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In mathematics, [[numerical analysis]], and numerical [[partial differential equation]]s, '''___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 the subdomains. 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]].▼
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▲In mathematics, [[numerical analysis]] and numerical [[partial differential equation]]s, '''___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 the subdomains. 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]].
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]].
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[[Mortar method]]s are discretization methods for partial differential equations, which use separate discretization on nonoverlapping subdomains. The meshes on the subdomains do not match on the interface, and the equality of the solution is enforced by Lagrange multipliers, judiciously chosen to preserve the accuracy of the solution. In the engineering practice in the finite element method, continuity of solutions between non-matching subdomains is implemented by [[multiple-point constraint]]s.
== External links ==▼
* [http://www.ddm.org The official Domain Decomposition Methods page]▼
==See also==
*[[Multigrid method]]
*[[Fictitious ___domain method]]
▲== External links ==
▲* [http://www.ddm.org The official Domain Decomposition Methods page]
[[Category:Domain decomposition methods]]
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