[Nek5000-users] Newton

[nek5000-users at lists.mcs.anl.gov]

Hi Nek's

I'm trying to code in Nek5000 the Newton algorithm. In order to do so,  I'm
referring to the Tuckerman's paper "Bifurcation analysis for timesteppers"
of 2000.

I would like to take advantage from the semi-implicit temporal scheme in
order to precondition the Bi-CGStab algorithm to solve the linear problem
that carry out the Newton step.

As explained in the Tuckerman's paper, in order to get a good
preconditioning, I should have a time step with a dt which is about 100 to
1000 times greater than that which ensures the CFL condition.
I'm not able to increase the dt has the Helmholtz fails in the projection
methods.

So, I tried to preconditioning the Bi-CGStab routine with a one step of
Stoke problem always with a large dt because if L is the linear operator:

U(n+1) = (I-dt*L^-1)U(n) ~ (-dt*L^-1)U(n)

but the Helmholtz Helmholtz fails too.

I would like to know if I can do somethings like:

r0 = K^(-1)*r0

where r0 = is the residue vector in the Bi-CGStab routine and K^(-1) is the
inverse of the stiffness matrix.

In the stokes problem, using a large DT, H (Helmholtz) tends to the limit K
so i could do a matrix-vector problem H^(-1)*r0 if there is a way to call a
routine the do this yet for the pressure preconditioning.

Can someone please help me?
thanks

Alessandro

PhD student at Dynfluid Laboratory
Ecole Nationale Supérieure d'Arts et Métiers de Paris - Paristech
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