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The additive Schwarz method is usually presented as a preconditioner for aPDE linearization based on overlapping subsets of nodes from a globaldiscretization. It has previously been shown how to apply Schwarzpreconditioning to a nonlinear problem. By first replacing the original globalPDE with the Schwarz overlapping problem, the global discretization becomes asimple union of subdomain discretizations, and unknowns do not need to beshared. In this way restrictive-type updates can be avoided, and subdomainsneed to communicate only via interface interpolations. The resultingpreconditioner can be applied linearly or nonlinearly. In the latter casenonlinear subdomain problems are solved independently in parallel, and thefrequency and amount of interprocess communication can be greatly reducedcompared to linearized preconditioning.

Preconditioned nonlinear iterations for overlapping Chebyshev discretizations with independent grids