CutCellMomentsImplem.H

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#ifdef CH_LANG_CC
/*
 *      _______              __
 *     / ___/ /  ___  __ _  / /  ___
 *    / /__/ _ \/ _ \/  V \/ _ \/ _ \
 *    \___/_//_/\___/_/_/_/_.__/\___/
 *    Please refer to Copyright.txt, in Chombo's root directory.
 */
#endif

#ifndef _CUTCELLMOMENTSIMPLEM_H_
#define _CUTCELLMOMENTSIMPLEM_H_

#if defined(CH_Darwin) && defined(__GNUC__) && ( __GNUC__ == 3 )
// deal with the broken isnan()/isinf() in GCC on MacOS
#include <unistd.h>
#define _GLIBCPP_USE_C99 1
#endif

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <iomanip>
#include <string>

#include "MayDay.H"

#include "LSProblem.H"

#include "NamespaceHeader.H"

// Null constructor
template <int dim> CutCellMoments<dim>::CutCellMoments()
{
}

// Copy constructor
template <int dim> CutCellMoments<dim>::CutCellMoments(const CutCellMoments<dim>& a_cutCellMoments)
  :m_moments         (a_cutCellMoments.m_moments),
   m_EBmoments       (a_cutCellMoments.m_EBmoments),
   m_bdCutCellMoments(a_cutCellMoments.m_bdCutCellMoments),
   m_IFData          (a_cutCellMoments.m_IFData),
   m_bdCCOn          (a_cutCellMoments.m_bdCCOn),
   m_residual        (a_cutCellMoments.m_residual),
   m_numActiveBounds (a_cutCellMoments.m_numActiveBounds),
   m_badNormal       (a_cutCellMoments.m_badNormal)
{
}

// Use this for initializing
template <int dim> CutCellMoments<dim>::CutCellMoments(const IFData<dim>& a_info)
  :m_IFData(a_info),
   m_numActiveBounds(0)
{
  m_bdCCOn    = false;
  m_badNormal = false;

  for (int hilo = 0; hilo < 2; ++hilo)
  {
    for (int idir = 0; idir < dim; ++idir)
    {
      //identifier for which boundary cutCellMoment
      Iv2 bdId;
      bdId[BDID_DIR] = idir;
      bdId[BDID_HILO] = hilo;

      IFData<dim-1> reducedInfo(a_info,a_info.m_maxOrder+1,idir,hilo);
      CutCellMoments<dim-1>bdCutCellMoments(reducedInfo);

      m_bdCutCellMoments[bdId] = bdCutCellMoments;


      // Notice whether reducedInfo coincides with the interface
      if (reducedInfo.m_allVerticesOn)
      {
        m_bdCCOn = true;
      }

      // Notice whether reducedInfo.m_normal = zero vector
      if (reducedInfo.m_badNormal)
      {
        m_badNormal = true;
      }

    }
  }
}

// Destructor
template <int dim> CutCellMoments<dim>::~CutCellMoments()
{
}

template <int dim> const CutCellMoments<dim - 1> CutCellMoments<dim>::getBdCutCellMoments(const Iv2 & a_bdId) const
{
  typename BdCutCellMoments::const_iterator it = m_bdCutCellMoments.find(a_bdId);

  if (it == m_bdCutCellMoments.end())
  {
    MayDay::Abort("Can't find this bdId in m_bdCutCellMoments");
  }

  return it->second;
}

// This function is called to fill the boundary moments from the higher
// dimension: it fills the moments in a_coarseCutCell using either the
// moments in the current cutcell map or the full cell/covered cell answers
// depending on the value of a_IFData.m_allVerticesIn/Out
template <int dim> void CutCellMoments<dim>::addBdMoments(CutCellMoments<dim>     & a_coarseBdCutCell,
                                                          const IFData<dim+1>     & a_IFData,
                                                          const int               & a_degreePmax,
                                                          const bool              & a_useConstraints,
                                                          const IndexTM<Real,dim> & a_refinedCenterDelta,
                                                          const IndexTM<int,dim>  & a_hilo)
{
  typedef map<IvDim,int > PthMomentLoc;

