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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2024; 61(4): 659-681

Online first article June 20, 2024      Printed July 1, 2024

https://doi.org/10.4134/JKMS.j230054

Copyright © The Korean Mathematical Society.

Multigrid methods for 3$D$ $H(\mathbf{curl})$ problems with nonoverlapping domain decomposition smoothers

Duk-Soon Oh

Chungnam National University

Abstract

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We propose V--cycle multigrid methods for vector field problems arising from the lowest order hexahedral N\'{e}d\'{e}lec finite element. Since the conventional scalar smoothing techniques do not work well for the problems, a new type of smoothing method is necessary. We introduce new smoothers based on substructuring with nonoverlapping domain decomposition methods. We provide the convergence analysis and numerical experiments that support our theory.

Keywords: Multigrid method, nonoverlapping domain decomposition, $\HCurl$, N\'{e}d\'{e}lec finite element

MSC numbers: 65N55, 65N30, 65F08, 65F10

Supported by: This work was supported by research fund of Chungnam National University.

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