Overlapping localized exponential time differencing methods for diffusion problems
- Univ. of South Carolina, Columbia, SC (United States); University of South Carolina
- Univ. of South Carolina, Columbia, SC (United States)
The localized exponential time differencing (ETD) based on overlapping domain decomposition has been recently introduced for extreme-scale phase field simulations of coarsening dynamics, which displays excellent parallel scalability in supercomputers. This paper serves as the first step toward building a solid mathematical foundation for this approach. We study the overlapping localized ETD schemes for a model time-dependent diffusion equation discretized in space by the standard central difference. Two methods are proposed and analyzed for solving the fully discrete localized ETD systems: the first one is based on Schwarz iteration applied at each time step and involves solving stationary problems in the subdomains at each iteration, while the second one is based on the Schwarz waveform relaxation algorithm in which time-dependent subdomain problems are solved at each iteration. The convergences of the associated iterative solutions to the corresponding fully discrete localized ETD solution and to the exact semidiscrete solution are rigorously proved. Finally, numerical experiments are also carried out to confirm theoretical results and to compare the performance of the two methods.
- Research Organization:
- Univ. of South Carolina, Columbia, SC (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); National Science Foundation (NSF)
- Grant/Contract Number:
- SC0016540
- OSTI ID:
- 1593992
- Alternate ID(s):
- OSTI ID: 1542045
- Journal Information:
- Communications in Mathematical Sciences, Journal Name: Communications in Mathematical Sciences Journal Issue: 6 Vol. 16; ISSN 1539-6746
- Publisher:
- International PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems
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journal | February 2020 |
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