foam-extend4.1-coherent-io/applications/solvers/solidMechanics/solidModels/interpolation/leastSquaresVolPointInterpolation/leastSquaresVolPointInterpolation.C

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#include "leastSquaresVolPointInterpolation.H"

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

namespace Foam
{

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

defineTypeNameAndDebug(leastSquaresVolPointInterpolation, 0);


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

void leastSquaresVolPointInterpolation::calcA(List<scalarSquareMatrix>& A) const
{
    //Info << "leastSquaresVolPointInterpolation calcA" << endl;

    const fvMesh& mesh = mesh_;
    const pointField& points = mesh.points();

    //- construct 4x4 A matrix for each point
    //List<scalarSquareMatrix>& A = A_;

    //- populate A matrix
    forAll(points, pointi)
    {
        const labelList& pointCells = mesh.pointCells()[pointi];

        //- this component of matrix does not depend on coordinates
        A[pointi][3][3] = pointCells.size();

        //- fill the A matrices
        forAll(pointCells, pointCelli)
        {
            const label& celli = pointCells[pointCelli];

            const scalar& x = mesh.C()[celli].component(vector::X);
            const scalar& y = mesh.C()[celli].component(vector::Y);
            const scalar& z = mesh.C()[celli].component(vector::Z);

            A[pointi][0][0] += x*x;
            A[pointi][0][1] += x*y;
            A[pointi][0][2] += x*z;
            A[pointi][0][3] += x;

            A[pointi][1][0] += x*y;
            A[pointi][1][1] += y*y;
            A[pointi][1][2] += y*z;
            A[pointi][1][3] += y;

            A[pointi][2][0] += x*z;
            A[pointi][2][1] += y*z;
            A[pointi][2][2] += z*z;
            A[pointi][2][3] += z;

            A[pointi][3][0] += x;
            A[pointi][3][1] += y;
            A[pointi][3][2] += z;
            //A[pointi][3][3] = pointCells.size(); // set above
        }
    }

    //- for boundary points we will include the surrounding face centres
    forAll(mesh.boundary(), patchi)
    {
        const vectorField& faceCentres = mesh.boundaryMesh()[patchi].faceCentres();
        const labelListList& pointFaces = mesh.boundaryMesh()[patchi].pointFaces();

        if(mesh.boundary()[patchi].coupled()) //- for proc boundaries
        {
            //- for coupled patches we will use the values at the neighbourField cell centres and we will
            //- not use the boundary face values
            //- neighbour cell centre are equal to the faceCell centres plus the delta vector
            vectorField pDelta = mesh.boundary()[patchi].delta();
            vectorField faceCellC(faceCentres.size(), vector::zero);
            forAll(faceCentres, facei)
            {
                label celli = mesh.boundaryMesh()[patchi].faceCells()[facei];
                faceCellC[facei] = mesh.C()[celli];
            }
            vectorField neiCellC = faceCellC + pDelta;

            forAll(pointFaces, pointi)
            {
                forAll(pointFaces[pointi], pointFacei)
                {
                    label neiCelli = pointFaces[pointi][pointFacei];
                    const scalar& x = neiCellC[neiCelli].component(vector::X);
                    const scalar& y = neiCellC[neiCelli].component(vector::Y);
                    const scalar& z = neiCellC[neiCelli].component(vector::Z);

                    label globalPointi = mesh.boundaryMesh()[patchi].meshPoints()[pointi];

                    A[globalPointi][0][0] += x*x;
                    A[globalPointi][0][1] += x*y;
                    A[globalPointi][0][2] += x*z;
                    A[globalPointi][0][3] += x;

                    A[globalPointi][1][0] += x*y;
                    A[globalPointi][1][1] += y*y;
                    A[globalPointi][1][2] += y*z;
                    A[globalPointi][1][3] += y;

                    A[globalPointi][2][0] += x*z;
                    A[globalPointi][2][1] += y*z;
                    A[globalPointi][2][2] += z*z;
                    A[globalPointi][2][3] += z;

