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{{math-stub}}
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
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]].
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.
Non-overlapping ___domain decomposition methods are also called '''iterative substructuring methods'''.
[[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 ==
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