SundanceMaximalQuadratureIntegral.cpp

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// ************************************************************************
// 
//                              Sundance
//                 Copyright (2005) Sandia Corporation
// 
// Copyright (year first published) Sandia Corporation.  Under the terms 
// of Contract DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government 
// retains certain rights in this software.
// 
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
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//  
// This library is distributed in the hope that it will be useful, but
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//                                                                                 
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// License along with this library; if not, write to the Free Software
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// Questions? Contact Kevin Long (krlong@sandia.gov), 
// Sandia National Laboratories, Livermore, California, USA
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#include "SundanceMaximalQuadratureIntegral.hpp"
#include "SundanceGaussianQuadrature.hpp"
#include "SundanceSpatialDerivSpecifier.hpp"
#include "SundanceOut.hpp"
#include "PlayaTabs.hpp"
#include "Teuchos_TimeMonitor.hpp"

using namespace Sundance;
using namespace Teuchos;

using std::endl;
using std::setw;
using std::setprecision;

extern "C" 
{
int dgemm_(const char* transA, const char* transB,
  const int* M, const int *N, const int* K,
  const double* alpha, 
  const double* A, const int* ldA,
  const double* B, const int* ldB,
  const double* beta,
  double* C, const int* ldC);
}

static Time& maxCellQuadrature0Timer() 
{
  static RCP<Time> rtn
    = TimeMonitor::getNewTimer("max cell 0-form quadrature"); 
  return *rtn;
}

static Time& maxCellQuadrature1Timer() 
{
  static RCP<Time> rtn
    = TimeMonitor::getNewTimer("max cell 1-form quadrature"); 
  return *rtn;
}

static Time& maxCellQuadrature2Timer() 
{
  static RCP<Time> rtn
    = TimeMonitor::getNewTimer("max cell 2-form quadrature"); 
  return *rtn;
}


MaximalQuadratureIntegral::MaximalQuadratureIntegral(
  const CellType& cellType,
  const QuadratureFamily& quad,
  const ParametrizedCurve& globalCurve,
  const Mesh& mesh,
  int verb)
  : ElementIntegral(dimension(cellType), cellType, dimension(cellType),
    cellType, true, globalCurve, mesh, verb),
    quad_(quad),
    quadPts_(),
    quadWeights_(),
    W_(),
    useSumFirstMethod_(true)
{
  Tabs tab0(0);
  
  SUNDANCE_MSG1(setupVerb(), tab0 << "MaximalQuadratureIntegral ctor for 0-form");
  if (setupVerb()) describe(Out::os());
  
  SUNDANCE_MSG1(setupVerb(), tab0 << "quadrature family=" << quad);  

  /* create the quad points and weights */
  quad.getPoints(cellType, quadPts_, quadWeights_);
  int nQuad = quadPts_.size();
      
  W_.resize(nQuad);
      
  for (int q=0; q<nQuad; q++)
  {
    W_[q] = quadWeights_[q];
  }
}


MaximalQuadratureIntegral::MaximalQuadratureIntegral(
  const CellType& cellType,
  const BasisFamily& testBasis,
  int alpha,
  int testDerivOrder,
  const QuadratureFamily& quad,
  const ParametrizedCurve& globalCurve,
  const Mesh& mesh,
  int verb)
  : ElementIntegral(dimension(cellType), cellType, dimension(cellType),
    cellType, testBasis,
    alpha, testDerivOrder, true, globalCurve, mesh, verb),
    quad_(quad),
    quadPts_(),
    quadWeights_(),
    W_(),
    useSumFirstMethod_(true)
{
  Tabs tab0(0);
  
  SUNDANCE_MSG1(setupVerb(), tab0 << "MaximalQuadratureIntegral ctor for 1-form");
  if (setupVerb()) describe(Out::os());
  assertLinearForm();

  
  SUNDANCE_MSG1(setupVerb(), tab0 << "quadrature family=" << quad);  
  
  quad.getPoints(cellType, quadPts_, quadWeights_);
  int nQuad = quadPts_.size();
      
  W_.resize(nQuad * nRefDerivTest() * nNodesTest());

  SUNDANCE_MSG1(setupVerb(), tab0 << "num nodes for test function " << nNodesTest());

