RUNNING LARGE AIR-POLLUTION MODELS ON HIGH-SPEED COMPUTERS

The long-range transport of air pollutants (LRTAP) over Europe is studied, at the Air Pollution Laboratory of the Danish Agency of Environmental Protection, by a mathematical model based on a system of partial differential equations (PDE's). Four different physical processes, advection, diffusion, deposition and chemical reactions (together with emission sources), are the main components of the LRTAP. These four processes are described by different terms in the model (the system of PDE's). Since the space domain is very large (including the whole of Europe together with parts of the Atlantic Ocean, Asia and Africa), the discretization of the system of PDE's leads to huge systems of linear algebraic equations (LAE's). In the three dimensional case on a 32X32X9 grid the number of LAE's that are to be solved at each time-step is more than 10(6) when 29 chemical species are involved in the model. Even if the model is considered as a two-dimensional model, the number of LAE's is still very large; more than 10(5). This explains why one should make some simplifications in the model description (which are not always very well justified physically, but lead to a model that can be handled on the computer used) and/or one should use high-speed computers. In the latter case, high performance can be achieved by efficiently implementing certain kernels which perform the bulk of the computational work. Fortunately, regular grids are to be used during the discretization of the LRTAP model. This leads to the solution of LAE's whose coefficient matrices are banded and whose solution dominates the computational load. Several such kernels for solving banded systems of LAE's will be described. Experimental results obtained on the AMDAHL VP-1100, CRAY X-MP and Alliant FX/8 will be presented and discussed.