Rosenbrock23.C

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    \\  /    A nd           | Copyright (C) 2013-2015 OpenFOAM Foundation
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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  * * * * * * * * * * * * * //
 
Foam::scalar Foam::Rosenbrock23::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(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 normalizeError(y0, y, err_);
}
 
 
void Foam::Rosenbrock23::solve
(
    scalar& x,
    scalarField& y,
    scalar& dxTry
) const
{
    adaptiveSolver::solve(odes_, x, y, dxTry);
}
 
 
// ************************************************************************* //