Rosenbrock23.C

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#include "Rosenbrock23.H"
#include "addToRunTimeSelectionTable.H"

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

namespace Foam
{
    defineTypeNameAndDebug(Rosenbrock23, 0);
    addToRunTimeSelectionTable(ODESolver, Rosenbrock23, dictionary);

const scalar
    Rosenbrock23::a21 = 1,
    Rosenbrock23::a31 = 1,
    Rosenbrock23::a32 = 0,

    Rosenbrock23::c21 = -1.0156171083877702091975600115545,
    Rosenbrock23::c31 = 4.0759956452537699824805835358067,
    Rosenbrock23::c32 = 9.2076794298330791242156818474003,

    Rosenbrock23::b1 = 1,
    Rosenbrock23::b2 = 6.1697947043828245592553615689730,
    Rosenbrock23::b3 = -0.4277225654321857332623837380651,

    Rosenbrock23::e1 = 0.5,
    Rosenbrock23::e2 = -2.9079558716805469821718236208017,
    Rosenbrock23::e3 = 0.2235406989781156962736090927619,

    Rosenbrock23::gamma = 0.43586652150845899941601945119356,
    Rosenbrock23::c2 = 0.43586652150845899941601945119356,

    Rosenbrock23::d1 = 0.43586652150845899941601945119356,
    Rosenbrock23::d2 = 0.24291996454816804366592249683314,
    Rosenbrock23::d3 = 2.1851380027664058511513169485832;
}


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

Foam::Rosenbrock23::Rosenbrock23(const ODESystem& ode, const dictionary& dict)
:
    ODESolver(ode, dict),
    adaptiveSolver(ode, dict),
    k1_(n_),
    k2_(n_),
    k3_(n_),
    err_(n_),
    dydx_(n_),
    dfdx_(n_),
    dfdy_(n_, n_),
    a_(n_, n_),
    pivotIndices_(n_)
{}


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

bool Foam::Rosenbrock23::resize()
{
    if (ODESolver::resize())
    {
        adaptiveSolver::resize(n_);

        resizeField(k1_);
        resizeField(k2_);
        resizeField(k3_);
        resizeField(err_);
        resizeField(dydx_);
        resizeField(dfdx_);
        resizeMatrix(dfdy_);
        resizeMatrix(a_);
        resizeField(pivotIndices_);

        return true;
    }
    else
    {
        return false;
    }
}


Foam::scalar Foam::Rosenbrock23::solve
(
    const scalar x0,
    const scalarField& y0,
    const label li,
    const scalarField& dydx0,
    const scalar dx,
    scalarField& y
) const
{
    odes_.jacobian(x0, y0, li, 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, li, dydx_);

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

    LUBacksubstitute(a_, pivotIndices_, k2_);

    // Calculate k3:
    forAll(k3_, i)
    {
        k3_[i] = dydx_[i] + dx*d3*dfdx_[i]
          + (c31*k1_[i] + c32*k2_[i])/dx;
    }

    LUBacksubstitute(a_, pivotIndices_, k3_);

    // Calculate error and update state:
    forAll(y, i)
    {
        y[i] = y0[i] + b1*k1_[i] + b2*k2_[i] + b3*k3_[i];
        err_[i] = e1*k1_[i] + e2*k2_[i] + e3*k3_[i];
    }

    return normaliseError(y0, y, err_);
}


void Foam::Rosenbrock23::solve
(
    scalar& x,
    scalarField& y,
    const label li,
    scalar& dxTry
) const
{
    adaptiveSolver::solve(odes_, x, y, li, dxTry);
}


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