Parallel algorithms for the chemical part of large air pollution models

Mathematical models can successfully be used to study many environmental problems. The reliability of the results from these models is an essential requirement. One has to describe in an adequate way all important physical and chemical processes in order to obtain reliable results. This leads (after the application of appropriate discretization and splitting rules) to the solution of several huge ODE systems, corresponding to the major physical and chemical processes involved in the model, that are to be treated during many steps. The ODE systems contain up to several million equations. The number of time-steps vary in the different applications from several hundreds to several hundred thousands. Moreover, many runs, up to several thousands, have to be performed in a typical simulation based on long series of scenarios. The treatment of the chemical part of the models is normally the most expensive part of the computational process because the chemical ODE systems are both very stiff and very badly scaled. Therefore it is important to select good numerical algorithms for these systems and to implement these algorithms on parallel computers. Some results obtained in this direction based on the use of special sparse matrix techniques and on parallel computations, will be described.