orthpoly.cc

Go to the documentation of this file.

//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
//LIC// $LastChangedDate$
//LIC// 
//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
//LIC// modify it under the terms of the GNU Lesser General Public
//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
//LIC// 
//LIC// This library is distributed in the hope that it will be useful,
//LIC// but WITHOUT ANY WARRANTY; without even the implied warranty of
//LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//LIC// Lesser General Public License for more details.
//LIC// 
//LIC// You should have received a copy of the GNU Lesser General Public
//LIC// License along with this library; if not, write to the Free Software
//LIC// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
//LIC// 02110-1301  USA.
//LIC// 
//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
#include "orthpoly.h"

namespace oomph
{

namespace Orthpoly
{
// Calculates the Gauss Lobatto Legendre abscissas for degree p = NNode-1
void gll_nodes(const unsigned &Nnode, Vector<double> &x)
{
  double z,zold,del;
  unsigned p=Nnode-1;
  x.resize(Nnode);
  if(Nnode<2) 
   {
    throw OomphLibError("Invalid number of nodes",
                        OOMPH_CURRENT_FUNCTION,
                        OOMPH_EXCEPTION_LOCATION);
   }
  else if (Nnode==2){
    x[0]=-1.0;x[1]=1.0;
  }
  else if (Nnode==3){
    x[0]=-1;x[1]=0.0;x[2]=1.0;
  }
  else if (Nnode==4){
    x[0]=-1.0;x[1]=-std::sqrt(5.0)/5.0;x[2]=-x[1];x[3]=1.0;
  }
  else
    {
      unsigned mid;
      if(p%2==0){
        mid = p/2;
        x[mid]=0.0;
      }
      else mid=p/2+1;
      for(unsigned j=1;j<mid;j++) 
        {
          z=-std::cos(j*MathematicalConstants::Pi/double(p));
          do{
           del= dlegendre(p,z)/ddlegendre(p,z);
           zold=z;
           z=zold-del;
          } while(std::fabs(z-zold) > eps);
          x[j]=z;
          x[p-j]=-z;
        }
      x[0]=-1.0;x[p]=1.0;
    }
}

// This version of gll_nodes calculates the abscissas AND weights
void gll_nodes(const unsigned &Nnode, Vector<double> &x, Vector<double> &w)
{
 gll_nodes(Nnode,x);
 // Now calculate the corresponding weights
 double l_z;
 unsigned p = Nnode-1;
 for (unsigned i=0;i<p+1;i++){
  l_z=legendre(p,x[i]);
  w[i]=2.0/(p*(p+1)*l_z*l_z);
 }
}


// Calculates the Gauss Legendre abscissas of degree p=Nnode-1
void gl_nodes(const unsigned &Nnode, Vector<double> &x)
{
 double z,zold,del;
 unsigned p=Nnode-1;
 x.resize(Nnode);
 if(Nnode<2)
  {
   throw OomphLibError("Invalid number of nodes",
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  }
 else if (Nnode==2){
  x[0]=-1.0/3.0*std::sqrt(3.0);x[1]=-x[0];
 }
 else
  {
   unsigned mid;
   if(p%2==0){
    mid = p/2;
    x[mid]=0.0;
   }
   else mid=p/2+1;
   for(unsigned j=0;j<mid;j++) 
    {
     z=-std::cos((2.0*j+1.0)*MathematicalConstants::Pi/(2*double(p)+2.0));
     do{
      del = legendre(p+1,z)/dlegendre(p+1,z);
      zold=z;
            z=zold-del;
     } while(std::fabs(z-zold)>eps);
     x[j]=z;
     x[p-j]=-z;
    }
  }
}

// This version of gl_nodes calculates the abscissas AND weights
void gl_nodes(const unsigned &Nnode, Vector<double> &x, Vector<double> &w)
{
 gl_nodes(Nnode,x);
  // Now calculate the corresponding weights
  double dl_z;
  unsigned p = Nnode-1;
  for (unsigned i=0;i<p+1;i++){
   dl_z=dlegendre(p+1,x[i]);
   w[i]=2.0/(1-x[i]*x[i])/(dl_z*dl_z);
  }
}
}

}