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- Neumann–Neumann_methods abstract "In mathematics, Neumann–Neumann methods are domain decomposition preconditioners named so because they solve a Neumann problem on each subdomain on both sides of the interface between the subdomains. Just like all domain decomposition methods, so that the number of iterations does not grow with the number of subdomains, Neumann–Neumann methods require the solution of a coarse problem to provide global communication. The balancing domain decomposition is a Neumann–Neumann method with a special kind of coarse problem.More specifically, consider a domain Ω, on which we wish to solve the Poisson equationfor some function f. Split the domain into two non-overlapping subdomains Ω1 and Ω2 with common boundary Γ and let u1 and u2 be the values of u in each subdomain. At the interface between the two subdomains, the two solutions must satisfy the matching conditionswhere n is the unit normal vector to Γ.An iterative method for approximating each ui satisfying the matching conditions is to first solve the decoupled problems (i=1,2)for some function λ(k) on Γ. We then solve the two Neumann problemsWe then obtain the next iterate by settingfor some parameters ω, θ1 and θ2.This procedure can be viewed as a Richardson extrapolation for the iterative solution of the equations arising from the Schur complement method.This continuous iteration can be discretized by the finite element method and then solved—in parallel—on a computer. The extension to more subdomains is straightforward, but using this method as stated as a preconditioner for the Schur complement system is not scalable with the number of subdomains; hence the need for a global coarse solve.".
- Neumann–Neumann_methods wikiPageID "16252918".
- Neumann–Neumann_methods wikiPageRevisionID "551349127".
- Neumann–Neumann_methods subject Category:Domain_decomposition_methods.
- Neumann–Neumann_methods comment "In mathematics, Neumann–Neumann methods are domain decomposition preconditioners named so because they solve a Neumann problem on each subdomain on both sides of the interface between the subdomains. Just like all domain decomposition methods, so that the number of iterations does not grow with the number of subdomains, Neumann–Neumann methods require the solution of a coarse problem to provide global communication.".
- Neumann–Neumann_methods label "Neumann–Neumann methods".
- Neumann–Neumann_methods sameAs Neumann%E2%80%93Neumann_methods.
- Neumann–Neumann_methods sameAs Q7001956.
- Neumann–Neumann_methods sameAs Q7001956.
- Neumann–Neumann_methods wasDerivedFrom Neumann–Neumann_methods?oldid=551349127.