We presented an optimal coarse space for RAS called OHEM, which leads to convergence of RAS in one iteration, both when used as an iterative solver and as a preconditioner for GMRES. We then proposed an approximation called SHEM based on multiscale finite elements in each subdomain, enriched with spectral harmonic functions. We showed numerically that SHEM is robust for problems with high contrast, and also derived an adaptive variant.
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