Advances In The Theory Of Computation And Computational Mathematics Numerical Solution Of Nonlinear Elliptic Problems Via Preconditioning Operators Theory And Applications

Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications

A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.

The book’s general scope covers the latest advances in the development of artificial intelligence systems and their applications in engineering and manufacturing. The book comprises refereed papers presented at the International Symposium on Engineering and Manufacturing (ISEM2021), held in Kyiv, Ukraine, on December 24–26, 2021. Given the rapid development of artificial intelligence systems, the book emphasizes the need for the intensification of training of a growing number of relevant specialists, in particular in engineering and manufacturing, to increase the effectiveness of the creation and diagnosis of appropriate technical solutions. In digital artificial intelligence systems, scientists endeavor to reproduce the innate intellectual abilities of humans and other organisms. In-depth studies of biological and self-organizing systems can provide new approaches to create more and more effective artificial intelligence methods. The topics of the included papers concern thematic materials in the following spheres: mathematics and computer algorithms; analysis of some technical solutions; technological. The book is a compilation of state-of-the-art papers in the field, covering a comprehensive range of subjects that are relevant to business managers and engineering professionals alike. The breadth and depth of these proceedings make them an excellent resource for asset management practitioners, researchers, and academics, as well as undergraduate and postgraduate students interested in artificial intelligence systems and their growing applications. Specialists, students, and other groups of people who want to know how artificial intelligence systems can be used in the future will be the target audience for this book.

This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Large-Scale Scientific Computations, LSSC 2009, held in Sozopol, Bulgaria, in June 2009. The 93 revised full papers presented together with 5 plenary and invited papers were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers are organized in topical sections on multilevel and multiscale preconditioning methods multilevel and multiscale methods for industrial applications, environmental modeling, control and uncertain systems, application of metaheuristics to large scale problems, monte carlo: methods, applications, distributed computing, grid and scientific and engineering applications, reliable numerical methods for differential equations, novel applications of optimization ideas to the numerical Solution of PDEs, and contributed talks.

In the not too distant future, every researcher and professional in science and engineering fields will have to understand parallel and distributed computing. With hyperthreading in Intel processors, hypertransport links in AMD processors, multi-core silicon in today's high-end microprocessors from IBM and emerging cluster and grid computing, parallel and distributed computers have moved into the mainstream of computing. To fully exploit these advances in computer architectures, researchers and professionals must start to design parallel or distributed software, systems and algorithms for their scientific and engineering applications. Parallel and distributed scientific and engineering computing has become a key technology which will play an important part in determining, or at least shaping, future research and development activities in many academic and industrial branches. This book reports on the recent important advances in the area of parallel and distributed computing for science and engineering applications. Included in the book are selected papers from prestigious workshops such as PACT-SHPSEC, IPDPS-PDSECA and ICPP-HPSECA together with some invited papers from prominent researchers around the world. The book is basically divided into five main sections. These chapters not only provide novel ideas, new experimental results and handful experience in this field, but also stimulate the future research activities in the area of parallel and distributed computing for science and engineering applications.

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the development fields discussed, to demonstrate their mathematical complexity and, more importantly, to encourage mathematicians to contribute to the further success of such practical applications as weather forecasting and climate change projections. Written by leading experts in the field, the book provides an attractive and diverse introduction to areas in which mathematicians and modellers from the meteorological community can cooperate and help each other solve the problems that operational weather centres face, now and in the near future. Readers engaged in meteorological research will become more familiar with the corresponding mathematical background, while mathematicians working in numerical analysis, partial differential equations, or stochastic analysis will be introduced to further application fields of their research area, and will find stimulation and motivation for their future research work.

The explosive growth of the Internet and the web have created an ever-growing demand for web-based information systems, and ever-growing challenges for Information Systems Engineering. Some of them include the emerging web services technology, database technologies and application integration, as well as data analysis and knowledge discovery. This book is a showcase of recent, significant advances in web-based information systems as well as data integration and analysis. It provides an overview of various technologies used for building innovative information systems applied to real business solutions. It includes eight chapters that are divided into five parts, namely: web services, database technologies, data and application integration, data analysis and knowledge discovery, and recommended bibliography. The material presented in these chapters will help the reader have an overall idea of the research that is being carried out in universities and companies to develop today's innovative business solutions. Contents: Preface; Web Services; Web Services Technologies for Outsourcing; Conceptual Modelling with Dynamic Object Roles; Temporal Versioning in Data Warehouse; Missing Inform