On Mon, 13 Feb 2017 17:07:21 +0100, Jed Brown wrote:
Pierre Jolivet <[email protected]> writes:
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).
Are all of these blocks distributed on your communicator or do they
have
some locality? PCFieldSplit is intended for problems where the
blocks
All the blocks are distributed indeed.
are all distributed and solving them sequentially is acceptable. The
other limiting case for an additive preconditioner like you have
above
is block Jacobi (perhaps with multi-process subdomains or multiple
subdomains per process; such decompositions are supported).
Yes, that is basically what I need, block Jacobi with subdomains
defined as aggregation of multiple processes, but I don't know how to do
this and thought of using an additive FieldSplit. Could you give me a
pointer to such a distribution, please?
Thanks in advance.
