Optimized domain decomposition methods for the spherical Laplacian

摘要

The Schwarz iteration decomposes a boundary value problem over a large domain Ω into smaller subproblems by iteratively solving Dirichlet problems on a cover Ω_1,...,Ω_p of Ω. In this paper, we discuss alternate transmission conditions that lead to faster convergence for the Laplacian on the sphere Ω. We look at Robin conditions, second order tangential conditions, and a discretized version of an optimal but nonlocal operator.