TY - GEN

T1 - The development of coarse spaces for domain decomposition algorithms

AU - Widlund, Olof B.

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

AB - The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

UR - http://www.scopus.com/inward/record.url?scp=78651573016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651573016&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02677-5_26

DO - 10.1007/978-3-642-02677-5_26

M3 - Conference contribution

AN - SCOPUS:78651573016

SN - 9783642026768

T3 - Lecture Notes in Computational Science and Engineering

SP - 241

EP - 248

BT - Domain Decomposition Methods in Science and Engineering XVIII

T2 - 18th International Conference of Domain Decomposition Methods

Y2 - 12 January 2008 through 17 January 2008

ER -