{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:52Z","timestamp":1787329312224,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>This paper is devoted to the fast solution of interface concentrated finite element equations. The interface concentrated finite element schemes are constructed on the basis of a nonoverlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in every subdomain. Similar to boundary element domain decomposition methods, the total number of unknowns per subdomain behaves like $O((H\/h)^{(d-1)})$, where H, h, and d denote the usual scaling parameter of the subdomains, the average discretization parameter of the subdomain boundaries, and the spatial dimension, respectively. We propose and analyze primal and dual substructuring iterative methods which asymptotically exhibit the same or at least almost the same complexity as the number of unknowns. In particular, the so-called all-floating finite element tearing and interconnecting solvers are highly parallel and very robust with respect to large coefficient jumps.<\/jats:p>","DOI":"10.1137\/070691723","type":"journal-article","created":{"date-parts":[[2008,8,1]],"date-time":"2008-08-01T18:08:34Z","timestamp":1217614114000},"page":"2818-2842","source":"Crossref","is-referenced-by-count":9,"title":["Primal and Dual Interface Concentrated Iterative Substructuring Methods"],"prefix":"10.1137","volume":"46","author":[{"given":"Sven","family":"Beuchler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tino","family":"Eibner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ulrich","family":"Langer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/040605151"},{"key":"R2","unstructured":"S. Beuchler, T. Eibner, and U. Langer,\n                      Primal and dual boundary concentrated iterative substructuring methods\n                      , Technical report 2007-07, RICAM, Linz, Austria, 2007."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0842125-3"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1988-0917816-8"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s002110200397"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502412887"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.881"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01399311"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01410102"},{"key":"R10","unstructured":"T. Eibner,\n                      Randkonzentrierte und adaptive hp-FEM\n                      , Ph.D. thesis, TU Chemnitz, Chemnitz, Germany, 2006."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.10.034"},{"key":"R12","first-page":"752","volume":"27","author":"Eibner T.","year":"2007","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<687::AID-NLA219>3.0.CO;2-S"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320604"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(96)90009-4"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02253431"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02253432"},{"key":"R18","first-page":"173","volume":"2","author":"Haase G.","year":"1994","journal-title":"East-West J. Numer. Math."},{"key":"R19","first-page":"231","volume":"5","author":"Haase G.","year":"1997","journal-title":"East-West J. Numer. Math."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0047-9"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-005-0008-3"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901391852"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-002-1452-2"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018988028583"},{"key":"R25","doi-asserted-by":"crossref","unstructured":"A. Klawonn,\n                      An iterative substructuring method with Lagrange multipliers for elasticity problems using approximate Neumann subdomain solvers\n                      , in Multifield Problems, Springer-Verlag, Berlin, 2000, pp. 193\u2013200.","DOI":"10.1007\/978-3-662-04015-7_21"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1758"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599352495"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0312(200101)54:1<57::AID-CPA3>3.0.CO;2-D"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"V. G. Korneev and U. Langer,\n                      Domain decomposition and preconditioning\n                      , in Encyclopedia of Computational Mechanics, Vol. 1, E. Stein, R. de Borst, and Th.J.R. Hughes, eds., John Wiley & Sons, New York, 2004, pp. 617\u2013647.","DOI":"10.1002\/0470091355.ecm019"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1137\/050636243"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-003-0018-2"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"U. Langer and O. Steinbach,\n                      Coupled finite and boundary element domain decomposition methods\n                      , in Boundary Element Analysis: Mathematical Aspects and Application, M. Schanz and O. Steinbach, eds., Lect. Notes Appl. Comput. Mech. 29, Springer-Verlag, Berlin, 2007, pp. 61\u201395.","DOI":"10.1007\/978-3-540-47533-0_3"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1002\/nla.341"},{"key":"R34","first-page":"61","volume":"29","author":"Matsokin A. M.","year":"1985","journal-title":"Izv. Vyssh. Uchebn. Zaved. Mat.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-3446","issn-type":"print"},{"key":"R35","first-page":"45","volume":"33","author":"Matsokin A. M.","year":"1993","journal-title":"Comput. Maths Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0965-5425","issn-type":"print"},{"key":"R36","first-page":"1","volume":"28","author":"Melenk J. M.","year":"2008","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"key":"R37","unstructured":"J. Ne\u010das,\n                      Les m\u00e9thodes directes en th\u00e9orie des \u00e9quations elliptiques\n                      , Masson et Cie, \u00c9diteurs, Paris, 1967."},{"key":"R38","unstructured":"S. V. Nepomnyaschikh,\n                      Domain Decomposition and Schwarz Methods in a Subspace for the Approximate Solution of Elliptic Boundary Value Problems\n                      , Ph.D. thesis, Computing Center of Siberian Division of Russian Academy of Sciences, Moscow, 1986."},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1515\/rnam.1991.6.2.151"},{"key":"R40","unstructured":"G. Of,\n                      BETI-Gebietszerlegungsmethoden mit schnellen Randelementverfahren und Anwendungen\n                      , Ph.D. thesis, Universit\u00e4t Stuttgart, Stuttgart, Germany, 2006."},{"key":"R41","doi-asserted-by":"crossref","unstructured":"P. Oswald,\n                      Multilevel Finite Element Approximation\n                      , Teubner Skripten zur Numerik, Teubner, Stuttgart, Germany, 1994.","DOI":"10.1007\/978-3-322-91215-2"},{"key":"R42","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385709"},{"key":"R43","doi-asserted-by":"crossref","unstructured":"Y. Saad,\n                      Iterative Methods for Sparse Linear Systems\n                      , 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1137\/0912082"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(03)00426-2"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/24.1.123"},{"key":"R47","doi-asserted-by":"crossref","unstructured":"A. Toselli and O. Widlund,\n                      Domain Decoposition Methods: Algorithms and Theory\n                      , Springer Ser. Comput. Math. 34, Springer-Verlag, Berlin, 2004.","DOI":"10.1007\/b137868"},{"key":"R48","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019157313043"},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-01-01324-2"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070691723","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:19Z","timestamp":1787325259000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070691723"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":49,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070691723"],"URL":"https:\/\/doi.org\/10.1137\/070691723","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}