Download or read book Domain Decomposition Methods Algorithms and Theory written by Andrea Toselli and published by Springer Science & Business Media. This book was released on 2006-06-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Download or read book An Introduction to Domain Decomposition Methods written by Victorita Dolean and published by SIAM. This book was released on 2015-12-08 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?
Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
Download or read book Domain Decomposition Methods 10 written by Jan Mandel and published by American Mathematical Soc.. This book was released on 1998 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Tenth International Conference on Domain Decomposition Methods, which focused on the latest developments in realistic applications in structural mechanics, structural dynamics, computational fluid dynamics, and heat transfer. The proceedings of these conferences have become standard references in the field and contain seminal papers as well as the latest theoretical results and reports on practical applications.
Download or read book Domain Decomposition written by Barry Smith and published by Cambridge University Press. This book was released on 2004-03-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.
Download or read book Computational Partial Differential Equations written by Hans Petter Langtangen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.
Download or read book Parallel Numerical Algorithms written by David E. Keyes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.
Download or read book Discretization Methods and Iterative Solvers Based on Domain Decomposition written by Barbara I. Wohlmuth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.
Download or read book Domain Decomposition Methods in Science and Engineering written by Ralf Kornhuber and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.
Download or read book Defect Correction Methods written by K. Böhmer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years ago, the term "defect correction" was introduced to characterize a class of methods for the improvement of an approximate solution of an operator equation. This class includes many well-known techniques (e.g. Newton's method) but also some novel approaches which have turned out to be quite efficient. Meanwhile a large number of papers and reports, scattered over many journals and institutions, have appeared in this area. Therefore, a working conference on "Error Asymptotics and Defect Corrections" was organized by K. Bohmer, V. Pereyra and H. J. Stetter at the Mathematisches Forschungsinstitut Oberwolfach in July 1983, a meeting which aimed at bringing together a good number of the scientists who are active in this field. Altogether 26 persons attended, whose interests covered a wide spectrum from theoretical analyses to applications where defect corrections may be utilized; a list of the participants may be found in the Appendix. Most of the colleagues who presented formal lectures at the meeting agreed to publish their reports in this volume. It would be presumptuous to call this book a state-of-the-art report in defect corrections. It is rather a collection of snapshots of activities which have been going on in a number of segments on the frontiers of this area. No systematic coverage has been attempted. Some articles focus strongly on the basic concepts of defect correction; but in the majority of the contributions the defect correction ideas appear rather as instruments for the attainment of some specified goal.
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Download or read book Advances in Electric Power and Energy written by Mohamed E. El-Hawary and published by John Wiley & Sons. This book was released on 2021-03-03 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the role of static state estimation in the mitigation of potential system failures With contributions from a noted panel of experts on the topic, Advances in Electric Power and Energy: Static State Estimation addresses the wide-range of issues concerning static state estimation as a main energy control function and major tool for evaluating prevailing operating conditions in electric power systems worldwide. This book is an essential guide for system operators who must be fully aware of potential threats to the integrity of their own and neighboring systems. The contributors provide an overview of the topic and review common threats such as cascading black-outs to model-based anomaly detection to the operation of micro-grids and much more. The book also includes a discussion of an effective mathematical programming approach to state estimation in power systems. Advances in Electric Power and Energy reviews the most recent developments in the field and: Offers an introduction to the topic to help non-experts (and professionals) get up-to-date on static state estimation Covers the essential information needed to understand power system state estimation written by experts on the subject Discusses a mathematical programming approach Written for electric power system planners, operators, consultants, power system software developers, and academics, Advances in Electric Power and Energy is the authoritative guide to the topic with contributions from experts who review the most recent developments.
