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Domain Decomposition Methods - Algorithms and Theory

Domain Decomposition Methods - Algorithms and Theory
Author: Andrea Toselli
Publisher: Springer Science & Business Media
Total Pages: 454
Release: 2006-06-20
Genre: Mathematics
ISBN: 3540266623

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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.


An Introduction to Domain Decomposition Methods

An Introduction to Domain Decomposition Methods
Author: Victorita Dolean
Publisher: SIAM
Total Pages: 242
Release: 2015-12-08
Genre: Science
ISBN: 1611974054

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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.?


Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Author: Tarek Mathew
Publisher: Springer Science & Business Media
Total Pages: 775
Release: 2008-06-25
Genre: Mathematics
ISBN: 354077209X

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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.


Domain Decomposition

Domain Decomposition
Author: Barry Smith
Publisher: Cambridge University Press
Total Pages: 244
Release: 2004-03-25
Genre: Computers
ISBN: 9780521602860

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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.


Stability Estimates for Hybrid Coupled Domain Decomposition Methods

Stability Estimates for Hybrid Coupled Domain Decomposition Methods
Author: Olaf Steinbach
Publisher: Springer Science & Business Media
Total Pages: 132
Release: 2003-03-10
Genre: Computers
ISBN: 9783540002772

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Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods.


Elliptic Marching Methods and Domain Decomposition

Elliptic Marching Methods and Domain Decomposition
Author: Patrick J. Roache
Publisher: CRC Press
Total Pages: 212
Release: 1995-06-29
Genre: Mathematics
ISBN: 9780849373787

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One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathematics, and the physical sciences.


Domain Decomposition Methods in Science and Engineering

Domain Decomposition Methods in Science and Engineering
Author: Alfio Quarteroni
Publisher: American Mathematical Soc.
Total Pages: 510
Release: 1994
Genre: Mathematics
ISBN: 0821851586

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This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Much of the work in this field focuses on developing numerical methods for large algebraic systems.


Domain Decomposition Methods in Science and Engineering XVI

Domain Decomposition Methods in Science and Engineering XVI
Author: Olof Widlund
Publisher: Springer Science & Business Media
Total Pages: 783
Release: 2007-07-30
Genre: Technology & Engineering
ISBN: 3540344691

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Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.


Domain Decomposition Methods in Science and Engineering XIX

Domain Decomposition Methods in Science and Engineering XIX
Author: Yunqing Huang
Publisher: Springer Science & Business Media
Total Pages: 484
Release: 2010-10-27
Genre: Mathematics
ISBN: 3642113044

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These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.


Domain Decomposition Methods in Science and Engineering XVIII

Domain Decomposition Methods in Science and Engineering XVIII
Author: Michel Bercovier
Publisher: Springer Science & Business Media
Total Pages: 384
Release: 2009-09-01
Genre: Mathematics
ISBN: 364202677X

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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.