With contributions from: H. Akiba, J.M. Bahi, R. Couturier, C.-H. Lai, D. Laiymani, Y. Maday, F. Magoulès, T. Miyamura, K. Moriya, T. Nodera, D. Rixen, A. Suzuki, M. Tabata, C. Venet, L. Zhang.
Domain decomposition methods are well suited for parallel computations. Indeed, the division of a problem into smaller subproblems, through artificial subdivisions of the domain, is a means for introducing parallelism. Domain decomposition and substructuring 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 volume presents in nine chapters a selection of some of the most important domain decomposition and substructuring methods. The main topics considered in the book include: the parareal in time algorithm, transformation methods and induced parallel properties for the temporal domain, asynchronous iterative methods, asynchronous sub-structuring methods, asynchronous multi-splitting methods, parallel iterative methods, coarse grid conjugate gradient, multi-point constraints in domain decomposition methods, approximate inverse preconditioning techniques, congruent sub-domains, linear and non-linear problems.
The contents of this book are wide ranging and demonstrate the extensive use of substructuring and domain decomposition methods in fluid mechanics, structural mechanics and computational finance.
Saxe-Coburg Publications, hardback: 272 pages, 9 chapters
2010: ISBN 978-1-874672-33-3 price £95
ISSN 1759-3158 volume 24