  if (a_IFData.m_allVerticesIn)
  {
    // The boundary map doesn't exist, we need to compute the full cell
    // quadrature for all monomial in order to use the changecoordinates
    // function.  Generate a full cell quadrature map.
    PthMoment fullCellMap;

    for (int iDegree = a_degreePmax; iDegree > 0; iDegree--)
    {
      // Creating a lsproblem generates the monomial map that is
      // needed to fill the moment maps
      LSProblem<dim> lsp(iDegree,a_useConstraints);
      const PthMomentLoc& momMap = lsp.getMonomialLocMapDegreePLess1();

      for (typename PthMomentLoc::const_iterator it = momMap.begin(); it != momMap.end(); ++it)
      {
        //        pout()<<"mono = "<<it->first<<endl;
        fullCellMap[it->first] = fullCellQuadrature(it->first,m_IFData.m_cellCenterCoord);
      }
    }

    for (int iDegree = a_degreePmax; iDegree > 0; iDegree--)
    {
      LSProblem<dim> lsp(iDegree,a_useConstraints);

      // Change the coordinates of the refined moments using the full
      // cell quadrature map.  Add up the obtained moment to the
      // coarse map
      const PthMomentLoc& momMap = lsp.getMonomialLocMapDegreePLess1();

      for (typename PthMomentLoc::const_iterator it = momMap.begin(); it != momMap.end(); ++it)
      {
        Real bdMoment = getBdMoment(it->first,a_IFData,a_refinedCenterDelta,fullCellMap);
        a_coarseBdCutCell.m_moments[it->first] += bdMoment;
      }
    }
  }
  else
  {
    for (int iDegree = a_degreePmax; iDegree > 0; iDegree--)
    {
      LSProblem<dim> lsp(iDegree,a_useConstraints);

      // Get the moments from the refined cell map + change coordinates
      // function if the refined cell is irregular or they are 0 as all
      // vertices are out
      const PthMomentLoc& momMap = lsp.getMonomialLocMapDegreePLess1();

      for (typename PthMomentLoc::const_iterator it = momMap.begin(); it != momMap.end(); ++it)
      {
        Real bdMoment = getBdMoment(it->first,a_IFData,a_refinedCenterDelta);
        a_coarseBdCutCell.m_moments[it->first] += bdMoment;
      }
    }
  }

  for (int iDegree = a_degreePmax; iDegree >= 0; iDegree--)
  {
    LSProblem<dim> lsp(iDegree,a_useConstraints);

    // EB moments are either found in the EB moment map or equals to 0
    // (allIn or allOut)
    const PthMomentLoc& momMapP = lsp.getMonomialLocMapDegreeP();

    for (typename PthMomentLoc::const_iterator it = momMapP.begin(); it != momMapP.end(); ++it)
    {
      Real bdEBMoment = getBdEBMoment(it->first,a_IFData,a_refinedCenterDelta);
      a_coarseBdCutCell.m_EBmoments[it->first] += bdEBMoment;
    }
  }

  IndexTM<int,2> bdId;

  for (int idir = 0; idir < dim; idir++)
  {
    bdId[0] = idir;

    // The refined cell center in dim-1 is needed to change the coordinate
    // system of the refined moments to the coordinate system where they are
    // needed.
    IndexTM<Real,dim-1> localRefinedCellCenter;
    IndexTM<int,dim-1> localHilo;

    for (int jdir = 0; jdir < dim; jdir++)
    {
      if (jdir < idir)
      {
        localRefinedCellCenter[jdir] = a_refinedCenterDelta[jdir];
        localHilo[jdir] = a_hilo[jdir];
      }
      else if (jdir > idir)
      {
        localRefinedCellCenter[jdir-1] = a_refinedCenterDelta[jdir];
        localHilo[jdir-1] = a_hilo[jdir];
      }
    }

    if (a_hilo[idir] != LARGEINTVAL)
    {
      bdId[1] = a_hilo[idir];
      // Drop one dimension to add up the boundary moments. Dropping one
      // dimension allows an easier implementation as 1D is a particular
      // case
      (m_bdCutCellMoments[bdId]).addBdMoments(a_coarseBdCutCell.m_bdCutCellMoments[bdId],m_IFData,a_degreePmax+1,a_useConstraints,localRefinedCellCenter,localHilo);
    }
    else
    {
      for (int side = 0; side < 2; side++)
      {
        bdId[1]=side;
        (m_bdCutCellMoments[bdId]).addBdMoments(a_coarseBdCutCell.m_bdCutCellMoments[bdId],m_IFData,a_degreePmax,a_useConstraints,localRefinedCellCenter,localHilo);
      }
    }
  }
}

