[petsc-users] Solving a coupled linear system of equations in parallel

[Felipe Giacomelli]

Hello,

I would like to use PETSc to solve coupled linear systems, such as the ones
that originate from the discretization of Navier Stokes equations. In a two
dimensions, incompressible, steady state case, one would have the following
set of equations (Finite Volume Method):


A_uu      0             A_up           u              b_u

0            A_vv        A_vp           v       =    b_v

A_pu      A_pv        0                p               b_p


What would be the standard approach to solve this linear system? How can
one “split” this linear system among several processes?


When there is only one variable involved, as in heat transfer problems, I
use METIS to decompose the domain (graph partition). Thus, each process
build its block of the major linear system of equations. However, if
there’s more than one variable per node, I don’t know what would be the
best way to assemble the system of equations in a parallel context.


Notes:

The discretization method employed is the Element based Finite Volume
Method.

METIS is used to decompose the domain (graph partition).

I understand how PETSc is used to solve linear systems of equation when
there is only one variable per node.

I would like to keep the domain decomposition, if that’s possible.

Articles or other reading suggestions would be appreciated.


Thank you,

-- 
Felipe M Wallner Giacomelli
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20170912/27590ba0/attachment.html>