  Array<Array<Array<Array<double> > > > testBasisVals(nRefDerivTest());

  for (int r=0; r<nRefDerivTest(); r++)
  {
    Tabs tab3;
    SUNDANCE_MSG1(setupVerb(), tab3 
      << "evaluating basis functions for ref deriv direction " << r);
    MultiIndex mi;
    testBasisVals[r].resize(testBasis.dim());
    if (testDerivOrder==1) mi[r] = 1;
    SpatialDerivSpecifier deriv(mi);
    testBasis.refEval(evalCellType(), quadPts_, deriv, 
      testBasisVals[r], setupVerb());
  }

  int vecComp = 0;
  W_ACI_F1_.resize(nQuad);
  for (int q=0; q<nQuad; q++)
  {
    W_ACI_F1_[q].resize(nRefDerivTest());
    for (int t=0; t<nRefDerivTest(); t++)
    {
      W_ACI_F1_[q][t].resize(nNodesTest());
      for (int nt=0; nt<nNodesTest(); nt++)
      {
        wValue(q, t, nt) 
          = chop(quadWeights_[q] * testBasisVals[t][vecComp][q][nt]) ;
        W_ACI_F1_[q][t][nt] = chop(testBasisVals[t][vecComp][q][nt]);
      }
    }
  }

  addFlops(2*nQuad*nRefDerivTest()*nNodesTest());
}




MaximalQuadratureIntegral::MaximalQuadratureIntegral(
  const CellType& cellType,
  const BasisFamily& testBasis,
  int alpha,
  int testDerivOrder,
  const BasisFamily& unkBasis,
  int beta,
  int unkDerivOrder,
  const QuadratureFamily& quad,
  const ParametrizedCurve& globalCurve,
  const Mesh& mesh,
  int verb)
  : ElementIntegral(dimension(cellType), cellType, dimension(cellType),
    cellType, testBasis,
    alpha, testDerivOrder, unkBasis, beta, unkDerivOrder, true,
    globalCurve, mesh, 
    verb),
    quad_(quad),
    quadPts_(),
    quadWeights_(),
    W_(),
    useSumFirstMethod_(true)
{
  Tabs tab0(0);
  
  SUNDANCE_MSG1(setupVerb(), tab0 << "MaximalQuadratureIntegral ctor for 2-form");
  if (setupVerb()) describe(Out::os());
  assertBilinearForm();

  // store the quadrature points and weights  
  quad.getPoints(cellType, quadPts_, quadWeights_);
  int nQuad = quadPts_.size();

  W_.resize(nQuad * nRefDerivTest() * nNodesTest()  
    * nRefDerivUnk() * nNodesUnk());


  /* compute the basis functions */
  Array<Array<Array<Array<double> > > > testBasisVals(nRefDerivTest());
  Array<Array<Array<Array<double> > > > unkBasisVals(nRefDerivUnk());
  

  for (int r=0; r<nRefDerivTest(); r++)
  {
    testBasisVals[r].resize(testBasis.dim());
    MultiIndex mi;
    if (testDerivOrder==1) mi[r] = 1;
    SpatialDerivSpecifier deriv(mi);
    testBasis.refEval(evalCellType(), quadPts_, deriv, 
      testBasisVals[r], setupVerb());
  }
  
  for (int r=0; r<nRefDerivUnk(); r++)
  {
    unkBasisVals[r].resize(unkBasis.dim());
    MultiIndex mi;
    if (unkDerivOrder==1) mi[r] = 1;
    SpatialDerivSpecifier deriv(mi);
    unkBasis.refEval(evalCellType(), 
      quadPts_, deriv, unkBasisVals[r], setupVerb());
  }
  

