[Nek5000-users] Linear Systems and Solvers in Nek5000

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

Hello Nek users,

This could be a simple question to some, but any help would be great here.
I am working on a project that is aiming to suggest appropriate solvers for
the system Ax = b, using Machine Learning, given the matrix A.

I know that there are many matrix datasets online, but for specific
reasons, we want to extract matrices from Nek5000 (compute features from
that) and note the solvers it uses for those linear systems.

The Navier-Stokes equation is non-linear due to the advection term, but in
certain cases, the governing equations reduce to being linear. I am trying
to understand what those cases are and the solvers that Nek uses to handle
those linear systems.

Based on my reading from various sources, it looks like Nek handles the
following linear system cases. Any comments on this would be very helpful:

1)
*System:* Poisson equation for Pressure (incompressible case?)
*Solvers:* Nek supports GMRES and PCG with Parameter P042 (from
http://nek5000.github.io/NekDoc/Nek_usersch7.html#x9-750007.1)

2) https://www.mcs.anl.gov/~fischer/Nek5000/nek_tutorial_1.pdf - Page 44
What is the Helmholtz solve for velocity here? Is this the only "solver"
for velocity?

3) http://nek5000.github.io/NekDoc/Nek_usersch1.html#x3-50001.1
*System*: Energy equation behaves as a transport equation for temperature
right?
*Solvers*: Helmholz, CVODE, CVODE with user-supplied Jacobian.

4) All Stokes flow cases with constant viscosity?

Does this seem correct? If you need any other information, please let me
know.

Thanking You,
K.N.Ramachandran
(Ram)
Ph: 814-441-4279
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