Speaker: Atle Loneland, UiB/HiB
Title: An Improved Multiscale Coarse Spaces for the Additive Schwarz Method
Abstract: It is well known that jumps or discontinuities in the material coefficients of a problem can slow down or even break the convergence of standard domain decomposition methods. In this talk, we first provide some examples showing that the multiscale coarse space is a remedy against this if the discontinuities of the coefficient are located inside subdomains or across subdomain boundaries. Still, discontinuities which are alongside subdomain boundaries will slow down the convergence rate and therefore make these types of methods unsuitable for many industrial applications.
We then proceed by showing that if we enrich the multiscale coarse space with spectral and bubble type of basis functions, the corresponding method can be shown to be, both numerically and theoretically, robust against any number of discontinuities or jumps in the material coefficient both inside subdomains and across and along subdomain boundaries.