Rosenbrock12.C

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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    \\  /    A nd           | Copyright (C) 2013-2016 OpenFOAM Foundation
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#include "Rosenbrock12.H"
#include "addToRunTimeSelectionTable.H"

// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //

namespace Foam
{
    defineTypeNameAndDebug(Rosenbrock12, 0);
    addToRunTimeSelectionTable(ODESolver, Rosenbrock12, dictionary);

const scalar
    Rosenbrock12::gamma = 1 + 1.0/std::sqrt(2.0),
    Rosenbrock12::a21 = 1.0/gamma,
    Rosenbrock12::c2 = 1.0,
    Rosenbrock12::c21 = -2.0/gamma,
    Rosenbrock12::b1 = (3.0/2.0)/gamma,
    Rosenbrock12::b2 = (1.0/2.0)/gamma,
    Rosenbrock12::e1 = b1 - 1.0/gamma,
    Rosenbrock12::e2 = b2,
    Rosenbrock12::d1 = gamma,
    Rosenbrock12::d2 = -gamma;
}


// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

Foam::Rosenbrock12::Rosenbrock12(const ODESystem& ode, const dictionary& dict)
:
    ODESolver(ode, dict),
    adaptiveSolver(ode, dict),
    k1_(n_),
    k2_(n_),
    err_(n_),
    dydx_(n_),
    dfdx_(n_),
    dfdy_(n_, n_),
    a_(n_, n_),
    pivotIndices_(n_)
{}


// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

Foam::scalar Foam::Rosenbrock12::solve
(
    const scalar x0,
    const scalarField& y0,
    const scalarField& dydx0,
    const scalar dx,
    scalarField& y
) const
{
    odes_.jacobian(x0, y0, dfdx_, dfdy_);

    for (label i=0; i<n_; i++)
    {
        for (label j=0; j<n_; j++)
        {
            a_(i, j) = -dfdy_(i, j);
        }

        a_(i, i) += 1.0/(gamma*dx);
    }

    LUDecompose(a_, pivotIndices_);

    // Calculate k1:
    forAll(k1_, i)
    {
        k1_[i] = dydx0[i] + dx*d1*dfdx_[i];
    }

    LUBacksubstitute(a_, pivotIndices_, k1_);

    // Calculate k2:
    forAll(y, i)
    {
        y[i] = y0[i] + a21*k1_[i];
    }

    odes_.derivatives(x0 + c2*dx, y, dydx_);

    forAll(k2_, i)
    {
        k2_[i] = dydx_[i] + dx*d2*dfdx_[i] + c21*k1_[i]/dx;
    }

    LUBacksubstitute(a_, pivotIndices_, k2_);

    // Calculate error and update state:
    forAll(y, i)
    {
        y[i] = y0[i] + b1*k1_[i] + b2*k2_[i];
        err_[i] = e1*k1_[i] + e2*k2_[i];
    }

    return normalizeError(y0, y, err_);
}


void Foam::Rosenbrock12::solve
(
    scalar& x,
    scalarField& y,
    scalar& dxTry
) const
{
    adaptiveSolver::solve(odes_, x, y, dxTry);
}


// ************************************************************************* //