Parallel Implicit-Explicit General Linear Methods

doi:10.1007/s42967-020-00083-5

Abstract

Abstract: High-order discretizations of partial diferential equations (PDEs) necessitate high-order time integration schemes capable of handling both stif and nonstif operators in an efcient manner. Implicit-explicit (IMEX) integration based on general linear methods (GLMs) ofers an attractive solution due to their high stage and method order, as well as excellent stability properties. The IMEX characteristic allows stif terms to be treated implicitly and nonstif terms to be efciently integrated explicitly. This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel. The frst approach is based on diagonally implicit multi-stage integration methods (DIMSIMs) of types 3 and 4. The second is a parallel generalization of IMEX Euler and has the interesting feature that the linear stability is independent of the order of accuracy. Numerical experiments confrm the theoretical rates of convergence and reveal that the new schemes are more efcient than serial IMEX GLMs and IMEX Runge–Kutta methods.

Key words: Parallel, Time integration, IMEX methods, General linear methods

CLC Number:

Steven Roberts, Arash Sarshar, Adrian Sandu. Parallel Implicit-Explicit General Linear Methods[J]. Communications on Applied Mathematics and Computation, 2021, 3(4): 649-669.

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