Geometric multigrid with multiplicative Schwarz smoothers for eddy-current and Maxwell’s equations in deal.II

authored by

Sebastian Kinnewig, Julian Roth, Thomas Wick

Abstract

In this work, we consider the design of a geometric multigrid method with multiplicative Schwarz smoothers for the eddy-current problem and the time-harmonic Maxwell equations. The main purpose is to show numerically that a straightforward application works for the former problem, but not for the latter. The well-known key is a special decomposition of the function spaces within the multigrid algorithm. The failures and performance are shown with the help of a numerical test, implemented in the modern finite element library deal.II, including a github link to the eddy-current implementation.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

Type

Article

Journal

Examples and Counterexamples

Volume

1

Publication date

11.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mathematics, Applied Mathematics, Mathematics (miscellaneous)

Electronic version(s)

https://doi.org/10.1016/j.exco.2021.100027 (Access: Open)