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arXiv · 1301.3794

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

Carl A. Bauer·Gregory R. Werner·John R. Cary
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Abstract

For embedded boundary electromagnetics using the Dey-Mittra 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 https://github.com/bauerca/maxwell) 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, 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.

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Carl A. Bauer, Gregory R. Werner, John R. Cary. 2013-01-16. A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh. https://doi.org/10.1016/j.jcp.2013.06.002

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