Publication Date:
15 June 2019
Journal:
Electronic Transactions on Numerical Analysis
Last Updated:
2021-03-14T13:56:05.483+00:00
Volume:
51
DOI:
10.1553/etna_vol51s135
page:
135-150
abstract:
Copyright © 2019, Kent State University. McDonald, Pestana, and Wathen [SIAM J. Sci. Comput., 40 (2018), pp. A1012-A1033] present a method for preconditioning time-dependent PDEs via an approximation by a nearby time-periodic problem, that is, they employ circulant-related matrices as preconditioners for the non-symmetric block Toeplitz matrices which arise from an all-at-once formulation. They suggest that such an approach might be efficiently implemented in parallel. In this short article, we present parallel numerical results for their preconditioner which exhibit strong scaling. We also extend their preconditioner via a Neumann series approach which also allows for efficient parallel execution. Results are shown for both parabolic and hyperbolic PDEs. Our simple implementation (in C++ and MPI) is available at the Git repository PARALAAOMPI.
Symplectic id:
987947
Submitted to ORA:
Submitted
Publication Type:
Journal Article