Implementation of multirate time integration methods for air pollution modelling 1Leibniz Institute for Tropospheric Research, Permoserstraße 15, 04318 Leipzig, Germany
2Martin Luther University Halle-Wittenberg, Institute of Mathematics, 06099 Halle (Saale), Germany
Received: 11 July 2011 – Published in Geosci. Model Dev. Discuss.: 15 November 2011 Abstract. Explicit time integration methods are characterised by a small numerical
effort per time step. In the application to multiscale problems
in atmospheric modelling, this benefit is often more than compensated
by stability problems and step size restrictions resulting from stiff
chemical reaction terms and from a locally varying
Courant-Friedrichs-Lewy (CFL) condition for the advection terms.
Splitting methods may be applied to efficiently combine implicit and
explicit methods (IMEX splitting). Complementarily multirate time integration
schemes allow for a local adaptation of the time step size to the grid size.
In combination, these approaches lead to schemes which are efficient
in terms of evaluations of the right-hand side. Special challenges arise
when these methods are to be implemented. For an efficient implementation,
it is crucial to locate and exploit redundancies. Furthermore, the more
complex programme flow may lead to computational overhead which, in the worst
case, more than compensates the theoretical gain in efficiency.
We present a general splitting approach which allows both for IMEX splittings
and for local time step adaptation. The main focus is on an efficient
implementation of this approach for parallel computation on computer clusters.
Revised: 05 September 2012 – Accepted: 09 October 2012 – Published: 12 November 2012
Citation: Schlegel, M., Knoth, O., Arnold, M., and Wolke, R.: Implementation of multirate time integration methods for air pollution modelling, Geosci. Model Dev., 5, 1395-1405, doi:10.5194/gmd-5-1395-2012, 2012.