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// This file is part of ff3d - http://www.freefem.org/ff3d
// Copyright (C) 2001, 2002, 2003 Stphane Del Pino
// 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: ConformTransformation.cpp,v 1.13 2005/12/13 23:18:51 delpinux Exp $
#include <Domain.hpp>
#include <ConformTransformation.hpp>
#include <UserFunction.hpp>
real_t
ConformTransformationQ1Hexahedron::integrate(const UserFunction& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0;
}
//! Computes Xhat, the point which transformed is (x,y,z)
bool
ConformTransformationQ1Hexahedron::invertT(const real_t& x,
const real_t& y,
const real_t& z,
TinyVector<3,real_t>& Xhat) const
{
// initialization
for(size_t i=0; i<3; ++i)
Xhat[i] = 0.5;
TinyVector<3,real_t> X;
TinyVector<3,real_t> f;
TinyVector<3> delta;
const size_t maxiter = 100;
size_t niter = 0;
do {
niter++;
//! Computing F(Xhat) - (x,y,z).
value(Xhat,f);
f[0] -= x;
f[1] -= y;
f[2] -= z;
// Evaluation of the Jacobian
TinyMatrix<3,3,real_t> J;
dx(Xhat,X);
for (size_t i=0; i<3; ++i)
J(0,i) = X[i];
dy(Xhat,X);
for (size_t i=0; i<3; ++i)
J(1,i) = X[i];
dz(Xhat,X);
for (size_t i=0; i<3; ++i)
J(2,i) = X[i];
delta = f/J;
Xhat -= delta;
if ((niter>maxiter)or(Norm(f)>10)) {
value(Xhat,X);
return false;
}
} while(Norm(f)>1E-2);
value(Xhat,X);
return true;
}
real_t
ConformTransformationP1Tetrahedron::integrate(const UserFunction& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0;
}
real_t
ConformTransformationQ1CartesianHexahedron::
integrateCharacteristic(const Domain& d) const
{
// Here we use order 4 Lobatto quadrature
TinyVector<4, real_t> x;
x[0] = 0.;
x[1] = .27639320225002103036; //(1-sqrt(5)/5)/2.;
x[2] = .72360679774997896964; //(1+sqrt(5)/5)/2.;
x[3] = 1.;
TinyVector<4, real_t> w;
w[0] = 1./12.;
w[1] = 5./12.;
w[2] = 5./12.;
w[3] = 1./12.;
real_t sum = 0;
TinyVector<3, real_t> X_hat;
TinyVector<3, real_t> X;
for (unsigned i=0; i<4; ++i) {
X_hat[0] = x[i];
for (unsigned j=0; j<4; ++j) {
X_hat[1] = x[j];
for (unsigned k=0; k<4; ++k) {
X_hat[2] = x[k];
this->value(X_hat, X);
sum += w[i]*w[j]*w[k] * (d.inside(X) ? 1 : 0);
}
}
}
return sum;
}
real_t
ConformTransformationP1Triangle::integrate(const UserFunction& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0.;
}
real_t
ConformTransformationQ1Quadrangle::integrate(const UserFunction& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0.;
}
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