                    A[globalPointi][3][0] += x;
                    A[globalPointi][3][1] += y;
                    A[globalPointi][3][2] += z;
                    A[globalPointi][3][3] += 1; // = pointCells.size();
                 }
            }
        }
        else
        {
            //- each point must use at least 4 neighbouring locations otherwise A is singular
            //- and simpleMatrix will cannot invert it
            //- therefore empty patches values are included to make sure A is not singular
            forAll(pointFaces, pointi)
            {
                label globalPointi = mesh.boundaryMesh()[patchi].meshPoints()[pointi];

                forAll(pointFaces[pointi], pointFacei)
                {
                    //- fix: use pointFace not face philipc
                    label facei = pointFaces[pointi][pointFacei];
                    const scalar& x = faceCentres[facei].component(vector::X);
                    const scalar& y = faceCentres[facei].component(vector::Y);
                    const scalar& z = faceCentres[facei].component(vector::Z);

                    A[globalPointi][0][0] += x*x;
                    A[globalPointi][0][1] += x*y;
                    A[globalPointi][0][2] += x*z;
                    A[globalPointi][0][3] += x;

                    A[globalPointi][1][0] += x*y;
                    A[globalPointi][1][1] += y*y;
                    A[globalPointi][1][2] += y*z;
                    A[globalPointi][1][3] += y;

                    A[globalPointi][2][0] += x*z;
                    A[globalPointi][2][1] += y*z;
                    A[globalPointi][2][2] += z*z;
                    A[globalPointi][2][3] += z;

                    A[globalPointi][3][0] += x;
                    A[globalPointi][3][1] += y;
                    A[globalPointi][3][2] += z;
                    A[globalPointi][3][3] += 1; // = pointCells.size();
                }
            }
        } //- end of else
    } //- end of forAll boundary
}


void leastSquaresVolPointInterpolation::calcB(List<Field<vector> >& B, const GeometricField<vector, fvPatchField, volMesh>& vf) const
{
    //Info << "leastSquaresVolPointInterpolation calcB" << endl;

    const fvMesh& mesh = mesh_;
    const pointField& points = mesh.points();

    //List<Field<vector> >& B = B_;

    for (direction compi = 0; compi < 3; compi++)
    {
        forAll(points, pointi)
        {
            const labelList& pointCells = mesh.pointCells()[pointi];

            forAll(pointCells, pointCelli)
            {
                const label& celli = pointCells[pointCelli];

                const scalar& x = mesh.C()[celli].component(vector::X);
                const scalar& y = mesh.C()[celli].component(vector::Y);
                const scalar& z = mesh.C()[celli].component(vector::Z);

                const scalar& phiCompi = vf.internalField()[celli].component(compi);

                B[pointi][0].component(compi) += phiCompi*x;
                B[pointi][1].component(compi) += phiCompi*y;
                B[pointi][2].component(compi) += phiCompi*z;
                B[pointi][3].component(compi) += phiCompi;
            }
        }

        //- for boundary points we will include the surrounding face centres
        forAll(mesh.boundary(), patchi)
        {
            const vectorField& faceCentres = mesh.boundaryMesh()[patchi].faceCentres();
            const labelListList& pointFaces = mesh.boundaryMesh()[patchi].pointFaces();
            const labelList& faceCells = mesh.boundaryMesh()[patchi].faceCells();

            //- fix: do not calculate B for empty patches - philipc
            if(mesh.boundary()[patchi].coupled())
            {
                //- for coupled patches we will use the values at the neighbourField cell centres and we will
                //- not use the boundary face values
                //- neighbour cell centre are equal to the faceCell centres plus the delta vector
                vectorField pDelta = mesh.boundary()[patchi].delta();
                vectorField faceCellC(faceCentres.size(), vector::zero);
                forAll(faceCentres, facei)
                {
                    label celli = mesh.boundaryMesh()[patchi].faceCells()[facei];
                    faceCellC[facei] = mesh.C()[celli];
                }
                vectorField neiCellC = faceCellC + pDelta;

                vectorField phiNeiField = vf.boundaryField()[patchi].patchNeighbourField();

                forAll(pointFaces, pointi)
                {
                    forAll(pointFaces[pointi], pointFacei)
                    {
                        label neiCelli = pointFaces[pointi][pointFacei];
                        const scalar& x = neiCellC[neiCelli].component(vector::X);
                        const scalar& y = neiCellC[neiCelli].component(vector::Y);
                        const scalar& z = neiCellC[neiCelli].component(vector::Z);

                        label globalPointi = mesh.boundaryMesh()[patchi].meshPoints()[pointi];

                        //- this is the value of phi at the cell centre in the neighbour (i.e. across the interface)
                        scalar phiCompi = phiNeiField[neiCelli].component(compi);

