tensor2D.C

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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
     \\/     M anipulation  |
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License
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    under the terms of the GNU General Public License as published by
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#include "tensor2D.H"
#include "quadraticEqn.H"

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

template<>
const char* const Foam::tensor2D::vsType::typeName = "tensor2D";

template<>
const char* const Foam::tensor2D::vsType::componentNames[] =
{
    "xx", "xy",
    "yx", "yy"
};

template<>
const Foam::tensor2D Foam::tensor2D::vsType::vsType::zero
(
    tensor2D::uniform(0)
);

template<>
const Foam::tensor2D Foam::tensor2D::vsType::one
(
    tensor2D::uniform(1)
);

template<>
const Foam::tensor2D Foam::tensor2D::vsType::max
(
    tensor2D::uniform(vGreat)
);

template<>
const Foam::tensor2D Foam::tensor2D::vsType::min
(
    tensor2D::uniform(-vGreat)
);

template<>
const Foam::tensor2D Foam::tensor2D::vsType::rootMax
(
    tensor2D::uniform(rootVGreat)
);

template<>
const Foam::tensor2D Foam::tensor2D::vsType::rootMin
(
    tensor2D::uniform(-rootVGreat)
);

template<>
const Foam::tensor2D Foam::tensor2D::I
(
    1, 0,
    0, 1
);


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

Foam::vector2D Foam::eigenValues(const tensor2D& t)
{
    // Coefficients of the characteristic quadratic polynomial (a = 1)
    const scalar b = - t.xx() - t.yy();
    const scalar c = t.xx()*t.yy() - t.xy()*t.yx();

    // Solve
    Roots<2> roots = quadraticEqn(1, b, c).roots();

    // Check the root types
    vector2D lambda = vector2D::zero;
    forAll(roots, i)
    {
        switch (roots.type(i))
        {
            case rootType::real:
                lambda[i] = roots[i];
                break;
            case rootType::complex:
                WarningInFunction
                    << "Complex eigenvalues detected for tensor: " << t
                    << endl;
                lambda[i] = 0;
                break;
            case rootType::posInf:
                lambda[i] = vGreat;
                break;
            case rootType::negInf:
                lambda[i] = - vGreat;
                break;
            case rootType::nan:
                FatalErrorInFunction
                    << "Eigenvalue calculation failed for tensor: " << t
                    << exit(FatalError);
        }
    }

    // Sort the eigenvalues into ascending order
    if (lambda.x() > lambda.y())
    {
        Swap(lambda.x(), lambda.y());
    }

    return lambda;
}


Foam::vector2D Foam::eigenVector
(
    const tensor2D& T,
    const scalar lambda,
    const vector2D& direction1
)
{
    // Construct the linear system for this eigenvalue
    tensor2D A(T - lambda*tensor2D::I);

    // Evaluate the eigenvector using the largest divisor
    if (mag(A.yy()) > mag(A.xx()) && mag(A.yy()) > small)
    {
        vector2D ev(1, - A.yx()/A.yy());

        return ev/mag(ev);
    }
    else if (mag(A.xx()) > small)
    {
        vector2D ev(- A.xy()/A.xx(), 1);

        return ev/mag(ev);
    }

    // Repeated eigenvalue
    return vector2D(- direction1.y(), direction1.x());
}


Foam::tensor2D Foam::eigenVectors(const tensor2D& T, const vector2D& lambdas)
{
    vector2D Ux(1, 0), Uy(0, 1);

    Ux = eigenVector(T, lambdas.x(), Uy);
    Uy = eigenVector(T, lambdas.y(), Ux);

    return tensor2D(Ux, Uy);
}


Foam::tensor2D Foam::eigenVectors(const tensor2D& T)
{
    const vector2D lambdas(eigenValues(T));

    return eigenVectors(T, lambdas);
}


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