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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]]. Many ___domain decomposition methods can be written and analyzed as a special case of the [[abstract additive Schwarz method]].
In non-overlapping methods, the subdomains intersect only on their interface. In primal methods, such as [[Balancing ___domain decomposition]] and [[BDDC]], the continuity of the solution across subdomain interface is enforced by representing the value of the solution on all neighboring subdomains by the same unknown. In dual methods, such as [[FETI]], the continuity of the solution across the subdomain interface is enforced by [[Lagrange multiplier]]s. The [[FETI-DP]] method is hybrid between a dual and a primal method.
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