{"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/sparse-approximate-multifrontal-factorization","title":"Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations","arxiv_id":"2007.00202","date":"2020-07-01","proceeding":null,"authors":["Yang Liu","Pieter Ghysels","Lisa Claus","Xiaoye Sherry Li"],"abstract":"We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\\mathcal{O}(N\\log^2 N)$ computation and $\\mathcal{O}(N)$ memory complexity when applied to an $N\\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.","url_abs":"https://arxiv.org/abs/2007.00202v2","url_pdf":"https://arxiv.org/pdf/2007.00202v2.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":"sparse-approximate-multifrontal-factorization","repo_url":"https://github.com/liuyangzhuan/ButterflyPACK","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}