{"paper":{"title":"$\\ell$FEM: An efficient loop-free Matlab implementation of isoparametric bulk and surface finite elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"ℓFEM is a loop-free MATLAB package implementing isoparametric bulk and surface finite elements with high-order support, assembly details, and performance tests.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bal\\'azs Kov\\'acs, Michael Lantelme","submitted_at":"2026-05-13T18:54:40Z","abstract_excerpt":"The $\\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and therefore completely loop-free. We give a short and conscious description of high-order isoparametric surface finite elements, which is then used to describe the assembly process and the implementation.\n  We report on relevant numerical experiments (runtime comparisons, modifications for non-linear problems, etc.), and on additional functions, examples, and a testin"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"The ℓFEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces with completely loop-free matrix assemblies based on paged operators.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That MATLAB's paged operators deliver competitive performance for the described high-order isoparametric surface elements without hidden overheads that would negate the loop-free advantage.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ℓFEM is a loop-free MATLAB package implementing isoparametric bulk and surface finite elements with high-order support, assembly details, and performance tests.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"15168df6b91e70bacecb651e1b63a4b307d3a92db2deec902ec9da325aae1b5e"},"source":{"id":"2605.14035","kind":"arxiv","version":1},"verdict":{"id":"ec647fac-5c37-49f6-96da-5fa7afb54208","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:16:46.123243Z","strongest_claim":"The ℓFEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces with completely loop-free matrix assemblies based on paged operators.","one_line_summary":"ℓFEM is a loop-free MATLAB package implementing isoparametric bulk and surface finite elements with high-order support, assembly details, and performance tests.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That MATLAB's paged operators deliver competitive performance for the described high-order isoparametric surface elements without hidden overheads that would negate the loop-free advantage.","pith_extraction_headline":""},"references":{"count":40,"sample":[{"doi":"10.1023/a:1019155918070","year":1999,"title":"J. Alberty, C. Carstensen, and S. A. Funken , Remarks around 50 lines of Matlab: short finite element implementation, Numer. Algorithms, 20 (1999), pp. 117–137, https://doi.or g/10.1023/A:101915591807","work_id":"f732b7e6-b649-4ccf-953c-cde32e3ea20f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.camwa.2020.06.009","year":2021,"title":"R. Anderson, J. Andrej, A. Barker, J. Bramwell, J.-S. Camier, J. Cerveny, V. Dobrev, Y. Dudouit, A. Fisher, T. Kolev, W. Pazner, M. Stowell, V. Tomov, I. Akkerman, J. Dahm, D. Medina, and S. Zampini ,","work_id":"d6be8d1d-fec8-4205-b224-9d85600b3173","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"J. W. Barrett, H. Garcke, and R. Nürnberg , Parametric finite element approximations of curvature-driven interface evolutions, in Geometric partial differential equations. Part I, vol. 21 of Handb. Nu","work_id":"207f387c-3a15-44b2-b31c-80eea29a64e4","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"S. Bartels, C. Carstensen, and A. Hecht , P2Q2Iso2D = 2D isoparametric FEM in Matlab, J. Comput. Appl. Math., 192 (2006), pp. 219–250","work_id":"9a14da42-67b9-4d22-a172-bdd4b7e00781","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s00607-008-0004-9","year":2008,"title":"P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander , A generic grid interface for parallel and adaptive scientific computing. part ii: Implementation an","work_id":"afb2e5be-edef-48b5-a1e5-e634e83ed904","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":40,"snapshot_sha256":"26685257758ad713425010a74eec683d16c907e013a94707ddf46bfcc0e43a9a","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a8174c6b840c547c70eab424b6c64ea86077ee022b3069970ba89c4aaa1ab326"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}