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
