Ivan Dimov - Böcker

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

The protection of the environment is one of the most important problems facing us today. Reliable and robust strategies for keeping pollution caused by harmful chemicals under safe levels have to be developed and used routinely. Large mathematical models, incorporating all important physical and chemical processes, can solve this task, but the computational burden is huge. The papers presented here describe some of the difficult problems that have to be solved during the development of large scale air pollution models, and different ways to solve them. The work involves combined research by specialists in the fields of environmental modelling, numerical analysis and scientific computing. Further, if models are to run in real time (which may be vital in the case of accidental hazardous releases), then new and efficient methods that harness the potential power of parallel supercomputers must be developed, so that actual computing speed starts to approach the maximum available performance. The articles should be understandable by specialists in the field of air pollution modelling, as well as specialists in the many other related areas.

This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions.

Every day we need to solve large problems for which supercomputers are needed. High performance computing (HPC) is a paradigm that allows to efficiently implement large-scale computational tasks on powerful supercomputers unthinkable without optimization. We try to minimize our effort and to maximize the achieved profit.Many challenging real world problems arising in engineering, economics, medicine and other areas can be formulated as large-scale computational tasks.The volume is a comprehensive collection of extended contributions from the High performance computing conference held in Borovets, Bulgaria, September 2019.This book presents recent advances in high performance computing. The topics of interest included into this volume are: HP software tools, Parallel Algorithms and Scalability, HPC in Big Data analytics, Modelling, Simulation & Optimization in a Data Rich Environment, Advanced numerical methods for HPC, Hybrid parallel or distributed algorithms.The volume is focused on important large-scale applications like Environmental and Climate Modeling, Computational Chemistry and Heuristic Algorithms.

Every day we need to solve large problems for which supercomputers are needed. High performance computing (HPC) is a paradigm that allows to efficiently implement large-scale computational tasks on powerful supercomputers unthinkable without optimization. We try to minimize our effort and to maximize the achieved profit.Many challenging real world problems arising in engineering, economics, medicine and other areas can be formulated as large-scale computational tasks.The volume is a comprehensive collection of extended contributions from the High performance computing conference held in Borovets, Bulgaria, September 2019.This book presents recent advances in high performance computing. The topics of interest included into this volume are: HP software tools, Parallel Algorithms and Scalability, HPC in Big Data analytics, Modelling, Simulation & Optimization in a Data Rich Environment, Advanced numerical methods for HPC, Hybrid parallel or distributed algorithms.The volume is focused on important large-scale applications like Environmental and Climate Modeling, Computational Chemistry and Heuristic Algorithms.

The book serves as a synergistic link between the development of mathematical models and the emergence of stochastic (Monte Carlo) methods applied for the simulation of current transport in electronic devices.

The book serves as a synergistic link between the development of mathematical models and the emergence of stochastic (Monte Carlo) methods applied for the simulation of current transport in electronic devices.

This is the proceedings of the "8th IMACS Seminar on Monte Carlo Methods" held from August 29 to September 2, 2011 in Borovets, Bulgaria, and organized by the Institute of Information and Communication Technologies of the Bulgarian Academy of Sciences in cooperation with the International Association for Mathematics and Computers in Simulation (IMACS). Included are 24 papers which cover all topics presented in the sessions of the seminar: stochastic computation and complexity of high dimensional problems, sensitivity analysis, high-performance computations for Monte Carlo applications, stochastic metaheuristics for optimization problems, sequential Monte Carlo methods for large-scale problems, semiconductor devices and nanostructures.The history of the IMACS Seminar on Monte Carlo Methods goes back to April 1997 when the first MCM Seminar was organized in Brussels:1st IMACS Seminar, 1997, Brussels, Belgium2nd IMACS Seminar, 1999, Varna, Bulgaria 3rd IMACS Seminar, 2001, Salzburg, Austria 4th IMACS Seminar, 2003, Berlin, Germany 5th IMACS Seminar, 2005, Tallahassee, USA6th IMACS Seminar, 2007, Reading, UK7th IMACS Seminar, 2009, Brussels, Belgium8th IMACS Seminar, 2011, Borovets, Bulgaria

Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book.Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. 　 ContentsThe basic properties of Richardson extrapolationRichardson extrapolation for explicit Runge-Kutta methodsLinear multistep and predictor-corrector methodsRichardson extrapolation for some implicit methodsRichardson extrapolation for splitting techniquesRichardson extrapolation for advection problemsRichardson extrapolation for some other problemsGeneral conclusions

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Numerical Methods and Applications, NMA 2014, held in Borovets, Bulgaria, in August 2014. advanced numerical methods for scientific computing; advanced numerical techniques for PDEs and applications;

This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions.

This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016.

This volume of the Springer Series "Lecture Notes in Computer Science" c- tains refereed papers which were presented at the Fifth International Conf- ence on Numerical Methods and Applications, NMA 2002, held in Borovets, Bulgaria, during 20-24 August 2002. The NMA 2002 Conference was organized by the Central Laboratory for Parallel Processing at the Bulgarian Academy of Sciences in cooperation with SIAM (Society for Industrial and Applied Mat- matics) and GAMM (Gesellschaft fur .. Angewandte Mathematik und Mechanik). Co-organizers of this traditional scienti?c meeting were the Institute of Mat- matics and Informatics at the Bulgarian Academy of Sciences and the Faculty of Mathematics and Informatics at the University of So?a. The conference was devoted to the 70th anniversary of the distinguished Bulgarian mathematician academician Blagovest Sendov - the founder of the Bulgarian school in - merical analysis, the teacher of dozens of Ph. D. students, the author of more than 270 papers, textbooks, and monographs. He is the scholar who has been at the center of the mathematical life in Bulgaria for about 50 years.Over the years he headed the Bulgarian Academy of Sciences, the University of So?a, the Faculty of Mathematics and Informatics of the University of So?a, the C- tral Laboratory for Parallel Processing of the Bulgarian Academy of Sciences, the Department of Mathematical Modeling of the Institute of Mathematics and Informatics, the Union of Bulgarian Mathematicians, etc. He represented with distinctionBulgarianscienceinsuchworld-recognizedorganizationsasIFIP (- ternationalFederationforInformationProcessing),theInternationalAssociation ofUniversities,theInternationalCouncilofScienti?cUnions,theBalkanMat- maticalUnion,etc.