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![]() | A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations | ![]() |
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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.