int nr3DPoints ,
                               Array<Point>& linePoints ,
                               Array<Point>& quadPoints ,
                               Array<double>& pointWeights ,
                               Array<double>& weightsOut ,
                               double areFakt ) const {
    int xi,yi,zi;
    double xc,yc,zc, intR , valTmp , valBasisX , valBasisY , valBasisZ;

    for (int i = 0 ; i < nr3DPoints ; i++){
      zi = i/(nr1DPoints*nr1DPoints); yi = (i%(nr1DPoints*nr1DPoints)) / nr1DPoints;
      xi = (i%(nr1DPoints*nr1DPoints)) % nr1DPoints; intR = 0.0;
      // for each quadrature point
      for (int q = 0 ; q < pointWeights.size() ; q++){
        xc = quadPoints[q][0]; yc = quadPoints[q][1]; zc = quadPoints[q][2];
        valBasisX = evalLagrangePol(xi , linePoints , xc);
        valBasisY = evalLagrangePol(yi , linePoints , yc);
        valBasisZ = evalLagrangePol(zi , linePoints , zc);
        valTmp = pointWeights[q] * ( valBasisX * valBasisY * valBasisZ );
        intR = intR + valTmp;
        //SUNDANCE_MSG3(4, "i="<<i<< " , valBasisX=" << valBasisX  << " , valBasisY=" << valBasisY << " , valBasisZ=" << valBasisZ <<
        //    " , valBasis=" << valBasisX*valBasisY <<" , val=" << valTmp );
        //SUNDANCE_MSG3(4, "i="<<i<<",xi="<<xi<<",yi="<<yi<<",q="<<q<<",xc="<<xc<<",yc="<<yc<<",zc="<<zc<<
        //    ",pointWeights["<<q<<"]=" << pointWeights[q]);
      }
      intR = intR * areFakt ;
      weightsOut[i] = weightsOut[i] + intR;
    }
  }



  /** nr of points in 1D, the rest should be tensor product */
  int nrPointin1D_;

  /** the verbosity of the object*/
  int verb_;

  static const int quadsEdgesPoints[4][2];

  /** qvasi information for the 3D cut-cell integral*/
  static const int edge3DProjection[12];
};

}

#endif /* SUNDANCEGAUSSLOBATTOQUADRATURE_HPP_ */