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

Examples and Counterexamples

Julian Roth¹  Thomas Wick²  Sebastian Kinnewig² 

[1] Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering - Innovation Across Disciplines), Leibniz Universität Hannover, Germany;Leibniz University Hannover, Institute of Applied Mathematics, Welfengarten 1, 30167 Hannover, Germany;

关键词: Time-harmonic Maxwell;    Eddy-current problem;    Finite elements;    Geometric multigrid;    Multiplicative Schwarz smoother;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown