On Mon, 13 Feb 2017 10:00:48 -0600, Matthew Knepley wrote:
On Mon, Feb 13, 2017 at 9:46 AM, Pierre Jolivet wrote:
Hello,
Given this block matrix:
A = [A11,A12,A13,A14;
A21,A22,A23,A24;
A31,A32,A33,A34;
A41,A42,A43,A44];
It is trivial to precondition Ax = b with M^-1 = diag(A11^-1,
A22^-1, A33^-1, A44^-1);
My application requires a slightly fancier preconditionner which
should be M^-1 =
diag(inv([A11,A12;A21,A22]),inv([A33,A34;A43,A44]));
I'm not sure what is the right tool for this.
I've stopped at a 4x4 block matrix, but at scale I have a matrix
with few thousands x few thousands blocks (still with the nested 2
x
2 block structure).
1) should I implement a PCSHELL myself, or use a fieldsplit
preconditioner with "few thousands / 2" fields (i.e., does
PCFIELDSPLIT scale relatively well with the number of fields, or do
you recommend it only for "Stokes-like" problems?)?
FieldSplit is not that scalable right now (I think). For 4x4 blocks,
you want to solve 8x8 systems. You could use MATBAIJ with block size
8
and
then PBJACOBI. Would that work for you?
In the application, all my blocks are sparse matrices, and the
assumption that the number of rows of A_11, A_22, A_33, and A_44 are
equal does not hold. (That's also why in the MWE I sent I'm not using
ISCreateBlock)
Thanks,
Matt
2) I gave PCFIELDSPLIT a go, but I'm failing miserably. In the
attached tarball, I'm loading matrix A on four processes. Each
process owns 2 rows of A. I'm thus creating two ISes:
I will look at this as soon as I can, but I am really swamped right
now.
Matt
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener
Links:
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