Grid transfer operators for highly variable coefficient problems in two-level non-overlapping domain decomposition methods

Abstract

We propose a robust interpolation scheme for non-overlapping two-level domain decomposition methods applied to two-dimensional elliptic problems with discontinuous coefficients. This interpolation is used to design a preconditioner closely related to the BPS scheme proposed in [Bramble et al. (Math. Comput. 1986; 47(175): 103)]. Through numerical experiments, we show on structured and unstructured finite element problems that the new preconditioning scheme reduces to the BPS method on smooth problems but outperforms it on problems with discontinuous coefficients. In particular it maintains good scalable convergence behaviour even when the jumps in the coefficients are not aligned with subdomain interfaces. Copyright © 2003 John Wiley & Sons, Ltd.