Two-level DDM preconditioners for positive Maxwell equations

Bootland, N. and Dolean, V. and Nataf, F. and Tournier, P.-H. (2020) Two-level DDM preconditioners for positive Maxwell equations. Preprint / Working Paper. arXiv.org, Ithaca, N.Y..

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Abstract

In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. We design adaptive coarse spaces that complement the near-kernel space made of the gradient of scalar functions. This extends the results in [2] to the variable coefficient case and non-convex domains at the expense of a larger coarse space.

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