A domain decomposition method using efficient interface-acting preconditioners

The conjugate gradient boundary iteration (CGBI) is a domain decomposition method for symmetric elliptic problems on domains with large aspect ratio. High efficiency is reached by the construction of preconditioners that are acting only on the subdomain interfaces. The theoretical derivation of the method and some numerical results revealing a convergence rate of 0.04–0.1 per iteration step are given in this article. For the solution of the local subdomain problems, both finite element (FE) and spectral Chebyshev methods are considered.