Substructuring Techniques and Domain Decomposition Methods

Domain decomposition methods are well suited for parallel computations. Indeed, the division of a problem into smaller sub-problems, through artificial subdivisions of the domain, is a means for introducing parallelism. Domain decomposition strategies include in one way or another the following ingredients: a decomposer to split a mesh into subdomains using different heuristics; local solvers (direct or iterative, exact or approximate) to find solutions for the subdomains for specific boundary conditions on the interface; interface conditions (weak or strong) enforcing compatibility and equilibrium between overlapping or non-overlapping subdomains; and a solution strategy for the interface problem. The differences between the methods lie in how those ingredients are actually put to work and how they are combined to form an efficient solution strategy for the problem at hand.

This edited book describes some important domain decomposition methods and algorithms, from a Mathematics and algorithmic point of view. Applications in fluid mechanics, structural mechanics, and computational finance are also presented.

Editor: Frédéric Magoulès                Publisher: Saxe-Coburg Publications
Hardback: 272 pages                       2010: ISBN 978-1-874672-33-3, ISSN 1759-3158