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

作者：Bauer Carl A^*; Werner Gregory R; Cary John R

来源：Journal of Computational Physics, 2013, 251: 524-534.

DOI：10.1016/j.jcp.2013.06.002

• Electromagnetics
• Finite difference
• Yee
• Dey
• Mittra
• Algorithm
• Eigensolver
• Maxwell
• Accelerator
• Multigrid
• Cavity

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.

• 出版日期2013-10-15