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// This file is part of ff3d - http://www.freefem.org/ff3d
// Copyright (C) 2007 Driss Yakoubi
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2, or (at your option)
// any later version.
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software Foundation,
// Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
// $Id: GaussLobatto.cpp,v 1.2 2007/06/09 10:37:07 delpinux Exp $
#include <cmath>
#include <LegendreBasis.hpp>
#include <Interval.hpp>
#include <GaussLobatto.hpp>
void GaussLobatto::
__bisection(const Interval& interval,
real_t& root)
{
LegendreBasis Ln(__degree);
const real_t epsilon = 1e-10;
real_t a = interval.a();
real_t b = interval.b();
do {
root= 0.5*(a+b);
if (Ln.getDerivativeValue(root,__degree)== 0) return;
if (Ln.getDerivativeValue(root,__degree)*Ln.getDerivativeValue(a,__degree) <0) {
b=root;
} else {
a=root;
}
} while (std:: abs(b-a) > epsilon );
}
GaussLobatto::
GaussLobatto(const size_t& degree,
const bool computeWeight)
: __degree(degree),
__vertices(degree+1),
__weights(degree+1)
{
__vertices[0] = -1;
__vertices[degree] = 1;
if (__degree!=1) {
if (__degree==2) {
Interval intervalRef(-1.,1.);
__bisection(intervalRef,__vertices[1]);
} else {
Interval intervalRef(-1.,1.);
GaussLobatto gaussN_1(__degree-1,false);
for (size_t i=1; i<__degree; ++i) {
Interval interval( gaussN_1(i-1),gaussN_1(i));
__bisection(interval,__vertices[i]);
}
}
}
if (computeWeight) {
const real_t w0= 2./(__degree*(__degree+1));
__weights[0]= w0;
__weights[__degree]=w0;
LegendreBasis Ln(__degree);
for (size_t i=1;i<__degree; ++i) {
__weights[i]= w0 / (Ln.getValue(__vertices[i],__degree) * Ln.getValue(__vertices[i],__degree));
}
}
}
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