  int vecComp = 0;
  /* form the products of basis functions at each quad pt */
  W_ACI_F2_.resize(nQuad);
  for (int q=0; q<nQuad; q++)
  {
    W_ACI_F2_[q].resize(nRefDerivTest());
    for (int t=0; t<nRefDerivTest(); t++)
    {
      W_ACI_F2_[q][t].resize(nNodesTest());
      for (int nt=0; nt<nNodesTest(); nt++)
      {
        W_ACI_F2_[q][t][nt].resize(nRefDerivUnk());
        for (int u=0; u<nRefDerivUnk(); u++)
        {
          W_ACI_F2_[q][t][nt][u].resize(nNodesUnk());
          for (int nu=0; nu<nNodesUnk(); nu++)
          {
            wValue(q, t, nt, u, nu)
              = chop(quadWeights_[q] * testBasisVals[t][vecComp][q][nt] 
                * unkBasisVals[u][vecComp][q][nu]);
            W_ACI_F2_[q][t][nt][u][nu] =
              chop(testBasisVals[t][vecComp][q][nt] * unkBasisVals[u][vecComp][q][nu]);
          }
        }
      }
    }
  }

  addFlops(3*nQuad*nRefDerivTest()*nNodesTest()*nRefDerivUnk()*nNodesUnk()
    + W_.size());
  for (int i=0; i<W_.size(); i++) W_[i] = chop(W_[i]);

}


void MaximalQuadratureIntegral
::transformZeroForm(const CellJacobianBatch& JTrans,  
  const CellJacobianBatch& JVol,
  const Array<int>& isLocalFlag,
  const Array<int>& facetIndex,
  const RCP<Array<int> >& cellLIDs,
  const double* const coeff,
  RCP<Array<double> >& A) const
{
  TimeMonitor timer(maxCellQuadrature0Timer());
  Tabs tabs;
  SUNDANCE_MSG1(integrationVerb(), tabs << "doing zero form by quadrature");

  TEUCHOS_TEST_FOR_EXCEPTION(order() != 0, std::logic_error,
    "MaximalQuadratureIntegral::transformZeroForm() called "
    "for form of order " << order());

  TEUCHOS_TEST_FOR_EXCEPTION( (int) isLocalFlag.size() != 0 
    && (int) isLocalFlag.size() != JVol.numCells(),
    std::runtime_error,
    "mismatch between isLocalFlag.size()=" << isLocalFlag.size()
    << " and JVol.numCells()=" << JVol.numCells());

  bool checkLocalFlag = (int) isLocalFlag.size() != 0;

  const Array<int>* cellLID = cellLIDs.get();
  int nQuad = quadWeights_.size();


  double& a = (*A)[0];
  SUNDANCE_MSG5(integrationVerb(), tabs << "input A=");
  if (integrationVerb() >= 5) writeTable(Out::os(), tabs, *A, 6);
  double* coeffPtr = (double*) coeff;
  const Array<double>& w = W_;

  if (globalCurve().isCurveValid()) /* ---------- ACI ------------- */
  {
    Array<double> quadWeightsTmp = quadWeights_;
    Array<Point> quadPointsTmp = quadPts_;
    int fc = 0;
    bool isCutByCurve;

    for (int c=0; c<JVol.numCells(); c++)
    {
      if (checkLocalFlag && !isLocalFlag[c]) 
      {
        coeffPtr += nQuad;
        continue;
      }
      double detJ = fabs(JVol.detJ()[c]);
      
      quad_.getAdaptedWeights(cellType(), dim(), (*cellLID)[c], fc ,mesh(),
        globalCurve(), quadPointsTmp, quadWeightsTmp, isCutByCurve);
      /* if we have special weights then do the same as before */
      if (isCutByCurve)
      {
        for (int q=0; q<nQuad; q++, coeffPtr++)
        {
          a += quadWeightsTmp[q]*(*coeffPtr)*detJ;
        }
      } // end cut by curve
      else
      {
        for (int q=0; q<nQuad; q++, coeffPtr++)
        {
          a += w[q]*(*coeffPtr)*detJ;
        }
      }
    }
  }
  else /* --------- No ACI ------------- */
  {
    for (int c=0; c<JVol.numCells(); c++)
    {
      if (checkLocalFlag && !isLocalFlag[c]) 
      {
        coeffPtr += nQuad;
        continue;
      }
      double detJ = fabs(JVol.detJ()[c]);
      
      for (int q=0; q<nQuad; q++, coeffPtr++)
      {
        a += w[q]*(*coeffPtr)*detJ;
      }
    }
  }
  SUNDANCE_MSG5(integrationVerb(), tabs << "output A = ");
  if (integrationVerb() >= 5) writeTable(Out::os(), tabs, *A, 6);

