[petsc-users] AIJ vs BAIJ when using ILU factorization

[Fande Kong]

Hi All,

There is a system of equations arising from the discretization of 3D
incompressible Navier-Stoke equations using a finite element method. 4
unknowns are placed on each mesh point, and then there is a 4x4 saddle
point block on each mesh vertex.  I was thinking to solve the linear
equations using an incomplete LU factorization (that will be eventually
used as a subdomain solver for ASM).

Right now, I am trying to study the ILU performance using AIJ and BAIJ,
respectively. From my understanding, BAIJ should give me better results
since it inverses the 4x4 blocks exactly, while AIJ does not. However, I
found that both BAIJ and AIJ gave me identical results in terms of the
number of iterations.  Was that just coincident?  Or in theory, they are
just identical.  I understand the runtimes may be different because BAIJ
has a better data locality.


Please see the attached files for the results and solver configuration.


Thanks,

Fande,
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