Computational complexity of weighted splitting schemes on parallel computers

Abstract

In models of complicated physical–chemical processes operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The recently rediscovered weighted splitting schemes have the great advantage of being parallelizable on operator level, which allows us to reduce the computational time if parallel computers are used.

In this paper, the computational times needed for the weighted splitting methods are studied in comparison with the sequential (S) splitting and the Marchuk–Strang (MSt) splitting and are illustrated by numerical experiments performed by use of simplified versions of the Danish Eulerian model (DEM).

Keywords:

• Operator splitting
• Computational complexity
• Air pollution modeling
• Distributed memory
• Shared memory

Acknowledgements

The experimental results were obtained during the visit of P. Csomós and Á. Havasi in the Institute for Parallel Processing, Bulgarian Academy of Sciences, Sofia within the framework of the project Center of Excellence (grant ICA1-CT-2000-70016). The work was also supported in part by EC grant , as well as by the Bulgarian Academy of Sciences and Hungarian Academy of Sciences (contract No. 6/2003). Ágnes Havasi is a grantee of the Bolyai János Scholarship.