[petsc-users] Questions about AMG and Jacobian Contruction

[Jed Brown]

"Smith, Barry F. via petsc-users" <petsc-users at mcs.anl.gov> writes:

>    We've found that the additive Schwarz methods (PCASM) or even block
>    Jacobi PCBJACOBI often work well for network problems, better than
>    GAMG. GAMG doesn't know anything about the structure of networks,
>    it is for PDEs on meshes, so there is no reason to think it would
>    work particularly well for network problems.

The number of iterations for one-level methods (like Jacobi/block
Jacobi) is roughly proportional to the diameter of your network.  If
your network has small diameter, those methods may be fast already.  PDE
meshes generally have large diameter with bounded degree; the AMG
methods in PETSc are good for such problems.  If you have large diameter
with unbounded degree, then more specialized AMG variants such as
https://arxiv.org/abs/1705.06266 can be better.