Details

Autor(en) / Beteiligte

• Falgout, Robert D.
• Lecouvez, Matthieu
• Woodward, Carol S.

Titel

A parallel-in-time algorithm for variable step multistep methods

Ist Teil von

• Journal of computational science, 2019-10, Vol.37 (na), p.101029, Article 101029

Ort / Verlag

United States: Elsevier B.V

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• •Parallel-in-time approach speeds up higher-order BDF methods.•Adaptive-in-time approach solves problems on variably-spaced temporal grids.•Method solves nonlinear differential algebraic equations of index 1.•Results for diffusion and two nonlinear IEEE power grid test problems.•Comparison of BDF and Runge-Kutta 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. 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.