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========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2021 OpenFOAM Foundation
\\/ M anipulation |
-------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM 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 3 of the License, or
(at your option) any later version.
OpenFOAM 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 OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
\*---------------------------------------------------------------------------*/
#include "ODESystem.H"
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
Foam::ODESystem::ODESystem()
{}
// * * * * * * * * * * * * * * * * Destructor * * * * * * * * * * * * * * * //
Foam::ODESystem::~ODESystem()
{}
// * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * * //
void Foam::ODESystem::check
(
const scalar x,
const scalarField& y,
const scalarField& dy,
const label li
) const
{
// Evaluate the derivatives using the derivatives method
scalarField dfdx0(nEqns());
derivatives(x, y, li, dfdx0);
// Evaluate the derivatives and the Jacobian using the Jacobian method
scalarField dfdx1(nEqns());
scalarSquareMatrix d2fdxdyAnalytic(nEqns());
jacobian(x, y, li, dfdx1, d2fdxdyAnalytic);
// Compare derivatives
Info<< "[derivatives] dfdx = ( ";
forAll(dfdx0, i) { Info<< dfdx0[i] << ' '; }
Info<< ")" << nl;
Info<< "[ jacobian] dfdx = ( ";
forAll(dfdx1, i) { Info<< dfdx1[i] << ' '; }
Info<< ")" << nl;
Info<< "[ ratio] dfdx = ( ";
forAll(dfdx1, i) { Info<< dfdx1[i]/stabilise(dfdx0[i], rootVSmall) << ' '; }
Info<< ")" << nl;
// Construct a Jacobian using the finite differences and the derivatives
// method
scalarSquareMatrix d2fdxdyFiniteDifference(nEqns());
scalarField y0(y), y1(y);
for (label i = 0; i < nEqns(); ++ i)
{
y0[i] = y[i] - dy[i];
y1[i] = y[i] + dy[i];
derivatives(x, y0, li, dfdx0);
derivatives(x, y1, li, dfdx1);
for (label j = 0; j < nEqns(); j++)
{
d2fdxdyFiniteDifference(j, i) = (dfdx1[j] - dfdx0[j])/(2*dy[i]);
}
y0[i] = y[i];
y1[i] = y[i];
}
for (label i = 0; i < nEqns(); ++ i)
{
UList<scalar> FD(d2fdxdyFiniteDifference[i], nEqns());
Info<< "[derivatives] d2fdxdy[" << i << "] = ( ";
forAll(FD, i) { Info<< FD[i] << ' '; }
Info<< ")" << nl;
}
for (label i = 0; i < nEqns(); ++ i)
{
UList<scalar> A(d2fdxdyAnalytic[i], nEqns());
Info<< "[ jacobian] d2fdxdy[" << i << "] = ( ";
forAll(A, i) { Info<< A[i] << ' '; }
Info<< ")" << nl;
}
for (label i = 0; i < nEqns(); ++ i)
{
UList<scalar> FD(d2fdxdyFiniteDifference[i], nEqns());
UList<scalar> A(d2fdxdyAnalytic[i], nEqns());
Info<< "[ ratio] d2fdxdy[" << i << "] = ( ";
forAll(A, i) { Info<< A[i]/stabilise(FD[i], rootVSmall) << ' '; }
Info<< ")" << nl;
}
}
// ************************************************************************* //
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