Domain Decomposition Methods For The Numerical Solution Of Partial Differential Equations

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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Tarek Mathew
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations Book PDF

Author : Tarek Mathew
Publisher : Springer Science & Business Media
Page : 775 pages
File Size : 48,7 Mb
Release : 2008-06-25
Category : Mathematics
ISBN : 9783540772095

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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by Tarek Mathew Pdf

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 Methods in Optimal Control of Partial Differential Equations

John E. Lagnese,Günter Leugering
Domain Decomposition Methods in Optimal Control of Partial Differential Equations Book PDF

Author : John E. Lagnese,Günter Leugering
Publisher : Birkhäuser
Page : 443 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878852

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Domain Decomposition Methods in Optimal Control of Partial Differential Equations by John E. Lagnese,Günter Leugering Pdf

While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. This monograph emphasizes domain decomposition methods in the context of so-called virtual optimal control problems and treats optimal control problems for partial differential equations and their decompositions using an all-at-once approach.

Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters

H.G. Kaper,Marc Garbey
Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters Book PDF

Author : H.G. Kaper,Marc Garbey
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401118101

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Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters by H.G. Kaper,Marc Garbey Pdf

This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.

Domain Decomposition

Barry Smith,Petter Bjorstad,William Gropp
Domain Decomposition Book PDF

Author : Barry Smith,Petter Bjorstad,William Gropp
Publisher : Cambridge University Press
Page : 244 pages
File Size : 48,8 Mb
Release : 2004-03-25
Category : Computers
ISBN : 0521602866

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Domain Decomposition by Barry Smith,Petter Bjorstad,William Gropp Pdf

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.

Elliptic Marching Methods and Domain Decomposition

Patrick J. Roache
Elliptic Marching Methods and Domain Decomposition Book PDF

Author : Patrick J. Roache
Publisher : CRC Press
Page : 212 pages
File Size : 53,9 Mb
Release : 1995-06-29
Category : Mathematics
ISBN : 0849373786

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Elliptic Marching Methods and Domain Decomposition by Patrick J. Roache Pdf

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.

Stability Estimates for Hybrid Coupled Domain Decomposition Methods

Olaf Steinbach
Stability Estimates for Hybrid Coupled Domain Decomposition Methods Book PDF

Author : Olaf Steinbach
Publisher : Springer
Page : 126 pages
File Size : 45,8 Mb
Release : 2003-07-03
Category : Mathematics
ISBN : 9783540362500

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Stability Estimates for Hybrid Coupled Domain Decomposition Methods by Olaf Steinbach Pdf

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.

Domain Decomposition Methods for Nonconforming Finite Element Discretizations

Jinsheng Gu
Domain Decomposition Methods for Nonconforming Finite Element Discretizations Book PDF

Author : Jinsheng Gu
Publisher : Nova Publishers
Page : 168 pages
File Size : 55,7 Mb
Release : 1999
Category : Mathematics
ISBN : 1560726148

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Domain Decomposition Methods for Nonconforming Finite Element Discretizations by Jinsheng Gu Pdf

Domain decomposition refers to numerical methods for obtaining solutions of scientific and engineering problems by combining solutions to problems posed on physical subdomains, or, more generally, by combining solutions to appropriately constructed subproblems. It has been a subject of intense interest recently because of its suitability for implementation on high performance computer architectures. It is well known that the nonconforming finite elements are widely used in and effective for the solving of partial differential equations derived from mechanics and engineering, because they have fewer degrees of freedom, simpler basis functions and better convergence behavior. But, there has been no extensive study of domain decomposition methods with nonconforming finite elements which lack the global continuity. Therefore, a rather systematic investigation on domain decomposition methods with nonconforming elements is of great significance and this is what the present book achieves. The theoretical breakthrough is the establishment of a series of essential estimates, especially the extension theorems for nonconforming elements, which play key roles in domain decomposition analysis. There are also many originalities in the design of the domain decomposition algorithms for the nonconforming finite element discretizations, according to the features of the nonconforming elements. The existing domain decomposition methods developed in the conforming finite element discrete case can be revised properly and extended to the nonconforming finite element discrete case correspondingly. These algorithms, nonoverlap or overlap, are as efficient as their counterparts in the conforming cases, and even easier in implementation.

