int EVqrShifted(MAT &A,double mu,double tol,int maxiter){
int iter = 0 ;
MAT T(A);
MAT R(A.dim()), Q(A.dim()),muI(A.dim());
//since we are not able to access column of a matrix easily, so we access row of matrices as substitute.
for (int i =0 ; i < A.dim(); i++)
muI[i][i] = mu;
do{
for(int i=0;i<A.dim();i++){ //subtract mu*I before QR factorization
T[i][i] = T[i][i] - mu;
}
//QR decomposition
QRDecomp(T,Q,R);
T = R * Q;
//QR decomposition ends
for(int i=0;i<A.dim();i++){ //add mu*I back
T[i][i] = T[i][i] + mu;
}
iter++;
}while( (iter < maxiter) && (QRerror(T) > tol) );
printf("Largest 3 eigenvalues: ");
for (int i = 0; i < 3; i++)
printf(" %lf;",T[i][i]);
printf("\nSmallest 3 eigenvalues: ");
for (int i = A.dim()-1; i > A.dim()-4; i--)
printf(" %lf;",T[i][i]);
//printf("\niter %d\nerror: %E\n",iter,QRerror(A_k));
return iter;
}
Foam::tmp<Foam::volScalarField> Foam::dragModels::segregated::K() const
{
const fvMesh& mesh(pair_.phase1().mesh());
const volScalarField& alpha1(pair_.phase1());
const volScalarField& alpha2(pair_.phase2());
const volScalarField& rho1(pair_.phase1().rho());
const volScalarField& rho2(pair_.phase2().rho());
tmp<volScalarField> tnu1(pair_.phase1().nu());
tmp<volScalarField> tnu2(pair_.phase2().nu());
const volScalarField& nu1(tnu1());
const volScalarField& nu2(tnu2());
volScalarField L
(
IOobject
(
"L",
mesh.time().timeName(),
mesh
),
mesh,
dimensionedScalar("L", dimLength, 0),
zeroGradientFvPatchField<scalar>::typeName
);
L.internalField() = cbrt(mesh.V());
L.correctBoundaryConditions();
volScalarField I
(
alpha1
/max
(
alpha1 + alpha2,
residualAlpha_
)
);
volScalarField magGradI
(
max
(
mag(fvc::grad(I)),
residualAlpha_/L
)
);
volScalarField muI
(
rho1*nu1*rho2*nu2
/(rho1*nu1 + rho2*nu2)
);
volScalarField muAlphaI
(
alpha1*rho1*nu1*alpha2*rho2*nu2
/(alpha1*rho1*nu1 + alpha2*rho2*nu2)
);
volScalarField ReI
(
pair_.rho()
*pair_.magUr()
/(
magGradI
*max(alpha1*alpha2, sqr(residualAlpha_))
*muI
)
);
volScalarField lambda(m_*ReI + n_*muAlphaI/muI);
return lambda*sqr(magGradI)*muI;
}