  SUNDANCE_MSG1(integrationVerb(), tabs << "done zero form");
}


void MaximalQuadratureIntegral::transformOneForm(const CellJacobianBatch& JTrans,  
  const CellJacobianBatch& JVol,
  const Array<int>& facetIndex,
  const RCP<Array<int> >& cellLIDs,
  const double* const coeff,
  RCP<Array<double> >& A) const
{
  TimeMonitor timer(maxCellQuadrature1Timer());
  Tabs tabs;
  TEUCHOS_TEST_FOR_EXCEPTION(order() != 1, std::logic_error,
    "MaximalQuadratureIntegral::transformOneForm() called for form "
    "of order " << order());
  SUNDANCE_MSG2(integrationVerb(), tabs << "doing one form by quadrature");
  int flops = 0;
  const Array<int>* cellLID = cellLIDs.get();

  int nQuad = quadWeights_.size();

  /* If the derivative order is zero, the only thing to be done 
   * is to multiply by the cell's Jacobian determinant and sum over the
   * quad points */
  if (testDerivOrder() == 0)
  {
    double* aPtr = &((*A)[0]);
    SUNDANCE_MSG5(integrationVerb(), tabs << "input A = ");
    if (integrationVerb() >= 5) writeTable(Out::os(), tabs, *A, 6);
  
    double* coeffPtr = (double*) coeff;
    int offset = 0 ;
    const Array<double>& w = W_;

    if (globalCurve().isCurveValid()) /* ----- ACI logic ---- */
    {
      Array<double> quadWeightsTmp = quadWeights_;
      Array<Point> quadPointsTmp = quadPts_; 
      bool isCutByCurve;

      for (int c=0; c<JVol.numCells(); c++, offset+=nNodes())
      {
        Tabs tab2;
        double detJ = fabs(JVol.detJ()[c]);
        int fc = 0;

        SUNDANCE_MSG4(integrationVerb(), tab2 << "c=" << c << " detJ=" << detJ);
        
        /* call the special integration routine */
        quad_.getAdaptedWeights(cellType(), dim(), (*cellLID)[c] , fc ,
          mesh() , globalCurve() , quadPointsTmp , quadWeightsTmp , isCutByCurve );
        if (isCutByCurve)
        {
          Array<double> wi;
          wi.resize(nQuad * nNodes()); //recalculate the special weights
          for (int ii = 0 ; ii < wi.size() ; ii++ ) wi[ii] = 0.0;
          for (int n = 0 ; n < nNodes() ; n++)
          {
            for (int q=0 ; q < quadWeightsTmp.size() ; q++)
            {
              //Indexing: testNode + nNodesTest()*(testDerivDir + nRefDerivTest()*q)
              wi[n + nNodes()*q] +=
                chop(quadWeightsTmp[q] * W_ACI_F1_[q][0][n]);
            }
          }
          // if it is cut by curve then use this vector
          for (int q=0; q<nQuad; q++, coeffPtr++)
          {
            double f = (*coeffPtr)*detJ;
            for (int n=0; n<nNodes(); n++)
            {
              aPtr[offset+n] += f*wi[n + nNodes()*q];
            }
          }
        } // end isCutByCurve
        else 
        {
          for (int q=0; q<nQuad; q++, coeffPtr++)
          {
            double f = (*coeffPtr)*detJ;
            for (int n=0; n<nNodes(); n++)
            {
              aPtr[offset+n] += f*w[n + nNodes()*q];
            }
          }
        }

        if (integrationVerb() >= 4)
        {
          Out::os() << tab2 << "integration results on cell:" << std::endl;
          Out::os() << tab2 << setw(10) << "n" << setw(12) << "I_n" << std::endl;
          for (int n=0; n<nNodes(); n++) 
          {
            Out::os() << tab2 << setw(10) << n 
                      << setw(12) << setprecision(6) << aPtr[offset+n] << std::endl;
          }
        }
      }
    } 
    else /* -------- No ACI -------- */ 
    {
      for (int c=0; c<JVol.numCells(); c++, offset+=nNodes())
      {
        Tabs tab2;
        double detJ = fabs(JVol.detJ()[c]);
        SUNDANCE_MSG4(integrationVerb(), tab2 << "c=" << c << " detJ=" << detJ);

