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. ...
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.
- Use of templates in connection with the treatment of very large models
- Performance of comprehensive environmental studies
- Obtaining reliable and robust information about pollution levels
- Studying the impact of future climatic changes on high pollution levels
- Investigating trends related to critical levels of pollution
Zahari Zlatev received his MSc from the Sofia University and his PhD from the Sct. Petersbourg University. He is a senior scientist and a project leader (Long-range Transport Modelling) at NERI (National Environmental Research Institute, Roskilde, Denmark) since 1980. He has developed the Unified Danish Eulerian Model (UNI-DEM), which has been used in many environmental studies and scientific projects (see also http://www.dmu.dk/AtmosphericEnvironment/DEM).
Zahari Zlatev published five monographs (two in Kluwer, two in Springer and one in MIR Publishers), has been editor of four proceedings volumes, has 92 papers in international journals, 123 papers in proceedings of international conferences and more than 200 institutional reports. He has been involved in training young specialists; including graduated students and PhD students. Zahari Zlatev organized five international conferences and nine mini-symposia at international conferences; in Stanford (USA), in Hamburg (Germany), in Varna (Bulgaria), in Toronto (Canada), three in Sozopol (Bulgaria), in Limassol (Cyprus), in Copenhagen (Denmark) and in San Francisco (USA). He has been an invited speaker at 24 international conferences and in the organizing committee of many international workshops and conferences (see also http://www.dmu.dk/AtmosphericEnvironment/zlatev.htm).
Ivan Dimov received his MSc in 1976, PhD in 1980 and the Doctor of Sciences degree in 1984 in Moscow, Russia. He is professor in Mathematical modelling since 1996. From 1996 to 2004 he was director of the Institute for Parallel Processing of the Bulgarian Academy of Sciences and Head of the Bulgarian Information Society Center of Excellence BIS-21. Currently he is a research professor at the University of Reading, UK.
Ivan Dimov published more than 90 papers in refereed international scientific journals and series, has been editor of seven special volumes published by Kluwer, Springer (Lecture notes in Computer Science), World Scientific, and IOS Press.
He has been involved in training young specialists: graduated students, PhD students and young post-docs. Ivan Dimov has organized nine international conferences. He is involved as a director or co-director in 12 international scientific projects (mainly EU projects). He has been an invited speaker at 35 international conferences and scientific institutions and served in program and organizing committees of many international conferences and workshops (see also http://www.reading.ac.uk/~sis04itd).
1. PDE systems arising in air pollution modelling and justification of the need for high speed computers
2. Using splitting techniques in the treatment of air pollution models
3. Treatment of the advection-diffusion phenomena
4. Treatment of the chemical part: general ideas and major numerical methods
5. Error analysis of the partitioning procedures
6. Efficient organization of the matrix computations
7. Parallel computations
8. Studying high pollution levels
9. Impact of future climate changes on high pollution levels
10. Implementation of variational data assimilation
11. Discussion of some open questions
Appendix A: Colour plots