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 sy
Computational and numerical challenges in environmental modeling
β Scribed by Zahari Zlatev and Ivan Dimov (Eds.)
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Leaves
- 393
- Series
- Studies in Computational Mathematics 13
- Edition
- 1
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
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
β¦ Table of Contents
Content:
Preface
Pages vii-xi
Acknowledgements Original Research Article
Pages xiii-xiv
Chapter 1 PDE systems arising in air pollution modelling and justification of the need for high speed computers Original Research Article
Pages 1-41
Chapter 2 Using splitting techniques in the treatment of air pollution models Original Research Article
Pages 43-87
Chapter 3 Treatment of the advection-diffusion phenomena Original Research Article
Pages 89-108
Chapter 4 Treatment of the chemical part: general ideas and major numerical methods Original Research Article
Pages 109-135
Chapter 5 Error analysis of the partitioning procedures Original Research Article
Pages 137-155
Chapter 6 Efficient organization of the matrix computations Original Research Article
Pages 157-200
Chapter 7 Parallel computations Original Research Article
Pages 201-231
Chapter 8 Studying high pollution levels Original Research Article
Pages 233-244
Impact of future climate changes on high pollution levels Original Research Article
Pages 245-276
Chapter 10 Implementation of variational data assimilation Original Research Article
Pages 277-316
Chapter 11 Discussion of some open questions Original Research Article
Pages 317-326
Appendix A: Colour plots
Pages 327-332
Bibliography Original Research Article
Pages 333-356
Symbol table Original Research Article
Pages 357-358
Author index Original Research Article
Pages 359-365
Subject index Original Research Article
Pages 367-373
β¦ Subjects
ΠΠ°ΡΠΊΠΈ ΠΎ ΠΠ΅ΠΌΠ»Π΅;ΠΠ΅ΡΠ΅ΠΎΡΠΎΠ»ΠΎΠ³ΠΈΡ ΠΈ ΠΊΠ»ΠΈΠΌΠ°ΡΠΎΠ»ΠΎΠ³ΠΈΡ;
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