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Testing weighted splitting schemes on a one-column transport-chemistry model. (English) Zbl 1151.65343

Lirkov, Ivan (ed.) et al., Large-scale scientific computing. 4th international conference, LSSC 2003, Sozopol, Bulgaria, June 4–8, 2003. Revised papers. Berlin: Springer (ISBN 3-540-21090-3/pbk). Lecture Notes in Computer Science 2907, 295-302 (2004).
Summary: In many transport-chemistry models, a huge system of ODE’s of the advection-diffusion-reaction type has to be integrated in time. Typically, this is done with the help of operator splitting. Rosenbrock schemes combined with approximate matrix factorization (ROS-AMF) are an alternative to operator splitting which does not suffer from splitting errors. However, implementation of ROS-AMF schemes often requires serious changes in the code.
In this paper we test another classical second order splitting introduced by G. Strang [Arch. Ration. Mech. Anal. 12, 392–402 (1963; Zbl 0113.32303)], which, unlike the popular Strang splitting, seemed to be forgotten and rediscovered recently (partially due to its intrinsic parallellism). This splitting, called symmetrically weighted sequential (SWS) splitting, is simple and straightforward to apply, independent of the order of the operators and has an operator-level parallelism. In the experiments, the SWS scheme compares favorably to the Strang splitting, but is less accurate than ROS-AMF.
For the entire collection see [Zbl 1049.65004].

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
76M10 Finite element methods applied to problems in fluid mechanics

Citations:

Zbl 0113.32303

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