Two New Enriched Multiscale Coarse Spaces for the Additive Average Schwarz Method

摘要

We propose additive Schwarz methods with spectrally enriched coarse spaces for the standard finite element discretization of second order elliptic problems with highly varying and discontinuous coefficients. Such discontinuities may occur arbitrarily both inside and across subdomains. The convergence of the proposed methods depend linearly on the mesh parameter ratio H/h, and is independent of the distribution of the coefficient in the model problem when the coarse space is large enough. For similar work on domain decomposition methods addressing such problems, we refer to Galvis and Efendiev (2010); Spillane et al. (2014) and references therein.