Computational Challenges in the Numerical Treatment of Large Air Pollution Models

The air pollution, and especially the reduction of the air pollution to some acceptable levels, is an important environmental problem, which will become even more important in the next 10-20 years. This problem can successfully be studied only when high-resolution comprehensive models are developed and used on a routinely basis. However, such models are very time-consuming, also when modern high-speed computers are available. Indeed, if an air pollution model is to be applied on a large space domain by using ne grids, then its discretization will always lead to huge computational problems. Assume, for example, that the space domain is discretized by using a (480x480) grid and that the number of chemical species studied by the model is 35. Then several systems of ordinary di erential equations containing 8064000 equations have to be treated at every time-step (the number of time-steps being typically several thousand). If a three-dimensional version of the same air pollution model is to be used, then the above gure must be multiplied by the number of layers. It is extremely di cult to treat such large computational problems; even when the fastest computers that are available at present are used. There is an additional great di culty which is very often underestimated (or even neglected) when large application packages are moved from sequential computers to modern parallel machines. The high-speed computers have normally a very complicated memory architecture and, therefore, the task of producing an e cient code for the particular high-speed computer that is available is both extremely hard and very laborious. The use of standard parallelization tools in the solution of the problems sketched above is discussed in this paper. Results obtained on di erent types of parallel computers are given. It is demonstrated that the new e cient parallel algorithms allow us to solve more problems and bigger problems.