Rosenbrock34.C

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#include "Rosenbrock34.H"
#include "addToRunTimeSelectionTable.H"

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

namespace Foam
{
    defineTypeNameAndDebug(Rosenbrock34, 0);
    addToRunTimeSelectionTable(ODESolver, Rosenbrock34, dictionary);

const scalar
    // Constants by Shampine
    // More accurate than the L-Stable coefficients for small step-size
    // but less stable for large step-size
    Rosenbrock34::a21 = 2,
    Rosenbrock34::a31 = 48.0/25.0,
    Rosenbrock34::a32 = 6.0/25.0,

    Rosenbrock34::c21 = -8,
    Rosenbrock34::c31 = 372.0/25.0,
    Rosenbrock34::c32 = 12.0/5.0,

    Rosenbrock34::c41 = -112.0/125.0,
    Rosenbrock34::c42 = -54.0/125.0,
    Rosenbrock34::c43 = -2.0/5.0,

    Rosenbrock34::b1 = 19.0/9.0,
    Rosenbrock34::b2 = 1.0/2.0,
    Rosenbrock34::b3 = 25.0/108.0,
    Rosenbrock34::b4 = 125.0/108.0,

    Rosenbrock34::e1 = 34.0/108.0,
    Rosenbrock34::e2 = 7.0/36.0,
    Rosenbrock34::e3 = 0,
    Rosenbrock34::e4 = 125.0/108.0,

    Rosenbrock34::gamma = 1.0/2.0,
    Rosenbrock34::c2 = 1,
    Rosenbrock34::c3  = 3.0/5.0,

    Rosenbrock34::d1 = 1.0/2.0,
    Rosenbrock34::d2 = -3.0/2.0,
    Rosenbrock34::d3 = 605.0/250.0,
    Rosenbrock34::d4 = 29.0/250.0;

    /*
    // L-Stable constants from Hairer et. al.
    Rosenbrock34::a21 = 2,
    Rosenbrock34::a31 = 1.867943637803922,
    Rosenbrock34::a32 = 0.2344449711399156,

    Rosenbrock34::c21 = -7.137615036412310,
    Rosenbrock34::c31 = 2.580708087951457,
    Rosenbrock34::c32 = 0.6515950076447975,
    Rosenbrock34::c41 = -2.137148994382534,
    Rosenbrock34::c42 = -0.3214669691237626,
    Rosenbrock34::c43 = -0.6949742501781779,

    Rosenbrock34::b1 = 2.255570073418735,
    Rosenbrock34::b2 = 0.2870493262186792,
    Rosenbrock34::b3 = 0.435317943184018,
    Rosenbrock34::b4 = 1.093502252409163,

    Rosenbrock34::e1 = -0.2815431932141155,
    Rosenbrock34::e2 = -0.0727619912493892,
    Rosenbrock34::e3 = -0.1082196201495311,
    Rosenbrock34::e4 = -1.093502252409163,

    Rosenbrock34::gamma = 0.57282,
    Rosenbrock34::c2 = 1.14564,
    Rosenbrock34::c3 = 0.65521686381559,

    Rosenbrock34::d1 = 0.57282,
    Rosenbrock34::d2 = -1.769193891319233,
    Rosenbrock34::d3 = 0.7592633437920482,
    Rosenbrock34::d4 = -0.1049021087100450;
    */
}


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

Foam::Rosenbrock34::Rosenbrock34(const ODESystem& ode, const dictionary& dict)
:
    ODESolver(ode, dict),
    adaptiveSolver(ode, dict),
    k1_(n_),
    k2_(n_),
    k3_(n_),
    k4_(n_),
    err_(n_),
    dydx_(n_),
    dfdx_(n_),
    dfdy_(n_, n_),
    a_(n_, n_),
    pivotIndices_(n_)
{}


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

Foam::scalar Foam::Rosenbrock34::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 k3:
    forAll(y, i)
    {
        y[i] = y0[i] + a31*k1_[i] + a32*k2_[i];
    }

    odes_.derivatives(x0 + c3*dx, y, dydx_);

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

    LUBacksubstitute(a_, pivotIndices_, k3_);

    // Calculate k4:
    forAll(k4_, i)
    {
        k4_[i] = dydx_[i] + dx*d4*dfdx_[i]
          + (c41*k1_[i] + c42*k2_[i] + c43*k3_[i])/dx;
    }

    LUBacksubstitute(a_, pivotIndices_, k4_);

    // Calculate error and update state:
    forAll(y, i)
    {
        y[i] = y0[i] + b1*k1_[i] + b2*k2_[i] + b3*k3_[i] + b4*k4_[i];
        err_[i] = e1*k1_[i] + e2*k2_[i] + e4*k4_[i];
    }

    return normalizeError(y0, y, err_);
}


void Foam::Rosenbrock34::solve
(
    scalar& x,
    scalarField& y,
    scalar& dxTry
) const
{
    adaptiveSolver::solve(odes_, x, y, dxTry);
}


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