template <int dim> Real CutCellMoments<dim>::fullCellQuadrature(const IndexTM<int,dim>      & a_mono,
                                                                const CoordinateSystem<dim> & a_coord)
{
  Real moment = 1.0;

  for (int idir = 0; idir < dim; ++idir)
  {
    Real loPt = a_coord.convertDir(-0.5*m_IFData.m_cellCenterCoord.m_dx[idir],
                                   m_IFData.m_cellCenterCoord,
                                   idir);

    Real hiPt = a_coord.convertDir(0.5*m_IFData.m_cellCenterCoord.m_dx[idir],
                                   m_IFData.m_cellCenterCoord,
                                   idir);

    Real idirInt = pow(hiPt,a_mono[idir] + 1) - pow(loPt,a_mono[idir] + 1);

    idirInt /= (a_mono[idir] + 1);
    moment *= idirInt;
  }

  return moment;
}

template <int dim> Real CutCellMoments<dim>::changeMomentCoordinates(PthMoment        & a_refinedMomentMap,
                                                                     const IndexTM<int,dim>  & a_monomial,
                                                                     const IndexTM<Real,dim> & a_refinedCenterDelta)
{
  // This function outputs the moment in the coordinate system where the
  // origin is the current cell center, given the moment map of the refined
  // moments computed in the coordinate system where the origin is the
  // refined cell center it uses a Taylor development around 0 of the function
  // (x+xc)^p1*(y+yc)^p2*...
  Real moment = 0.0;

  // Degree is the degree of the monomial
  int degree = 0;

  for (int i = 0; i < dim; i++)
  {
    degree += a_monomial[i];
  }

  // Loop over the possible values of r in the development of the Taylor series
  // The Taylor series has a finite expansion as the function's derivatives
  // are zero for r>degree
  for (int r = 0; r <= degree; r++)
  {
    if (r >= 0)
    {
      // Generate all the possible monomials of degree r and add up the moment
      IndexTM<int,dim> derivative;

      for (int idir = 0; idir < dim; ++idir)
      {
        derivative[idir] = 0;
      }

      while (true)
      {
        for (int j = 1; j < dim-1; ++j)
        {
          int t = r;
          for (int k = j+1; k < dim; ++k)
          {
            t -= derivative[k];
          }

          if (derivative[j] >  t)
          {
            derivative[j+1] += 1;
            derivative[j  ]  = 0;
          }
          else
          {
            break;
          }
        }

        if (derivative[dim-1] > r)
        {
          break;
        }

        derivative[0] = r;

        for (int j = 1; j < dim; ++j)
        {
          derivative[0] -= derivative[j];
        }

        // Add up the relevant term of the refined moment map to the map
        Real coeff = 1.0;
        Real factorial = 1.0;

        for (int idir = 0; idir < dim; idir++)
        {
          for (int j = 0; j < derivative[idir]; j++)
          {
            coeff *= a_monomial[idir] - j;
            factorial *= j+1;
          }

          // This is to prevent the computation of 0*0^-1 which result
          // in a nan
          if (a_monomial[idir]-derivative[idir] < 0)
          {
            if (coeff != 0)
            {
              MayDay::Abort("Coeff should be zero when the derivative has higher coefficient than the monomial");
            }
          }
          else
          {
            coeff *= pow(a_refinedCenterDelta[idir],a_monomial[idir]-derivative[idir]);
          }
        }

        //pout()<<a_refinedMomentMap[derivative]<<endl;
        moment += coeff * a_refinedMomentMap[derivative] / factorial;

        // Increments to get to the next derivative
        derivative[1] += 1;
      }
    }
  }

  return moment;
}

template <int dim> void CutCellMoments<dim>::changeMomentCoordinatesToCellCenter()
{
  // Move moments from parent coord to cell center coord
  IndexTM<Real,dim> delta = m_IFData.m_cellCenterCoord.m_origin;
  delta                  -= m_IFData.m_parentCoord    .m_origin;

