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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Andreas Gaida
Copyright (C) 2008 Ralph Schreyer
Copyright (C) 2008 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
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 license for more details.
*/
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
namespace QuantLib {
FirstDerivativeOp::FirstDerivativeOp(
Size direction,
const ext::shared_ptr<FdmMesher>& mesher)
: TripleBandLinearOp(direction, mesher) {
const ext::shared_ptr<FdmLinearOpLayout> layout = mesher->layout();
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter!=endIter; ++iter) {
const Size i = iter.index();
const Real hm = mesher->dminus(iter, direction_);
const Real hp = mesher->dplus(iter, direction_);
const Real zetam1 = hm*(hm+hp);
const Real zeta0 = hm*hp;
const Real zetap1 = hp*(hm+hp);
if (iter.coordinates()[direction_] == 0) {
//upwinding scheme
lower_[i] = 0.0;
diag_[i] = -(upper_[i] = 1/hp);
}
else if ( iter.coordinates()[direction_]
== layout->dim()[direction]-1) {
// downwinding scheme
lower_[i] = -(diag_[i] = 1/hm);
upper_[i] = 0.0;
}
else {
lower_[i] = -hp/zetam1;
diag_[i] = (hp-hm)/zeta0;
upper_[i] = hm/zetap1;
}
}
}
}
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