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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: 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: 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: 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: Olaf Steinbach
Publisher: Springer Science & Business Media
ISBN: 9783540002772
Category : Computers
Languages : en
Pages : 132
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Book Description
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.
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: Alfio Quarteroni
Publisher: American Mathematical Soc.
ISBN: 0821851586
Category : Mathematics
Languages : en
Pages : 510
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Book Description
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.
Author: Olof Widlund
Publisher: Springer Science & Business Media
ISBN: 3540344691
Category : Technology & Engineering
Languages : en
Pages : 783
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Book Description
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.
Author: Susanne C. Brenner
Publisher: Springer Nature
ISBN: 3030950255
Category : Mathematics
Languages : en
Pages : 778
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Book Description
These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.
Author: Chang-Ock Lee
Publisher: Springer
ISBN: 3319523899
Category : Computers
Languages : en
Pages : 419
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Book Description
This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.
