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

Dolean, Victorita/ Jolivet, Pierre/ Nataf, Frédéric

Society for Industrial & Applied Mathematics,U.S.（2015/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 248 p.
• 言語 ENG
• 商品コード 9781611974058
• DDC分類 518

Full 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.
Systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts.
A new coarse space construction (two-level method) that adapts to highly heterogeneous problems.

Contents

Preface
Chapter 1: Schwarz methods
Chapter 2: Optimized Schwarz methods
Chapter 3: Krylov methods
Chapter 4: Coarse spaces
Chapter 5: Theory of two-level additive Schwarz methods
Chapter 6: Neumann-Neumann and FETI algorithms
Chapter 7: Robust coarse spaces via generalized eigenproblems: The GenEO method
Chapter 8: Parallel implementation of Schwarz methods
Index.