Distributed-memory parallel eigensolver for Maxwell’s equations. A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh. For embedded boundary electromagnetics using the Dey-Mittra algorithm [S. Dey and R. Mitra, “A locally conformal finite-difference time-domain (FDTD) algorithm for modeling three-dimensional perfectly conducting objects”, IEEE Microwave Guided Wave Lett. 7, No. 9, 273–275 (1997), doi:10.1109/75.622536], 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 [C. Nieter et al., J. Comput. Phys. 228, No. 21, 7902–7916 (2009; Zbl 1184.78080)], 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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