  PthMoment copyMoments = m_moments;
  for (typename PthMoment::const_iterator it = copyMoments.begin();
       it != copyMoments.end(); ++it)
    {
      IvDim mono = it->first;
      m_moments[mono] = changeMomentCoordinates(copyMoments, mono, delta);
    }

  PthMoment copyEBMoments = m_EBmoments;
  for (typename PthMoment::const_iterator it = copyEBMoments.begin(); it != copyEBMoments.end(); ++it)
    {
      IvDim mono = it->first;
      m_EBmoments[mono] = changeMomentCoordinates(copyEBMoments, mono, delta);
    }
}

template <int dim> void CutCellMoments<dim>::changeMomentCoordinatesToParentCenter()
{
  // Move moments from cell center coord to parent coord
  IndexTM<Real,dim> delta = m_IFData.m_parentCoord    .m_origin;
  delta                  -= m_IFData.m_cellCenterCoord.m_origin;

  PthMoment copyMoments = m_moments;
  for (typename PthMoment::const_iterator it = copyMoments.begin();
       it != copyMoments.end(); ++it)
    {
      IvDim mono = it->first;
      m_moments[mono] = changeMomentCoordinates(copyMoments, mono, delta);
    }

  PthMoment copyEBMoments = m_EBmoments;
  for (typename PthMoment::const_iterator it = copyEBMoments.begin(); it != copyEBMoments.end(); ++it)
    {
      IvDim mono = it->first;
      m_EBmoments[mono] = changeMomentCoordinates(copyEBMoments, mono, delta);
    }
}

template <int dim> void CutCellMoments<dim>::initialize(CutCellMoments<dim> & a_refinedCutCell)
{
  // This initialize the maps of the current cut cell moment to zero by
  // iterating through the refined maps
  initializeMap(m_EBmoments,a_refinedCutCell.m_EBmoments);
  initializeMap(m_moments,a_refinedCutCell.m_moments);

  // Initialize maps on the boundary
  IndexTM<int,2> bdId;

  for (int idir = 0; idir < dim; idir++)
  {
    bdId[0] = idir;

    for (int hilo = 0; hilo < 2; hilo++)
    {
      bdId[1] = hilo;
      CutCellMoments<dim-1> refinedBdCutCell = a_refinedCutCell.getBdCutCellMoments(bdId);

      m_bdCutCellMoments[bdId].initialize(refinedBdCutCell);
    }
  }
}

template <int dim> void CutCellMoments<dim>::initializeMap(PthMomentLesserDimension & a_map1,
                                                           PthMomentLesserDimension & a_map2)
{
  for (typename PthMomentLesserDimension::const_iterator it = a_map2.begin(); it != a_map2.end(); ++it)
  {
    a_map1[it->first] = 0.0;
  }
}

template <int dim> void CutCellMoments<dim>::initializeMap(PthMoment & a_map1,
                                                           PthMoment & a_map2)
{
  for (typename PthMoment::const_iterator it = a_map2.begin(); it != a_map2.end(); ++it)
  {
    a_map1[it->first] = 0.0;
  }
}


template <int dim> Real CutCellMoments<dim>::getBdMoment(const IvDim             & a_mono,
                                                         const IFData<dim+1>     & a_IFData,
                                                         const IndexTM<Real,dim> & a_refinedCenterDelta,
                                                         PthMoment                 a_fullCellMap)
{
  // This computes the moments on the fly in the case the refined cell (in
  // dim+1) was all in or all out (in that case the boundary moments were
  // never computed) or looks for them in the moment map
  Real moment = LARGEREALVAL;

  if (a_IFData.m_allVerticesOut)
  {
    moment = 0.0;
  }
  else if (a_IFData.m_allVerticesIn)
  {
    moment = changeMomentCoordinates(a_fullCellMap,a_mono,a_refinedCenterDelta);
  }
  else
  {
    moment = changeMomentCoordinates(m_moments,a_mono,a_refinedCenterDelta);
  }

