Computational and Numerical Challenges in Environmental ModellingBy
- Zahari Zlatev
- Ivan Dimov
Many large mathematical models, not only models arising and used in environmental studies, are described by systems of partial differential equations. The discretization of the spatial derivatives in such models leads to the solution of very large systems of ordinary differential equations. These systems contain many millions of equations and have to be handled over large time intervals by applying many time-steps (up to several hundred thousand time-steps). Furthermore, many scenarios are as a rule to be run. This explains the fact that the computational tasks in this situation are enormous. Therefore, it is necessary to select fast numerical methods; to develop parallel codes and, what is most important when the problems solved are very large to organize the computational process in a proper way.
The last item (which is very often underestimated but, let us re-iterate, which is very important) is the major topic of this book. In fact, the proper organization of the computational process can be viewed as a preparation of templates which can be used with different numerical methods and different parallel devices. The development of such templates is described in the book. It is also demonstrated that many comprehensive environmental studies can successfully be carried out when the computations are correctly organized. Thus, this book will help the reader to understand better that, while (a) it is very important to select fast numerical methods as well as (b) it is very important to develop parallel codes, this will not be sufficient when the problems solved are really very large. In the latter case, it is also crucial to exploit better the computer architecture by organizing properly the computational process.
Air Pollution Modeling, Scientific Computing and Numerical Analysis
Studies in Computational Mathematics
Hardbound, 392 Pages
Published: May 2006
- PrefaceAcknowledgementsContents1. PDE systems arising in air pollution modelling and justification of the need for high speed computers2. Using splitting techniques in the treatment of air pollution models3. Treatment of the advection-diffusion phenomena4. Treatment of the chemical part: general ideas and major numerical methods5. Error analysis of the partitioning procedures6. Efficient organization of the matrix computations7. Parallel computations8. Studying high pollution levels9. Impact of future climate changes on high pollution levels10. Implementation of variational data assimilation11. Discussion of some open questionsAppendix A: Colour plotsBibliographySymbol TableAuthor IndexSubject Index