Domain Decomposition Methods - Algorithms and Theory

Author: Andrea Toselli,Olof Widlund

Publisher: Springer Science & Business Media

ISBN: 3540266623

Category: Mathematics

Page: 450

View: 532

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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.

Domain Decomposition Methods in Science and Engineering XXII

Author: Thomas Dickopf,Martin J. Gander,Laurence Halpern,Rolf Krause,Luca F. Pavarino

Publisher: Springer

ISBN: 3319188275

Category: Computers

Page: 647

View: 9275

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These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland. With 172 participants from over 24 countries, this conference continued a long-standing tradition of internationally oriented meetings on Domain Decomposition Methods. The book features a well-balanced mix of established and new topics, such as the manifold theory of Schwarz Methods, Isogeometric Analysis, Discontinuous Galerkin Methods, exploitation of modern HPC architectures and industrial applications. As the conference program reflects, the growing capabilities in terms of theory and available hardware allow increasingly complex non-linear and multi-physics simulations, confirming the tremendous potential and flexibility of the domain decomposition concept.

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Author: Tarek Mathew

Publisher: Springer Science & Business Media

ISBN: 354077209X

Category: Mathematics

Page: 770

View: 7932

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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.

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: 8684

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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.

An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation

Author: Victorita Dolean,Pierre Jolivet,Frâdâric Nataf

Publisher: SIAM

ISBN: 1611974054

Category: Science

Page: 238

View: 5879

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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.÷

An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation

Author: Victorita Dolean,Pierre Jolivet,Frâdâric Nataf

Publisher: SIAM

ISBN: 1611974062

Category: Science

Page: 238

View: 4871

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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 in Science and Engineering XX

Author: Randolph E. Bank,Michael Holst,Olof B Widlund,Jinchao Xu

Publisher: Springer Science & Business Media

ISBN: 3642352758

Category: Mathematics

Page: 686

View: 8102

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These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.​

Domain Decomposition Methods in Science and Engineering

Author: Ralf Kornhuber,Ronald W. Hoppe,Jacques Periaux,Olivier Pironneau,Olof Widlund,Jinchao Xu

Publisher: Springer Science & Business Media

ISBN: 3540268251

Category: Mathematics

Page: 690

View: 5144

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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 XVII

Author: Ulrich Langer,Marco Discacciati,David E. Keyes,Olof Widlund,Walter Zulehner

Publisher: Springer Science & Business Media

ISBN: 9783540751991

Category: Mathematics

Page: 661

View: 7881

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Domain decomposition is an active, interdisciplinary research field concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models. This volume contains selected papers presented at the 17th International Conference on Domain Decomposition Methods in Science and Engineering. It presents the newest domain decomposition techniques and examines their use in the modeling and simulation of complex problems.

Domain Decomposition Methods in Science and Engineering XIX

Author: Yunqing Huang,Ralf Kornhuber,Olof Widlund,Jinchao Xu

Publisher: Springer Science & Business Media

ISBN: 9783642113048

Category: Mathematics

Page: 472

View: 2247

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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

Parallel Multilevel Methods for Elliptic Partial Differential Equations

Author: Barry Smith,Petter Bjorstad,William Gropp

Publisher: Cambridge University Press

ISBN: 9780521602860

Category: Computers

Page: 240

View: 6467

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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.

The Mathematical Theory of Finite Element Methods

Author: Susanne Brenner,Ridgway Scott

Publisher: Springer Science & Business Media

ISBN: 0387759336

Category: Mathematics

Page: 400

View: 3035

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This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Her volume formalizes basic tools that are commonly used by researchers in the field but not previously published. The book is ideal for mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes.

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: 995

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Recent Developments in Domain Decomposition Methods

With ... 54 Tables

Author: Luca F. Pavarino,Andrea Toselli,Eidgenössische Technische Hochschule Zürich

Publisher: Springer Science & Business Media

ISBN: 9783540434139

Category: Computers

Page: 243

View: 7198

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The main goal of this book is to provide an overview of some of the developments in the field of domain decomposition methods. Papers reflect some of the most active research areas in domain decomposition such as novel FETI, Neumann-Neumann, overlapping Schwarz and Mortar methods.

Computational Methods for Acoustics Problems

Author: F. Magoules

Publisher: N.A

ISBN: 9781874672302

Category: Technology & Engineering

Page: 338

View: 3452

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The measurement of acoustic effects is regarded today as one of the most challenging areas in scientific computation, and this collection of articles presents innovative approaches, techniques, and algorithms that improve high-performance acoustical computing. Discussing acoustic and vibro-acoustic problems, the material focuses on industrial applications and considers what the future holds for this exciting area of computer technology.

Design of Adaptive Finite Element Software

The Finite Element Toolbox ALBERTA

Author: Alfred Schmidt,Kunibert G. Siebert

Publisher: Springer Science & Business Media

ISBN: 3540271562

Category: Computers

Page: 315

View: 8827

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During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.