Domain Decomposition Methods in Science and Engineering

Ralf Kornhuber,Ronald W. Hoppe,Jacques Periaux,Olivier Pironneau,Olof Widlund,Jinchao Xu
Domain Decomposition Methods in Science and Engineering Book PDF

Author : Ralf Kornhuber,Ronald W. Hoppe,Jacques Periaux,Olivier Pironneau,Olof Widlund,Jinchao Xu
Publisher : Springer Science & Business Media
Page : 686 pages
File Size : 48,9 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783540268253

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Domain Decomposition Methods in Science and Engineering by Ralf Kornhuber,Ronald W. Hoppe,Jacques Periaux,Olivier Pironneau,Olof Widlund,Jinchao Xu Pdf

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.

Domain Decomposition Methods in Science and Engineering XVI

Olof B. Widlund,David E. Keyes
Domain Decomposition Methods in Science and Engineering XVI Book PDF

Author : Olof B. Widlund,David E. Keyes
Publisher : Springer Science & Business Media
Page : 783 pages
File Size : 43,5 Mb
Release : 2007-01-19
Category : Computers
ISBN : 9783540344681

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Domain Decomposition Methods in Science and Engineering XVI by Olof B. Widlund,David E. Keyes Pdf

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.

An Introduction to Domain Decomposition Methods

Victorita Dolean,Pierre Jolivet,Frederic Nataf
An Introduction to Domain Decomposition Methods Book PDF

Author : Victorita Dolean,Pierre Jolivet,Frederic Nataf
Publisher : SIAM
Page : 242 pages
File Size : 42,9 Mb
Release : 2015-12-08
Category : Science
ISBN : 9781611974065

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An Introduction to Domain Decomposition Methods by Victorita Dolean,Pierre Jolivet,Frederic Nataf Pdf

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 in Science and Engineering

Alfio Quarteroni
Domain Decomposition Methods in Science and Engineering Book PDF

Author : Alfio Quarteroni
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 42,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851586

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Domain Decomposition Methods in Science and Engineering by Alfio Quarteroni Pdf

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and different models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

Domain Decomposition Methods in Science and Engineering XXI

Jocelyne Erhel,Martin J. Gander,Laurence Halpern,Géraldine Pichot,Taoufik Sassi,Olof Widlund
Domain Decomposition Methods in Science and Engineering XXI Book PDF

Author : Jocelyne Erhel,Martin J. Gander,Laurence Halpern,Géraldine Pichot,Taoufik Sassi,Olof Widlund
Publisher : Springer
Page : 973 pages
File Size : 42,7 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783319057897

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Domain Decomposition Methods in Science and Engineering XXI by Jocelyne Erhel,Martin J. Gander,Laurence Halpern,Géraldine Pichot,Taoufik Sassi,Olof Widlund Pdf

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.

Recent Developments in Domain Decomposition Methods

Luca F. Pavarino,Andrea Toselli
Recent Developments in Domain Decomposition Methods Book PDF

Author : Luca F. Pavarino,Andrea Toselli
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642561184

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Recent Developments in Domain Decomposition Methods by Luca F. Pavarino,Andrea Toselli Pdf

The main goal of this book is to provide an overview of some of the most recent developments in the field of Domain Decomposition Methods. Domain decomposition relates to the construction of preconditioners for the large algebraic systems of equations which often arise in applications, by solving smaller instances of the same problem. It also relates to the construction of approximation methods built from different discretizations in different subdomains. The resulting methods are among the most successful parallel solvers for many large scale problems in computational science and engineering. The papers in this collection reflect some of the most active research areas in domain decomposition such as novel FETI, Neumann-Neumann, overlapping Schwarz and Mortar methods.

Numerical Approximation of Partial Differential Equations

Alfio Quarteroni,Alberto Valli
Numerical Approximation of Partial Differential Equations Book PDF

Author : Alfio Quarteroni,Alberto Valli
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 42,9 Mb
Release : 2009-02-11
Category : Mathematics
ISBN : 9783540852681

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Numerical Approximation of Partial Differential Equations by Alfio Quarteroni,Alberto Valli Pdf

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Domain Decomposition Methods in Scientific and Engineering Computing

David E. Keyes,Jinchao Xu
Domain Decomposition Methods in Scientific and Engineering Computing Book PDF

Author : David E. Keyes,Jinchao Xu
Publisher : American Mathematical Soc.
Page : 546 pages
File Size : 45,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851715

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Domain Decomposition Methods in Scientific and Engineering Computing by David E. Keyes,Jinchao Xu Pdf

This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term ``domain decomposition'' has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with so-called ``bad parameters'' in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the elliptically-dominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an up-to-date guide to the many facets of the theory and practice of domain decomposition.