        for (int q=0; q<nQuad; q++, coeffPtr++)
        {
          Tabs tab3;
          double f = (*coeffPtr)*detJ;
          SUNDANCE_MSG4(integrationVerb(), tab3 << "q=" << q << " coeff=" <<
            *coeffPtr << " coeff*detJ=" << f);
          for (int n=0; n<nNodes(); n++)
          {
            Tabs tab4;
            SUNDANCE_MSG4(integrationVerb(), tab4 << "n=" << n << " w=" <<
              w[n + nNodes()*q]);
            aPtr[offset+n] += f*w[n + nNodes()*q];
          }
        }

        if (integrationVerb() >= 4)
        {
          Out::os() << tab2 << "integration results on cell:" << std::endl;
          Out::os() << tab2 << setw(10) << "n" << setw(12) << "I_n" << std::endl;
          for (int n=0; n<nNodes(); n++) 
          {
            Out::os() << tab2 << setw(10) << n 
                      << setw(12) << setprecision(6) << aPtr[offset+n] << std::endl;
          }
        }
        
      }
    }

    SUNDANCE_MSG5(integrationVerb(), tabs << "output A = ");
    if (integrationVerb() >= 5) writeTable(Out::os(), tabs, *A, 6);
  }
  else
  {
    /* If the derivative order is nonzero, then we have to do a transformation. */
    
    createOneFormTransformationMatrix(JTrans, JVol);
    
    SUNDANCE_MSG4(transformVerb(), 
      Tabs() << "transformation matrix=" << G(alpha()));
    
    double* GPtr = &(G(alpha())[0]);      
    
    transformSummingFirst(JVol.numCells(), facetIndex, cellLIDs, GPtr, coeff, A);
  }
  addFlops(flops);
}


void MaximalQuadratureIntegral::transformTwoForm(const CellJacobianBatch& JTrans,
  const CellJacobianBatch& JVol,
  const Array<int>& facetIndex,
  const RCP<Array<int> >& cellLIDs,
  const double* const coeff,
  RCP<Array<double> >& A) const
{
  TimeMonitor timer(maxCellQuadrature2Timer());
  Tabs tabs;
  TEUCHOS_TEST_FOR_EXCEPTION(order() != 2, std::logic_error,
    "MaximalQuadratureIntegral::transformTwoForm() called for form "
    "of order " << order());
  SUNDANCE_MSG2(integrationVerb(), tabs << "doing one form by quadrature");

  int nQuad = quadWeights_.size();
  const Array<int>* cellLID = cellLIDs.get();


  /* If the derivative orders are zero, the only thing to be done 
   * is to multiply by the cell's Jacobian determinant and sum over the
   * quad points */
  if (testDerivOrder() == 0 && unkDerivOrder() == 0)
  {
    double* aPtr = &((*A)[0]);
    double* coeffPtr = (double*) coeff;
    int offset = 0 ;
    const Array<double>& w = W_;
    if (globalCurve().isCurveValid())
    {
      int fc = 0;
      Array<double> quadWeightsTmp = quadWeights_;
      Array<Point> quadPointsTmp = quadPts_;
      bool isCutByCurve;

