{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/kernel-compensation-method-for-maxwell","title":"Kernel compensation method for Maxwell eigenproblem with mimetic finite difference discretization","arxiv_id":"2503.19379","date":"2025-03-25","proceeding":null,"authors":["Chenhao Jin","Yinhua Xia","Yan Xu"],"abstract":"We present a kernel compensation method for Maxwell eigenproblem for photonic crystals to avoid the infinite-dimensional kernels that cause many difficulties in the calculation of energy gaps. The quasi-periodic problem is first transformed into a periodic one on the cube by the Floquet-Bloch theory. Then the compensation operator is introduced in Maxwell's equation with the shifted curl operator. The discrete problem depends on the compatible discretization of the de Rham complex, which is implemented by the mimetic finite difference method in this paper. We prove that the compensation term exactly fills up the kernel of the original problem and avoids spurious eigenvalues. Also, we propose an efficient preconditioner and its FFT and multigrid solvers, which allow parallel computing. Numerical experiments for different three-dimensional lattices are performed to validate the accuracy and effectiveness of the method.","url_abs":"https://arxiv.org/abs/2503.19379v1","url_pdf":"https://arxiv.org/pdf/2503.19379v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"kernel-compensation-method-for-maxwell","repo_url":"https://github.com/Epsilon-79th/linear-eigenvalue-problems-in-photonic-crystals","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}