On Mar 18, 2015, at 2:54 PM, Luc Berger-Vergiat <[email protected]> wrote:
Hi Barry,
I would like to compute S explicitly, I have a few good option to precondition
S but they are based on S not an approximation of S (i.e. I don't want to
compute my preconditioner using Sp different from S).
Also Jee is obtained using MatGetSubmatrix(J,isrow_e,iscol_e) and J is an AIJ
matrix so I assume that Jee is AIJ too.
I can convert Jee to BAIJ to take advantage of the block structure but from
your conversation with Chung-Kan it might require to reassemble?
In that case what about the following:
MatCreateBAIJ(comm, 5, Jee_inv)
for(i=0,i<nblocks,i++)
{
MatGetValues(Jee,5,[5*i+0,5*i+1,5*i+2,5*i+3,5*i+4],5,[5*i+0,5*i+1,5*i+2,5*i+3,5*i+4],
block_values)
some_package_inverts( block_values )
MatSetValuesBlocked(Jee_inv,5,[5*i+0,5*i+1,5*i+2,5*i+3,5*i+4],5,[5*i+0,5*i+1,5*i+2,5*i+3,5*i+4],
block_values)
}
MatAssemblyBegin()
MatAssemblyEnd()
With this I could then just go on and do matrix multiplications to finish my
Schur complement calculations.
Would this be decently efficient?
Best,
Luc
On 03/18/2015 03:22 PM, Barry Smith wrote:
Do you want to explicitly compute (as a matrix) S = Joo - joe * inv(Jee) jeo
or do you want to just have an efficient computation of
S y for any y vector?
Here is some possibly useful information. If you create Jee as a BAIJ matrix
of block size 5 and use MatILUFactor() it will efficiently factor this matrix
(each 5 by 5 block factorization is done with custom code) then you can use
MatSolve() efficiently with the result (note that internally when factoring a
BAIJ matrix PETSc actually stores the inverse of the diagonal blocks so in your
case the MatSolve() actually ends up doing little matrix-vector products (and
there are no triangular solves).
To use this with the MatCreateSchurComplement() object you can do
MatCreateSchurComplement(...,&S)
MatSchurComplementGetKSP(S,&ksp)
KSPSetType(ksp,KSPPREONLY);
now MatMult(S,y,z) will be efficient.
Of course you still have the question, how do you plan to solve S? This
depends on its structure and if you have a good way of preconditioning it.
If you want to explicitly form S you can use MatMatSolve( fact,jeo) but
this requires making jeo dense which seems to defeat the purpose.
Barry
On Mar 18, 2015, at 1:41 PM, Luc Berger-Vergiat <[email protected]>
wrote:
Hi all,
I am solving multi-physics problem that leads to a jacobian of the form:
[ Jee Jeo ]
[ Joe Joo ]
where Jee is 5by5 block diagonal. This feature makes it a very good candidate
for a Schur complement.
Indeed, Jee could be inverted in parallel with no inter-nodes communication.
My only issue is the fact that the Schur complement is not accessible directly
with PETSC, only an approximation is available, for direct solvers (usually
S~Joo or S~Joo-Joe* diag(Jee)^-1 *Jeo).
Any advice on how I could efficiently compute Jee^-1 for the given structure?
I am currently thinking about hard coding the formula for the inverse of a 5by5
and sweeping through Jee (with some threading) and storing the inverse
in-place. Instead of hard coding the formula for a 5by5 I could also do a
MatLUFactorSym on a 5by5 matrix but it would not give me an inverse, only a
factorization...
Thanks in advance for your suggestions!
--
Best,
Luc
