A parallel-in-time algorithm for variable step multistep methods
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Centre d'Etudes Scientifiques et Techniques d'Aquitaine, Le Barp (France)
This paper presents a multigrid reduction in time (MGRIT) algorithm for achieving time parallelism using multistep backward difference formula (BDF) methods on variably-spaced temporal grids. This MGRIT approach transforms the linear multistep methods into single step methods applied to groups of time steps. Stability considerations are addressed through lowering of the order on coarse grids. The methods are presented for fixed and variable time step formulations. Furthermore, numerical results show moderate speedups for the heat equation as well as two IEEE power grid test problems characterized by nonlinear differential algebraic equations (DAE) of index 1. The performance of MGRIT with BDF is compared to MGRIT with Runge-Kutta for both the fixed and variable step methods of the same order.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Energy Efficiency and Renewable Energy (EERE)
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1734610
- Alternate ID(s):
- OSTI ID: 1780023
- Report Number(s):
- LLNL-JRNL-739759; 893406
- Journal Information:
- Journal of Computational Science, Vol. 37, Issue na; ISSN 1877-7503
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
| PyMGRIT: A Python Package for the parallel-in-time method MGRIT | preprint | January 2020 |
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