      for (int c=0; c<JVol.numCells(); c++, offset+=nNodes())
      {
        double detJ = fabs(JVol.detJ()[c]);
        quadWeightsTmp = quadWeights_;
        quadPointsTmp = quadPts_;
        /* call the special integration routine */
        quad_.getAdaptedWeights(cellType(), dim(), (*cellLID)[c] , fc ,
          mesh() , globalCurve() , quadPointsTmp , quadWeightsTmp , isCutByCurve );
        if (isCutByCurve)
        {
          Array<double> wi;
          wi.resize(nQuad * nNodesTest() *nNodesUnk() ); //recalculate the special weights
          for (int ii = 0 ; ii < wi.size() ; ii++ ) wi[ii] = 0.0;
          /* Good coding practice: always use braces { } when nesting loops even if
           * there's only one line. Otherwise, if someone inserts a new line 
           * (e.g., a print statement) it can totally change the code logic */
          for (int nt = 0 ; nt < nNodesTest() ; nt++)
          {
            for (int nu=0; nu<nNodesUnk(); nu++)
            { 
              for (int q=0 ; q < quadWeightsTmp.size() ; q++)
              {
                //Indexing: unkNode + nNodesUnk()*(testNode + nNodesTest()*(unkDerivDir + nRefDerivUnk()*(testDerivDir + nRefDerivTest()*q)))
                wi[nu + nNodesUnk()*(nt + nNodesTest()*q)] +=
                  chop(quadWeightsTmp[q] * W_ACI_F2_[q][0][nt][0][nu]);
              }
            }
          }
          for (int q=0; q<nQuad; q++, coeffPtr++)
          {
            double f = (*coeffPtr)*detJ;
            for (int n=0; n<nNodes(); n++)
            {
              aPtr[offset+n] += f*wi[n + nNodes()*q];
            }
          }
        }// end isCutByCurve
        else
        {
          for (int q=0; q<nQuad; q++, coeffPtr++)
          {
            double f = (*coeffPtr)*detJ;
            for (int n=0; n<nNodes(); n++)
            {
              aPtr[offset+n] += f*w[n + nNodes()*q];
            }
          }
        }
      }
    }
    else  // No ACI
    {
      for (int c=0; c<JVol.numCells(); c++, offset+=nNodes())
      {
        double detJ = fabs(JVol.detJ()[c]);
        for (int q=0; q<nQuad; q++, coeffPtr++)
        {
          double f = (*coeffPtr)*detJ;
          for (int n=0; n<nNodes(); n++)
          {
            aPtr[offset+n] += f*w[n + nNodes()*q];
          }
        }
      }
    }

    addFlops( JVol.numCells() * (1 + nQuad * (1 + 2*nNodes())) );
  }
  else
  {
    createTwoFormTransformationMatrix(JTrans, JVol);
    double* GPtr;

    if (testDerivOrder() == 0)
    {
      GPtr = &(G(beta())[0]);
      SUNDANCE_MSG2(transformVerb(),
        Tabs() << "transformation matrix=" << G(beta()));
    }
    else if (unkDerivOrder() == 0)
    {
      GPtr = &(G(alpha())[0]);
      SUNDANCE_MSG2(transformVerb(),
        Tabs() << "transformation matrix=" << G(alpha()));
    }
    else
    {
      GPtr = &(G(alpha(), beta())[0]);
      SUNDANCE_MSG2(transformVerb(),
        Tabs() << "transformation matrix=" 
        << G(alpha(),beta()));
    }
        
      
    transformSummingFirst(JTrans.numCells(), facetIndex, cellLIDs, GPtr, coeff, A);
  }
}

void MaximalQuadratureIntegral
::transformSummingFirst(int nCells,
  const Array<int>& facetIndex,
  const RCP<Array<int> >& cellLIDs,
  const double* const GPtr,
  const double* const coeff,
  RCP<Array<double> >& A) const
{
  double* aPtr = &((*A)[0]);
  double* coeffPtr = (double*) coeff;
  const Array<int>* cellLID = cellLIDs.get();
  int nQuad = quadWeights_.size();
  
  int transSize = 0; 
  if (order()==2)
  {
    transSize = nRefDerivTest() * nRefDerivUnk();
  }
  else
  {
    transSize = nRefDerivTest();
  }

  /* The sum workspace is used to store the sum of untransformed quantities */
  static Array<double> sumWorkspace;

  int swSize = transSize * nNodes();
  sumWorkspace.resize(swSize);
  const Array<double>& w = W_;  
  
  /*
   * The number of operations for the sum-first method is 
   * 
   * Adds: (N_c * nNodes * transSize) * (N_q + 1) 
   * Multiplies: same as number of adds
   * Total: 2*(N_c * nNodes * transSize) * (N_q + 1) 
   */
  if (globalCurve().isCurveValid()) /* -------- ACI --------- */
  {
    Array<double> quadWeightsTmp = quadWeights_;
    Array<Point> quadPointsTmp = quadPts_;
    bool isCutByCurve;

    for (int c=0; c<nCells; c++)
    {
      /* sum untransformed basis combinations over quad points */
      for (int i=0; i<swSize; i++) sumWorkspace[i]=0.0;
      int fc = 0;