  return moment;
}

template <int dim> Real CutCellMoments<dim>::getBdEBMoment(const IvDim             & a_mono,
                                                           const IFData<dim+1>     & a_IFData,
                                                           const IndexTM<Real,dim> & a_refinedCenterDelta)
{
  // EB moments are 0 if the refined cell (in dim+1) is all in or all out,
  // otherwise they are in the current cell EB moment maps
  Real EBmoment = LARGEREALVAL;

  if (a_IFData.m_allVerticesOut || a_IFData.m_allVerticesIn)
  {
    EBmoment = 0.0;
  }
  else
  {
    EBmoment = changeMomentCoordinates(m_EBmoments,a_mono,a_refinedCenterDelta);
  }

  return EBmoment;
}

// Methods for reading moments that check the moment exists
template <int dim> Real CutCellMoments<dim>::getMoment(const IvDim   & a_mono,
                                                       const EBorVol & a_EBorVol) const
{
  Real moment = LARGEREALVAL;

  if (a_EBorVol == VolMoment)
  {
    // Find the vol in the map
    typename PthMoment::const_iterator it = m_moments.find(a_mono);

    if (it != m_moments.end())
    {
      moment = it->second;
    }
    else
    {
      MayDay::Abort("No volume moment in m_moments");
    }
  }
  else if (a_EBorVol == EBMoment)
  {
    // Find the vol in the EBmap
    typename PthMoment::const_iterator it = m_EBmoments.find(a_mono);

    if (it != m_EBmoments.end())
    {
      moment = it->second;
    }
    else
    {
      MayDay::Abort("No volume moment in m_bdMoments");
    }
  }
  else
  {
    MayDay::Abort("Must ask for EBMoment or VolMoment");
  }

  return moment;
}

template <int dim> Real CutCellMoments<dim>::getVol(const EBorVol& a_EBorVol) const
{
  Real volume;

  // Volume calculated by  integrating x^0 = 1
  IvDim zeroIv = IvDim::Zero;
  volume = getMoment(zeroIv,a_EBorVol);

  return volume;
}

template <int dim> IndexTM<Real,dim> CutCellMoments<dim>::getCentroid(const EBorVol& a_EBorVol) const
{
  // This call checks the string to be either "VolMoment" or "EBMoment"
  Real volume = getVol(a_EBorVol);

  RvDim centroid;

  // Mono= 0,0,...1,0,0
  for (int idir = 0; idir < dim; ++idir)
  {
    IvDim mono     = BASISV_TM<int,dim>(idir);
    centroid[idir] = getMoment(mono,a_EBorVol);

    if (volume < 0.0)
    {
      MayDay::Warning("CutCellMoments::getCentroid: Volume fraction is negative");
    }
    else if (volume == 0.0)
    {
      //MayDay::Abort("CutCellMoments::getCentroid: Volume fraction is zero");
    }

    centroid[idir] /= volume;
  }

  return centroid;
}

template <int dim> Real CutCellMoments<dim>::getResidual(const int & a_iDegree,
                                                         const int & a_normJ) const
{
  Real retval;
  if (isCovered() || isRegular())
    {
      retval = 0.0;
    }
  else
    {
      retval =  m_residual[a_iDegree][a_normJ];
    }

  return retval;
}

template <int dim> void CutCellMoments<dim>::setResidual(const Real& a_value,
                                                         const int & a_iDegree,
                                                         const int & a_normJ)
{
  if (isCovered() || isRegular())
    {
      MayDay::Abort("Invalid assignment to m_residual in covered or full cell");
    }
  else
    {
      m_residual[a_iDegree][a_normJ] = a_value;
    }
}

template <int dim> Vector<Real> CutCellMoments<dim>::sliceResidual(const int & a_iDegree) const
{
  if (isCovered() || isRegular())
    {
      pout()<<"Dim = "<< dim << endl;
      MayDay::Abort("Invalid attemtp to slice of m_residual in a covered or full CCM");
    }
  else
    {
      return m_residual[a_iDegree];
    }
}

template <int dim> bool CutCellMoments<dim>::isCovered() const
{
  return m_IFData.m_allVerticesOut;
}

template <int dim> bool CutCellMoments<dim>::isRegular() const
{
  return (m_IFData.m_allVerticesIn && (!m_bdCCOn));
}

