A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh

JOURNAL OF COMPUTATIONAL PHYSICS

卷:251

Article

Bauer, Carl A.^1,2  Werner, Gregory R.^1,2  Cary, John R.^1,2,3 

[1] Univ Colorado, Dept Phys, Boulder, CO 80309 USA

[2] Univ Colorado, Ctr Integrated Plasma Studies, Boulder, CO 80309 USA

[3] Tech X Corp, Boulder, CO 80303 USA

关键词: Electromagnetics;    Finite difference;    Yee;    Dey;    Mittra;    Algorithm;    Eigensolver;    Maxwell;    Accelerator;    Multigrid;    Cavity;   

DOI  :  10.1016/j.jcp.2013.06.002

来源: Elsevier

【 摘 要 】

For embedded boundary electromagnetics using the Dey-Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell's curl-curl matrix. Efficient curl-curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at [ofortt]https://github.com/bauerca/maxwell[cfortt]) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey-Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is required in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free