      /* call the special integration routine */
      quad_.getAdaptedWeights(cellType(), dim(), (*cellLID)[c] , fc ,
        mesh() , globalCurve() , quadPointsTmp , quadWeightsTmp , isCutByCurve );
      if (isCutByCurve)
      {
        Array<double> wi;
        if (order()==1)
        { // one form integral
          wi.resize(nQuad * nRefDerivTest() * nNodesTest()); //recalculate the special weights
          for (int ii = 0 ; ii < wi.size() ; ii++ ) wi[ii] = 0.0;

          for (int n = 0 ; n < nNodes() ; n++)
          {
            for (int t=0; t<nRefDerivTest(); t++)
            {
              for (int q=0 ; q < quadWeightsTmp.size() ; q++)
              {
                //Indexing: testNode + nNodesTest()*(testDerivDir + nRefDerivTest()*q)
                wi[n + nNodes()*(t + nRefDerivTest()*q)] +=
                  chop(quadWeightsTmp[q] * W_ACI_F1_[q][t][n]);
              }
            }
          }
        }
        else
        { // two from integrals
          wi.resize(nQuad * nRefDerivTest() * nNodesTest()
            * nRefDerivUnk() * nNodesUnk() ); //recalculate the special weights
          for (int ii = 0 ; ii < wi.size() ; ii++ ) wi[ii] = 0.0;

          for (int t=0; t<nRefDerivTest(); t++)
          {
            for (int nt = 0 ; nt < nNodesTest() ; nt++)
            {
              for (int u=0; u<nRefDerivUnk(); u++)
              {
                for (int nu=0; nu<nNodesUnk(); nu++)
                {
                  for (int q=0 ; q < quadWeightsTmp.size() ; q++)
                  {
                    //Indexing: unkNode + nNodesUnk()*(testNode + nNodesTest()*
                    //(unkDerivDir + nRefDerivUnk()*(testDerivDir + nRefDerivTest()*q)))
                    wi[nu + nNodesUnk()*(nt + nNodesTest()*(u + nRefDerivUnk()*(t + nRefDerivTest()*q)))] +=
                      chop(quadWeightsTmp[q] * W_ACI_F2_[q][t][nt][u][nu]);
                  }
                }
              }
            }
          }
        }// end two form integral
        
        for (int q=0; q<nQuad; q++, coeffPtr++)
        {
          double f = (*coeffPtr);
          for (int n=0; n<swSize; n++)
          {
            sumWorkspace[n] += f*wi[n + q*swSize];
          }
        }
        
      }
      else /* Cell not cut by curve */
      {
        for (int q=0; q<nQuad; q++, coeffPtr++)
        {
          double f = (*coeffPtr);
          for (int n=0; n<swSize; n++)
          {
            sumWorkspace[n] += f*w[n + q*swSize];
          }
        }
      }
    
      /* transform the sum for this cell */
      const double * const gCell = &(GPtr[transSize*c]);
      double* aCell = aPtr + nNodes()*c;
      for (int i=0; i<nNodes(); i++)
      {
        for (int j=0; j<transSize; j++)
        {
          aCell[i] += sumWorkspace[nNodes()*j + i] * gCell[j];
        }
      }
    }
  }
  else /* no ACI */
  {
    /* Sum */
    for (int c=0; c<nCells; c++)
    {
      /* sum untransformed basis combinations over quad points */
      for (int i=0; i<swSize; i++) sumWorkspace[i]=0.0;
      
      for (int q=0; q<nQuad; q++, coeffPtr++)
      {
        double f = (*coeffPtr);
        for (int n=0; n<swSize; n++)
        {
          sumWorkspace[n] += f*w[n + q*swSize];
        }
      }
    
      /* transform the sum */
      const double * const gCell = &(GPtr[transSize*c]);
      double* aCell = aPtr + nNodes()*c;
      for (int i=0; i<nNodes(); i++)
      {
        for (int j=0; j<transSize; j++)
        {
          aCell[i] += sumWorkspace[nNodes()*j + i] * gCell[j];
        }
      }
    }
  }
}