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Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Monday, July 19, 18:30 ~ 19:00 UTC-3

NO-SAS - Nonoverlapping Spectral Additive Schwarz Methods

Marcus Sarkis

Worcester Polytechnic Institute, USA , USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We design and analyze new preconditioners which combine features from both overlapping and non-overlapping additive Schwarz methods. These methods are designed for elliptic problems with highly heterogeneous coefficients. The methods are of the non-overlapping type without the need of Schur complements and the subdomain interactions are via the coarse space only. The coarse space is large however it can be solved very efficiently since the coarse matrix is a low-rank perturbation of a diagonal matrix, so Sherman–Morrison–Woodbury formula can be applied. The dimension of this perturbation is equal to the number of subdomains plus the number of local bad eigenvalues due to the heterogeneities of the coefficients inside the subdomains. We also characterize these bad eigenvalues with respect to the geometry of the coefficients (number of connected island/channels with large coefficients that touch the boundary of the subdomains. The NO-SAS methods are robust with respect any coefficient and has good parallelization properties. Numerical results are presented.

Joint work with Yu Yi ( WP, USAI) and Maksymilian Dryja (University of Warsaw, Poland).

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