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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 [[
In non-overlapping methods, the subdomains overlap 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 by 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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