A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
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.
Cite
@article{arxiv.1301.3794,
title = {A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh},
author = {Carl A. Bauer and Gregory R. Werner and John R. Cary},
journal= {arXiv preprint arXiv:1301.3794},
year = {2014}
}
Comments
Reviewed by and resubmitted to the Journal of Computational Physics, Elsevier. 23 pages, 6 figures, 3 tables