{"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/optimal-and-scalable-augmented-lagrangian","title":"Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems","arxiv_id":"2504.11339","date":"2025-04-15","proceeding":null,"authors":["Michele Benzi","Marco Feder","Luca Heltai","Federica Mugnaioni"],"abstract":"We present preconditioning techniques to solve linear systems of equations with a block two-by-two and three-by-three structure arising from finite element discretizations of the fictitious domain method with Lagrange multipliers. In particular, we propose two augmented Lagrangian-based preconditioners to accelerate the convergence of iterative solvers for such classes of linear systems. We consider two relevant examples to illustrate the performance of these preconditioners when used in conjunction with flexible GMRES: the Poisson and the Stokes fictitious domain problems. A spectral analysis is established for both exact and inexact versions of the preconditioners. We show the effectiveness of the proposed approach and the robustness of our preconditioning strategy through extensive numerical tests in both two and three dimensions.","url_abs":"https://arxiv.org/abs/2504.11339v1","url_pdf":"https://arxiv.org/pdf/2504.11339v1.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":"optimal-and-scalable-augmented-lagrangian","repo_url":"https://github.com/fdrmrc/fictitious_domain_al_preconditioners","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}