                        B[globalPointi][0].component(compi) += phiCompi*x;
                        B[globalPointi][1].component(compi) += phiCompi*y;
                        B[globalPointi][2].component(compi) += phiCompi*z;
                        B[globalPointi][3].component(compi) += phiCompi;
                    }
                }
            }
            else
            {
                //- each point must use at least 4 neighbouring locations otherwise A is singular
                //- and simpleMatrix will cannot invert it
                //- therefore empty patches values are included to make sure A is not singular
                forAll(pointFaces, pointi)
                {
                    forAll(pointFaces[pointi], pointFacei)
                    {
                        //- fix: use pointFace not face philipc
                        label facei = pointFaces[pointi][pointFacei];
                        const scalar& x = faceCentres[facei].component(vector::X);
                        const scalar& y = faceCentres[facei].component(vector::Y);
                       const scalar& z = faceCentres[facei].component(vector::Z);

                        label globalPointi = mesh.boundaryMesh()[patchi].meshPoints()[pointi];

                        scalar phiCompi = 0.0;
                        if(mesh.boundary()[patchi].type() == "empty")
                        {
                            //- use faceCell value for empty because empty patches do not store any values
                            const label& ci = faceCells[facei];
                            phiCompi = vf.internalField()[ci].component(compi);
                        }
                        else
                        {
                            phiCompi = vf.boundaryField()[patchi][facei].component(compi);
                        }

                        B[globalPointi][0].component(compi) += phiCompi*x;
                        B[globalPointi][1].component(compi) += phiCompi*y;
                        B[globalPointi][2].component(compi) += phiCompi*z;
                        B[globalPointi][3].component(compi) += phiCompi;
                    }
                }
            }
        } //- end of forAll boundary
    } //- end of for all components
}


void leastSquaresVolPointInterpolation::interpolate
(
    const GeometricField<vector, fvPatchField, volMesh>& vf,
    GeometricField<vector, pointPatchField, pointMesh>& pf //Field<vector>& pf
) const
{
    //Info << "Interpolating cell to point using leastSquaresVolPointInterpolation" << endl;

    const fvMesh& mesh = mesh_;
    const pointField& points = mesh.points();

    //- first check that point field is the correct size
    if(pf.size() != points.size())
    {
        FatalError << "pointfield should be equal to the number of points in the fvMesh" << endl;
    }

    //- calculate A and B vector
    // List<Field<vector> >& B = B_;
    // calcB(vf);
    // const List<scalarSquareMatrix>& A = A_;
    List<scalarSquareMatrix> A(mesh.points().size(), scalarSquareMatrix(4, 0.0));
    calcA(A);

    List<Field<vector> > B(mesh.points().size(), Field<vector>(4, pTraits<vector>::zero));
    calcB(B, vf);

    //- solve equations for each component of each point
    forAll(points, pointi)
    {
        Field<vector>& source = B[pointi];
        simpleMatrix<vector> leastSquaresMatrix(A[pointi], source);

        //- solve using Gauss elimination or LU decomposition with pivoting
        //Field<vector> leastSquaresSol = leastSquaresMatrix.solve();
        Field<vector> leastSquaresSol = leastSquaresMatrix.LUsolve();

        const scalar& x = mesh.points()[pointi].component(vector::X);
        const scalar& y = mesh.points()[pointi].component(vector::Y);
        const scalar& z = mesh.points()[pointi].component(vector::Z);

        //- calculate phi at vertex
        for (direction compi = 0; compi < 3; compi++)
        {
            const scalar& a = leastSquaresSol[0].component(compi);
            const scalar& b = leastSquaresSol[1].component(compi);
            const scalar& c = leastSquaresSol[2].component(compi);
            const scalar& d = leastSquaresSol[3].component(compi);

            pf[pointi].component(compi) = a*x + b*y + c*z + d;
        }
    }

    //- proc patches are synchronised
    pf.correctBoundaryConditions();
 }


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

leastSquaresVolPointInterpolation::leastSquaresVolPointInterpolation(const fvMesh& vm)
:
    mesh_(vm) //,
    //A_(vm.points().size(), scalarSquareMatrix(4, 0.0)),
    //B_(vm.points().size(), Field<vector>(4, vector::zero))
{
    //calcA();
}

// * * * * * * * * * * * * * * * Destructor  * * * * * * * * * * * * * * * * //

leastSquaresVolPointInterpolation::~leastSquaresVolPointInterpolation()
{}


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



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

} // End namespace Foam

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