A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations |

Parallel sweeping preconditioner

The setup and application stages of the sweeping preconditioner (Algs.
0.0.4 and 0.0.5) essentially consist of
multifrontal factorizations and solves, respectively.
The most important detail is that *the subdomain factorizations
can be performed in parallel, while the subdomain solves must happen
sequentially*.^{} When we also consider that each subdomain
factorization requires
work, while subdomain solves only
require
work, we see that, relative to the subdomain
factorizations, subdomain solves must extract a factor of
more
parallelism from a factor of
less operations.
We thus have a strong hint that, unless the subdomain solves are carefully
handled, they will be the limiting factor in the scalability of the sweeping
preconditioner.

- Parallel multifrontal algorithms
- Selective inversion
- Global vector distributions
- Parallel preconditioned GMRES(k)
- Clique
- Parallel Sweeping Preconditioner (PSP)

2014-08-20