template <int dim> void CutCellMoments<dim>::print(ostream& a_out) const
{
  string padding = "  ";
  for (int i = 0; i < GLOBALDIM - dim; i++)
  {
    padding += "  ";
  }

  a_out << padding << "Dim = " << dim << "\n";
  a_out << padding << "\n";

  for (typename PthMoment::const_iterator it = m_moments.begin(); it != m_moments.end(); ++it)
  {
    std::ios::fmtflags origFlags = a_out.flags();
    int origWidth = a_out.width();
    int origPrecision = a_out.precision();

    a_out << padding << "Integral "
                     << it->first
                     << " = "
                     << setw(23)
                     << setprecision(16)
                     << setiosflags(ios::showpoint)
                     << setiosflags(ios::scientific)
                     << it->second
                     << "\n";

    a_out.flags(origFlags);
    a_out.width(origWidth);
    a_out.precision(origPrecision);
  }

  if (m_moments.size() > 0)
  {
    a_out << padding << "\n";
  }

  for (typename PthMoment::const_iterator it = m_EBmoments.begin(); it != m_EBmoments.end(); ++it)
  {
    std::ios::fmtflags origFlags = a_out.flags();
    int origWidth = a_out.width();
    int origPrecision = a_out.precision();

    a_out << padding << "EBIntegral "
                     << it->first
                     << " = "
                     << setw(23)
                     << setprecision(16)
                     << setiosflags(ios::showpoint)
                     << setiosflags(ios::scientific)
                     << it->second
                     << "\n";

    a_out.flags(origFlags);
    a_out.width(origWidth);
    a_out.precision(origPrecision);
  }

  if (m_EBmoments.size() > 0)
  {
    a_out << padding << "\n";
  }

  a_out << padding << "Residuals:" << "\n";
  for (int i = 0; i < m_residual.size(); i++)
  {
    a_out << padding << "  " << i << ":";

    std::ios::fmtflags origFlags = a_out.flags();
    int origWidth = a_out.width();
    int origPrecision = a_out.precision();

    for (int j = 0; j < m_residual[i].size(); j++)
    {

      a_out << " "
            << setw(23)
            << setprecision(16)
            << setiosflags(ios::showpoint)
            << setiosflags(ios::scientific)
            << m_residual[i][j];
    }

    a_out.flags(origFlags);
    a_out.width(origWidth);
    a_out.precision(origPrecision);

    a_out << padding << "\n";
  }
  a_out << padding << "\n";

  a_out << padding << "IFData:" << "\n";
  a_out << padding << "\n";
  a_out << m_IFData;

  a_out << padding << "Number of bdCutCellMoments = "
                   << m_bdCutCellMoments.size()
                   << "\n";
  a_out << padding << "\n";

  for (typename BdCutCellMoments::const_iterator it = m_bdCutCellMoments.begin(); it != m_bdCutCellMoments.end(); ++it)
  {
    a_out << padding << "BdId = " << it->first << "\n";
    a_out << it->second;
  }
}

template <int dim> void CutCellMoments<dim>::dump() const
{
  print(pout());
}

// Operators
template <int dim> void CutCellMoments<dim>::operator=(const CutCellMoments<dim> & a_cutCellMoments)
{
  // Only copy if the objects are distinct
  if (this != &a_cutCellMoments)
  {
    m_moments          = a_cutCellMoments.m_moments;
    m_EBmoments        = a_cutCellMoments.m_EBmoments;
    m_bdCutCellMoments = a_cutCellMoments.m_bdCutCellMoments;
    m_IFData           = a_cutCellMoments.m_IFData;
    m_bdCCOn           = a_cutCellMoments.m_bdCCOn;
    m_residual         = a_cutCellMoments.m_residual;
    m_numActiveBounds  = a_cutCellMoments.m_numActiveBounds;
    m_badNormal        = a_cutCellMoments.m_badNormal;
  }
}

template <int dim> ostream& operator<<(ostream                   & a_out,
                                       const CutCellMoments<dim> & a_cutCellMoments)
{
  a_cutCellMoments.print(a_out);
  return a_out;
}

#include "NamespaceFooter.H"

#endif

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