Using Advanced Mathematical Tools in Complex Studies Related to Climate Changes and High Pollution Levels

Abstract

UNI-DEM is a large-scale environmental model described by a non-linear system of partial differential equations (PDEs) and used in many studies of air pollution levels in different European countries. The discretization of UNI-DEM leads to a long series of huge computational tasks, because it is necessary to run the discretized model with many different scenarios during long time-periods of many consecutive years. Therefore, both the storage requirements and the computational work are enormous. We had to resolve four difficult problems in the efforts to perform successfully the required simulations. More precisely, we had to do the following: (a) to implement fast numerical methods, (b) to select suitable splitting procedures, (c) to exploit efficiently the cache memories of the available high-speed computers (d) to parallelize the computer codes.