An accepted and popular technique in the numerical solution of large-scale, three-space dimensional transport-chemistry problems from air pollution modelling, is operator splitting or time splitting. Operator splitting is computationally attractive as it enables us to treat very different processes like advection, cumulus convection, diffusion and stiff chemistry with different methods. Despite its popularity, the literature does not give much evidence whether at large operator splitting leads to the best approach in terms of sufficient accuracy at low costs. In this lecture we will present results of comparisons between operator splitting and alternatives providing insight into the efficiency and accuracy. The comparisons are directed at real-life models and include source splitting and splitting at the level of the numerical algebra by means of approximate matrix factorization inside a stiff ODE solver of Rosenbrock type.

[1] Different preprints: http://www.cwi.nl/~gollum/MAS1.1/Papers.html

[2] J.G. Verwer, E.J. Spee, J.G. Blom and W. Hundsdorfer, A second order Rosenbrock method applied to photochemical dispersion problems, SIAM J. Sci. Comput. 20 (1999) 1456--1480 (no. 28 in [1]).

[3] J.G. Blom and J.G. Verwer, A comparison of integration methods for atmospheric transport-chemistry problems, to appear in J. Comp. Appl. Math, 2000 (no. 33 in [1]).

[4] D. Lanser and J.G. Verwer, Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling, J. Comp. Appl. Math. 111 (1999) 201--216 (no. 30 in [1]).

[5] J.G. Verwer, W. Hundsdorfer and J.G. Blom, Numerical time integration for air pollution models, to appear in Surveys for Mathematics in Industry (no. 31 in [1]).

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