A multiscale spectral generalized finite element method achieves provably exponential convergence for H(curl) elliptic problems and yields a two-level Schwarz preconditioner with a provable GMRES convergence rate.
New Analysis of Overlapping Schwarz Methods for Vector Field Problems in Three Dimensions with Generally Shaped Domains
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abstract
This paper introduces a novel approach to analyzing overlapping Schwarz methods for N\'{e}d\'{e}lec and Raviart--Thomas vector field problems. The theory is based on new regular stable decompositions for vector fields that are robust to the topology of the domain. Enhanced estimates for the condition numbers of the preconditioned linear systems are derived, dependent linearly on the relative overlap between the overlapping subdomains. Furthermore, we present the numerical experiments which support our theoretical results.
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Multiscale model reduction and two-level Schwarz preconditioner for H(curl) elliptic problems
A multiscale spectral generalized finite element method achieves provably exponential convergence for H(curl) elliptic problems and yields a two-level Schwarz preconditioner with a provable GMRES convergence rate.