[petsc-users] Fast LU solver for block diagonal matrix

[Luc Berger-Vergiat]

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