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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
"Models are often the only way of interpreting measurements to in vestigate long-range transport, and this is the reason for the emphasis on them in many research programs". B. E. A. Fisher: "A review of the processes and models of long-range transport of air pollutants", Atmospheric Environment, 17(1983), p. 1865. Mathematical models are (potentially, at least) powerful means in the efforts to study transboundary transport of air pollutants, source-receptor relationships and efficient ways of reducing the air pollution to acceptable levels. A mathematical model is a complicated matter, the development of which is based on the use of (i) various mechanisms describing mathematically the physical and chemical properties of the studied phenomena, (ii) different mathematical tools (first and foremost, partial differenti al equations), (iii) various numerical methods, (iv) computers (especially, high-speed computers), (v) statistical approaches, (vi) fast and efficient visualization and animation techniques, (vii) fast methods for manipulation with huge sets of data (input data, intermediate data and output data).
This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Large-Scale Scientific Computations, LSSC 2011, held in Sozopol, Bulgaria, in June 2011. The 74 revised full papers presented together with 3 plenary and invited papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on robust multigrid, multilevel and multiscale, deterministic and stochastic methods for modeling highly heterogeneous media, advanced methods for transport, control and uncertain systems, applications of metaheuristics to large-scale problems, environmental modelling, large scale computing on many-core architectures, multiscale industrial, enviromental and biomedical problems, efficient algorithms of computational geometry, high performance Monte Carlo simulations, voxel based computations and contributed papers.
This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.
This book gathers the peer-reviewed proceedings of the 13th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM'18, held in Sofia, Bulgaria. The general theme of BGSIAM'18 was industrial and applied mathematics with particular focus on: mathematical physics, numerical analysis, high performance computing, optimization and control, mathematical biology, stochastic modeling, machine learning, digitization and imaging, advanced computing in environmental, biomedical and engineering applications.
An understanding of long-range transport of air pollutants in the atmosphere requires a knowledge of the relevant atmospheric dynamic and chemical processes active at the regional scale as well as the temporal and spatial distribution of emissions. Numerical modeling is the most efficient way to determine the atmospheric transport, photochemistry and deposition pathways. The book therefore discusses the physical and chemical processes that determine regional air pollution and presents the relevant modeling techniques to describe the different atmospheric processes that are active at that scale.
This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Numerical Analysis and Its Applications, NAA 2004, held in Rousse, Bulgaria in June/July 2004. The 68 revised full papers presented together with 8 invited papers were carefully selected during two rounds of reviewing and improvement. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, fluid dynamics, visualization, etc.
High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.