An Introduction to Domain Decomposition Methods PDF Download
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Author: Victorita Dolean
Publisher: SIAM
ISBN: 1611974054
Category : Science
Languages : en
Pages : 242
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Book Description
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.?
Author: Victorita Dolean
Publisher: SIAM
ISBN: 1611974054
Category : Science
Languages : en
Pages : 242
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Book Description
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.?
Author: Tarek Mathew
Publisher: Springer Science & Business Media
ISBN: 354077209X
Category : Mathematics
Languages : en
Pages : 775
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Book Description
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.
Author: Andrea Toselli
Publisher: Springer Science & Business Media
ISBN: 3540266623
Category : Mathematics
Languages : en
Pages : 454
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Book Description
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.
Author: Patrick J. Roache
Publisher: CRC Press
ISBN: 9780849373787
Category : Mathematics
Languages : en
Pages : 212
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Book Description
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.
Author: Barry Smith
Publisher: Cambridge University Press
ISBN: 9780521602860
Category : Computers
Languages : en
Pages : 244
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Book Description
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.
Author: Juergen Geiser
Publisher: CRC Press
ISBN: 1439810974
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and num
Author: G. Adomian
Publisher: Springer Science & Business Media
ISBN: 9401582890
Category : Science
Languages : en
Pages : 367
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Book Description
The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.
Author: Holger Wendland
Publisher: Cambridge University Press
ISBN: 1107147131
Category : Computers
Languages : en
Pages : 419
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Book Description
This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
Author: Ralf Kornhuber
Publisher: Springer Science & Business Media
ISBN: 3540268251
Category : Mathematics
Languages : en
Pages : 686
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Book Description
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.
Author: K. Böhmer
Publisher: Springer Science & Business Media
ISBN: 3709170230
Category : Mathematics
Languages : en
Pages : 247
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Book Description
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.
