[petsc-users] Why use MATMPIBAIJ?

[Justin Chang]

Hi all,

1) I am guessing MATMPIBAIJ could theoretically have better performance
than simply using MATMPIAIJ. Why is that? Is it similar to the reasoning
that block (dense) matrix-vector multiply is "faster" than simple
matrix-vector?

2) I am looking through the manual and online documentation and it seems
the term "block" used everywhere. In the section on "block matrices" (3.1.3
of the manual), it refers to field splitting, where you could either have a
monolithic matrix or a nested matrix. Does that concept have anything to do
with MATMPIBAIJ?

It makes sense to me that one could create a BAIJ where if you have 5 dofs
of the same type of physics (e.g., five different primary species of a
geochemical reaction) per grid point, you could create a block size of 5.
And if you have different physics (e.g., velocity and pressure) you would
ideally want to separate them out (i.e., nested matrices) for better
preconditioning.

Thanks,
Justin
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