[petsc-users] ILU and Block Gauss Seidel smoothing

Gianluca Meneghello gianmail at gmail.com
Wed May 25 02:45:43 CDT 2011

Dear all,

I am writing a multigrid solver for the Navier Stokes Equations, using
PETSc. I am not using the dmmg structure because I need grid
refinement and, as far as I can see, that is not supported.

I have two questions concerning two different possibilities of smoothing:

1) ILU relaxation: in Multigrid (U. Trottenberg,Cornelis W.
Oosterlee,Anton Schüller), it is suggested that alternating ILU
represents a robust smoother. Given a routine for ILU decomposition,
my understanding is that alternation depends on the ordering of the
matrix. My code builds a linearized Navier Stokes operator where first
the u momentum equation, then the v momentum and then the p equation
are stored. Each equation is built in EN order — first comes the
bottom horizontal line, from West to East, then I move line by line
from South to North. Otherwise stated, the position of each unknown in
the matrix is given by P = cf*nx*ny + j*nx + i, where cf is the
variable number (0 = u, 1 = v, 2 = p) and i,j,nx,ny are as usual.

For "historical" reasons I'm not using the DM structure even if the
grids are logically rectangular, but I can change that.

My question: is there in PETSc a way of doing alternating ILU which
does not require rebuilding the matrix with different ordering each

Somehow related questions: what is the best ordering for the matrix
and which one is the one used by the DM structure?

2) Decoupled block-line Gauss Seidel relaxation: this is another
smoother I'm considering, which explains the matrix ordering above (I
use block horizontal lines smoothing, so that each line is stored
consecutively in the matrix). At the moment the full linearized
operator is first built and then parts of the matrix are extracted.
In reality though, I never need the full linearized operator to be
built except on the coarsest grid. Rather, I need it to be constructed
each block-line at a time. I've seen that for parallel applications
each part of the matrix is built on its corresponding processor. Is
there a way to do it sequentially and to have control on which part is

Any other suggestion on both subjects is of course welcome. Thanks in advance


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Amedeo Modigliani

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