Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Author: Tarek Mathew
Publisher: Springer Science & Business Media
Total Pages: 775
Release: 2008-06-25
Genre: Mathematics
ISBN: 354077209X

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.

An Introduction to Domain Decomposition Methods

An Introduction to Domain Decomposition Methods
Author: Victorita Dolean
Publisher: SIAM
Total Pages: 242
Release: 2015-12-08
Genre: Science
ISBN: 1611974054

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

Domain Decomposition Methods in Science and Engineering
Author: Ralf Kornhuber
Publisher: Springer Science & Business Media
Total Pages: 686
Release: 2006-03-30
Genre: Mathematics
ISBN: 3540268251

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 - Algorithms and Theory

Domain Decomposition Methods - Algorithms and Theory
Author: Andrea Toselli
Publisher: Springer Science & Business Media
Total Pages: 454
Release: 2006-06-20
Genre: Mathematics
ISBN: 3540266623

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 XX

Domain Decomposition Methods in Science and Engineering XX
Author: Randolph Bank
Publisher: Springer Science & Business Media
Total Pages: 702
Release: 2013-07-03
Genre: Mathematics
ISBN: 3642352758

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 XVI

Domain Decomposition Methods in Science and Engineering XVI
Author: Olof B. Widlund
Publisher: Springer Science & Business Media
Total Pages: 783
Release: 2007-01-19
Genre: Computers
ISBN: 3540344683

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.

Domain Decomposition

Domain Decomposition
Author: Barry Smith
Publisher: Cambridge University Press
Total Pages: 244
Release: 2004-03-25
Genre: Computers
ISBN: 9780521602860

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.

Discretization Methods and Iterative Solvers Based on Domain Decomposition

Discretization Methods and Iterative Solvers Based on Domain Decomposition
Author: Barbara I. Wohlmuth
Publisher: Springer Science & Business Media
Total Pages: 209
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642567673

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.

Domain Decomposition Methods in Science and Engineering XVII

Domain Decomposition Methods in Science and Engineering XVII
Author: Ulrich Langer
Publisher: Springer Science & Business Media
Total Pages: 656
Release: 2008-01-02
Genre: Mathematics
ISBN: 3540751998

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.