Download or read book Finite Element Methods written by Duc Thai Nguyen and published by Springer Science & Business Media. This book was released on 2006-07-18 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods (FEM), and its associated computer software have been widely accepted as one of the most effective general tools for solving large-scale, practical engineering and science applications. For implicit finite element codes, it is a well-known fact that efficient equation and eigen-solvers play critical roles in solving large-scale, practical engineering/science problems. Sparse matrix technologies have been evolved and become mature enough that all popular, commercialized FEM codes have already inserted sparse solvers into their software. However, a few FEM books have detailed discussions about Lanczos eigen-solvers, or explain domain decomposition (DD) finite element formulation (including detailed hand-calculator numerical examples) for parallel computing purposes. The materials from this book have been evolved over the past several years through the author's research work, and graduate courses.
Download or read book Computational Electromagnetics written by Jin-Fa Lee and published by . This book was released on 2017 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Developed for Computational Physicists, Researchers, and Software Developers at the Practical LevelIntegrating in-depth mathematical analysis with real-world engineering practice, Computational Electromagnetics: Domain Decomposition Methods and Practical Applications focuses on domain decomposition methods (DDMs) that adequately deal with the vector wave equation. Dedicated specifically to solving time harmonic Maxwell equations, it covers challenges that are typically hard to address using conventional numerical methods. This book adopts the philosophy throughout, that every residual will either equal identically to zero through restrictions on the trial functions or be tested by test functions by ways of dual-pairing. Explore the Use of DDM to Solve Large-Scale ProblemsThe material focuses on a multi-trace combined field integral equation formulation with multiple traces derived and analyzed for EM scattering from a single homogeneous scatter, and contains numerical examples demonstrating the benefits (accuracy and scalability) of DDM. It provides examples for analyzing and addressing scattering problems that include an electromagnetic wave scattering from a large complex large-scale composite mockup aircraft and an electromagnetic wave scattering from an electrically large inlet structure. Presenting numerous facets of the nonoverlapping domain decomposition methods and their applications, it reveals how these methods can help solve multi-scale time harmonic electromagnetic problems.This book covers:Large finite antenna arrays, metamaterials, antenna systems conformally mounted on large platforms, signal integrity analyses of complex integrated circuits and packaging, and radar echo area computation of complex composite targets applicationsAn alternative approach to formulate the corresponding boundary value problem by incorporating an additional vector variable defined only on the surfaceThe multi-solver domain decomposition method (MS-DDM) which is included in theory and practical engineering applicationsComputational Electromagnetics: Domain Decomposition Methods and Practical Applications covers the applied aspects of domain decomposition methods for computational electromagnetics, and helps to bridge the gap between multi-scale and multi-physics, and the hands-on application of practical engineering."--Provided by publisher.
Download or read book Numerical Conformal Mapping written by Nicolas Papamichael and published by World Scientific. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications. The reader will find a highly useful and up-to-date survey of available numerical methods and associated computer software for conformal mapping. The book also highlights the crucial role that function theory plays in the development of numerical conformal mapping methods, and illustrates the theoretical insight that can be gained from the results of numerical experiments.This is a valuable resource for mathematicians, who are interested in numerical conformal mapping and wish to study some of the recent developments in the subject, and for engineers and scientists who use, or would like to use, conformal transformations and wish to find out more about the capabilities of modern numerical conformal mapping.
Download or read book Finite Element Multidisciplinary Analysis written by Kajal K. Gupta and published by AIAA. This book was released on 2003 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book fills a gap within the finite element literature by addressing the challenges and developments in multidiscipli-nary analysis. Current developments include disciplines of structural mechanics, heat transfer, fluid mechanics, controls engineering and propulsion technology, and their interaction as encountered in many practical problems in aeronautical, aerospace, and mechanical engineering, among others. These topics are reflected in the 15 chapter titles of the book. Numerical problems are provided to illustrate the applicability of the techniques. Exercises may be solved either manually or by using suitable computer software. A version of the multidisciplinary analysis program STARS is available from the author. As a textbook, the book is useful at the senior undergraduate or graduate level. The practicing engineer will find it invaluable for solving full-scale practical problems.
Download or read book The Mathematical Theory of Finite Element Methods written by Susanne Brenner and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide
