Domain Decomposition Methods For Nonconforming Finite Element Discretizations
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Domain Decomposition Methods For Nonconforming Finite Element Discretizations
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Author : Jinsheng Gu
language : en
Publisher: Nova Publishers
Release Date : 1999
Domain Decomposition Methods For Nonconforming Finite Element Discretizations written by Jinsheng Gu and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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 For The Numerical Solution Of Partial Differential Equations
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Author : Tarek Mathew
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-25
Domain Decomposition Methods For The Numerical Solution Of Partial Differential Equations written by Tarek Mathew and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-25 with Mathematics categories.
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 Scientific And Engineering Computing
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Author : David E. Keyes
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Domain Decomposition Methods In Scientific And Engineering Computing written by David E. Keyes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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.
Domain Decomposition Methods 10
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Author : Jan Mandel
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Domain Decomposition Methods 10 written by Jan Mandel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
Domain Decomposition Methods In Science And Engineering
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Author : Ralf Kornhuber
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Domain Decomposition Methods In Science And Engineering written by Ralf Kornhuber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
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.
Discretization Methods And Iterative Solvers Based On Domain Decomposition
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Author : Barbara I. Wohlmuth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discretization Methods And Iterative Solvers Based On Domain Decomposition written by Barbara I. Wohlmuth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Recent Developments In Domain Decomposition Methods
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Author : Luca F. Pavarino
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Recent Developments In Domain Decomposition Methods written by Luca F. Pavarino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
Domain Decomposition Methods Algorithms And Theory
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Author : Andrea Toselli
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-20
Domain Decomposition Methods Algorithms And Theory written by Andrea Toselli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-20 with Mathematics categories.
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.
Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters
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Author : H.G. Kaper
language : en
Publisher: Springer
Release Date : 1992-11-30
Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters written by H.G. Kaper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-30 with Mathematics categories.
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 Methods In Science And Engineering Xxi
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Author : Jocelyne Erhel
language : en
Publisher: Springer
Release Date : 2014-10-10
Domain Decomposition Methods In Science And Engineering Xxi written by Jocelyne Erhel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-10 with Mathematics categories.
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.