SundanceTriangleQuadrature.cpp

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//                             Sundance
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#include "SundanceTriangleQuadrature.hpp"
#include "PlayaExceptions.hpp"
#include "SundanceOut.hpp"
#include "SundanceGauss1D.hpp"
#include "PlayaTabs.hpp"

using namespace Sundance;
using namespace Sundance;
using namespace Sundance;
using namespace Sundance;
using namespace Sundance;
using namespace Teuchos;

void TriangleQuadrature::getPoints(int order, Array<double>& wgt,
                                   Array<double>& x,
                                   Array<double>& y)
{
  if (!getSymmetricPoints(order, wgt, x, y)) 
    {
      getNonsymmetricPoints(order, wgt, x, y);
    }
}


bool TriangleQuadrature::getSymmetricPoints(int order, Array<double>& wgt,
                                            Array<double>& x,
                                            Array<double>& y)
{

  int np;
  Array<double> w;
  Array<int> multiplicity;
  Array<Array<double> > q;

  if (order==1)
    {
      multiplicity = tuple(1);
      np = 1;
      w = tuple(1.0);
      q.resize(1);
      q[0] = tuple(1.0/3.0, 1.0/3.0, 1.0/3.0);
    }
  else if (order==2)
    {
      multiplicity = tuple(3);
      np = 3;
      w = tuple(1.0/3.0);
      q.resize(1);
      q[0] = tuple(2.0/3.0, 1.0/6.0, 1.0/6.0);
    }
  else if (order==3)
    {
      multiplicity = tuple(6);
      np = 6;
      w = tuple(1.0/6.0);
      q.resize(1);
      q[0] = tuple(0.659027622374092, 0.231933368553031, 0.109039009072877);
    }
  else if (order==4)
    {
      multiplicity = tuple(3, 3);
      np = 6;
      w = tuple(0.109951743655322, 0.223381589678011);
      q.resize(2);
      q[0] = tuple(0.816847572980459, 0.091576213509771, 0.091576213509771);
      q[1] = tuple(0.108103018168070, 0.445948490915965, 0.445948490915965);
    }
  else if (order==5)
    {
      multiplicity = tuple(1, 3, 3);
      np = 7;
      q.resize(3);
      w = tuple(0.22500000000000, 0.125939180544827, 0.132394152788506);
      q[0] = tuple(1.0/3.0, 1.0/3.0, 1.0/3.0);
      q[1] = tuple(0.797426985353087, 0.101286507323456, 0.101286507323456);
      q[2] = tuple(0.059715871789770, 0.470142064105115, 0.470142064105115);
    }
  else if (order==6)
    {
      multiplicity = tuple(3, 3, 6);
      np = 12;
      q.resize(3);
      w = tuple(0.050844906370207, 0.116786275726379, 0.082851075618374);
      q[0] = tuple(0.873821971016996, 0.063089014491502, 0.063089014491502);
      q[1] = tuple(0.501426509658179, 0.249286745170910, 0.249286745170910);
      q[2] = tuple(0.636502499121399, 0.310352451033784, 0.053145049844817);
    }
  else
    {
      return false;
    }

  for (int i=0; i<q.length(); i++)
    {
      Array<Array<double> > qPerm;
      permute(multiplicity[i], q[i], qPerm);
      for (int j=0; j<multiplicity[i]; j++)
        {
          x.append(qPerm[j][0]);
          y.append(qPerm[j][1]);
          wgt.append(w[i]);
        }
    }
  
  return true;
}




void TriangleQuadrature::getNonsymmetricPoints(int order, Array<double>& wgt,
                                               Array<double>& x,
                                               Array<double>& y)
{
  int nNodes = (order+3)/2;
  Gauss1D rule(nNodes, -1.0, 1.0);
  Array<double> s = rule.nodes();
  Array<double> t = s;
  Array<double> w = rule.weights();
  int n = rule.nPoints();

  wgt.resize(n*n);
  x.resize(n*n);
  y.resize(n*n);

  int k=0;
  for (int i=0; i<n; i++)
    {
      double p = (1.0+s[i])/2.0;
      double J = 1.0-p;
      for (int j=0; j<n; j++, k++)
        {
          double q = (1.0 - p)*(1.0+t[j])/2.0;
          x[k] = p;
          y[k] = q;
          wgt[k] = 0.5*w[i]*w[j]*J;
        }
    }
}


void TriangleQuadrature::permute(int m, const Array<double>& q,
                                 Array<Array<double> >& qPerm)
{
  qPerm.resize(m);
  if (m==1)
    {
      qPerm[0] = q;
    }
  else if (m==3)
    {
      qPerm[0] = tuple(q[0], q[1], q[2]);
      qPerm[1] = tuple(q[1], q[0], q[2]);
      qPerm[2] = tuple(q[2], q[1], q[0]);
    }
  else if (m==6)
    {
      qPerm[0] = tuple(q[0], q[1], q[2]);
      qPerm[1] = tuple(q[0], q[2], q[1]);
      qPerm[2] = tuple(q[1], q[0], q[2]);
      qPerm[3] = tuple(q[1], q[2], q[0]);
      qPerm[4] = tuple(q[2], q[1], q[0]);
      qPerm[5] = tuple(q[2], q[0], q[1]);
    }
  else
    {
#ifndef TRILINOS_7
      SUNDANCE_ERROR("invalid multiplicity " 
                     << m <<
                     " in TriangleQuadrature::permute()");
#else
      SUNDANCE_ERROR7("invalid multiplicity " 
                     << m <<
                     " in TriangleQuadrature::permute()");
#endif
    }
}

bool TriangleQuadrature::test(int p)
{
  Array<double> w;
  Array<double> x;
  Array<double> y;

  getPoints(p, w, x, y);
  bool pass = true;
  
  for (int a=0; a<=p; a++)
    {
      for (int b=0; b<p-a; b++)
        {
          int cMax = p - a - b;
          for (int c=0; c<=cMax; c++)
            {
              double sum = 0.0;
              for (int q=0; q<w.length(); q++)
                {
                  sum += 0.5*w[q] * pow(x[q], (double) a) * pow(y[q], (double) b)
                    * pow(1.0 - x[q] - y[q], (double) c);
                }
              double err = fabs(sum - exact(a,b,c));
              bool localPass = err < 1.0e-14;
              pass = pass && localPass;
              if (!localPass)
                {
                  fprintf(stderr, "order=%d m (%d, %d, %d) q=%22.15g exact=%22.15g\n", p, a, b, c, sum, exact(a, b, c));
                  std::cerr << "error = " << err << std::endl;
                }
            }
        }
    }
  return pass;
}

double TriangleQuadrature::exact(int a, int b, int c)
{
  return fact(a)*fact(b)*fact(c)/fact(a+b+c+2);
}

double TriangleQuadrature::fact(int x)
{
  if (x==0) return 1.0;
  return x*fact(x-1);
}