Domain Decomposition Methods - Algorithms and Theory

Author: Andrea Toselli,Olof Widlund

Publisher: Springer Science & Business Media

ISBN: 3540266623

Category: Mathematics

Page: 450

View: 8207

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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.
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Domain Decomposition Methods in Science and Engineering XVIII

Author: Michel Bercovier,Martin Gander,Ralf Kornhuber,Olof Widlund

Publisher: Springer Science & Business Media

ISBN: 9783642026775

Category: Mathematics

Page: 376

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th This volume contains a selection of 41 refereed papers presented at the 18 International Conference of Domain Decomposition Methods hosted by the School of ComputerScience and Engineering(CSE) of the Hebrew Universityof Jerusalem, Israel, January 12–17, 2008. 1 Background of the Conference Series The International Conference on Domain Decomposition Methods has been held in twelve countries throughout Asia, Europe, the Middle East, and North America, beginning in Paris in 1987. Originally held annually, it is now spaced at roughly 18-month intervals. A complete list of past meetings appears below. The principal technical content of the conference has always been mathematical, but the principal motivation has been to make ef cient use of distributed memory computers for complex applications arising in science and engineering. The leading 15 such computers, at the “petascale” characterized by 10 oating point operations per second of processing power and as many Bytes of application-addressablem- ory, now marshal more than 200,000 independentprocessor cores, and systems with many millions of cores are expected soon. There is essentially no alternative to - main decomposition as a stratagem for parallelization at such scales. Contributions from mathematicians, computerscientists, engineers,and scientists are together n- essary in addressing the challenge of scale, and all are important to this conference.
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Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications

In Honor of Professor Raytcho Lazarov's 40 Years of Research in Computational Methods and Applied Mathematics

Author: Oleg P. Iliev,Svetozar D. Margenov,Peter D Minev,Panayot S. Vassilevski,Ludmil T Zikatanov

Publisher: Springer Science & Business Media

ISBN: 1461471729

Category: Mathematics

Page: 327

View: 2132

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One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.
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Dirichlet-dirichlet Domain Decomposition Methods For Elliptic Problems: H And Hp Finite Element Discretizations

Author: Korneev Vadim Glebiovich,Langer Ulrich

Publisher: World Scientific

ISBN: 9814578479

Category: Mathematics

Page: 484

View: 3361

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Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet-Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use.
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Domain Decomposition Methods in Science and Engineering XXI

Author: Jocelyne Erhel,Martin J. Gander,Laurence Halpern,Géraldine Pichot,Taoufik Sassi,Olof Widlund

Publisher: Springer

ISBN: 3319057898

Category: Mathematics

Page: 973

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This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.
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Domain Decomposition Methods in Science and Engineering XXIII

Author: Chang-Ock Lee,Xiao-Chuan Cai,David E. Keyes,Hyea Hyun Kim,Axel Klawonn,Eun-Jae Park,Olof B. Widlund

Publisher: Springer

ISBN: 3319523899

Category: Computers

Page: 415

View: 868

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This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.
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RAIRO.

Modélisation Mathématique Et Analyse Numérique : M2N.. Mathematical modelling and numerical analysis

Author: EDP Sciences

Publisher: N.A

ISBN: N.A

Category: Numerical analysis

Page: N.A

View: 1163

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