Parallel-In-Time Multigrid with Adaptive Spatial Coarsening for The Linear Advection and Inviscid Burgers Equations
- Red Deer College, Red Deer, AB (Canada)
- Monash Univ., Melbourne, VIC (Australia)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Memorial Univ. of Newfoundland, St. John's, NL (Canada)
- Univ. of New Mexico, Albuquerque, NM (United States)
We apply a multigrid reduction-in-time (MGRIT) algorithm to hyperbolic partial differential equations in one spatial dimension. This study is motivated by the observation that sequential time-stepping is a computational bottleneck when attempting to implement highly concurrent algorithms; thus parallel-in-time methods are desirable. MGRIT adds parallelism by using a hierarchy of successively coarser temporal levels to accelerate the solution on the finest level. In the case of explicit time-stepping, spatial coarsening is a suitable approach to ensure that stability conditions are satisfied on all levels, and it may be useful for implicit time-stepping by producing cheaper multigrid cycles. Unfortunately, uniform spatial coarsening results in extremely slow convergence when the wave speed is near zero, even if only locally. We present an adaptive spatial coarsening strategy that addresses this issue for the variable coefficient linear advection equation and the inviscid Burgers equation using first-order explicit or implicit time-stepping methods. Serial numerical results show this method offers significant improvements over uniform coarsening and is convergent for the inviscid Burgers equation with and without shocks. Parallel scaling tests on up to 128K cores indicate that run-time improvements over serial time-stepping strategies are possible when spatial parallelism alone saturates, and that scalability is robust for oscillatory solutions which change on the scale of the grid spacing.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1734604
- Report Number(s):
- LLNL-JRNL--737050; 889908
- Journal Information:
- SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 41; ISSN 1064-8275
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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