Mathematical treatment of environmental models

Zlatev, Z. and Faragó, István and Havasi, Ágnes (2014) Mathematical treatment of environmental models. In: Progress in industrial mathematics at ECMI 2012. Mathmatics in industry (19). Springer, Cham, pp. 65-70. ISBN 978-3-319-05365-3

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Abstract

Large-scale environmental models can successfully be used in different important for the modern society studies as, for example, in the investigation of the influence of the future climatic changes on pollution levels in different countries. Such models are normally described mathematically by non-linear systems of par- tial differential equations, which are defined on very large spatial domains and have to be solved numerically on very long time intervals. Moreover, very often many different scenarios have also to be developed and used in the investigations. There- fore, both the storage requirements and the computational work are enormous. The great difficulties can be overcome only if the following four tasks are successfully resolved: (a) fast and sufficiently accurate numerical methods are to be selected, (b) reliable and efficient splitting procedures are to be applied, (c) the cache memories of the available computers are to be efficiently exploited and (d) the codes are to be parallelized.

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