Domain decomposition methods: Difference between revisions

Revision as of 10:05, 25 July 2020

Revision as of 22:44, 27 November 2020

Line 1:

[[File:Ddm original logo.png|thumb|Domain decomposition methods]]

In [[mathematics]], [[numerical analysis]], and [[numerical partial differential equations]], '''___domain decomposition methods''' solve a [[boundary value problem]] by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. A [[coarse problem]] with one or few unknowns per subdomain is used to further coordinate the solution between the subdomains globally. The problems on the subdomains are independent, which makes ___domain decomposition methods suitable for [[parallel computing]]. Domain decomposition methods are typically used as [[preconditioner]]s for [[Krylov space]] [[iterative method]]s, such as the [[conjugate gradient method]] or, [[GMRES]], and [[LOBPCG]].

In overlapping ___domain decomposition methods, the subdomains overlap by more than the interface. Overlapping ___domain decomposition methods include the [[Schwarz alternating method]] and the [[additive Schwarz method]]. Many ___domain decomposition methods can be written and analyzed as a special case of the [[abstract additive Schwarz method]].