{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T19:12:34Z","timestamp":1772737954013,"version":"3.50.1"},"reference-count":42,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["441509557"],"award-info":[{"award-number":["441509557"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Multilevel extensions of overlapping Schwarz domain decomposition preconditioners of Generalized Dryja\u2013Smith\u2013Widlund (GDSW) type are considered in this paper.\nThe original GDSW preconditioner is a two-level overlapping Schwarz domain decomposition preconditioner, which can be constructed algebraically from the fully assembled stiffness matrix.\nThe FROSch software, which belongs to the ShyLU package of the Trilinos software library, provides parallel implementations of different variants of GDSW preconditioners.\nThe coarse problem can limit the parallel scalability of two-level GDSW preconditioners.\nAs a remedy, in the past, three-level GDSW approaches have been proposed, which can significantly extend the range of scalability.\nHere, a multilevel extension of the GDSW preconditioner is introduced and analyzed.\nFinally, parallel results for the implementation in FROSch for up to 40\u2009000 cores of the SuperMUC-NG supercomputer at Leibniz Supercomputing Centre (LRZ) and to 48\u2009000 cores of the JUWELS supercomputer at J\u00fclich Supercomputing Centre (JSC) are presented.<\/jats:p>","DOI":"10.1515\/cmam-2022-0168","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T14:51:10Z","timestamp":1689087070000},"page":"953-968","source":"Crossref","is-referenced-by-count":3,"title":["A Multilevel Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions"],"prefix":"10.1515","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1578-8104","authenticated-orcid":false,"given":"Alexander","family":"Heinlein","sequence":"first","affiliation":[{"name":"Delft Institute of Applied Mathematics , Faculty of Electrical Engineering Mathematics & Computer Science , Delft University of Technology , Mekelweg 4, 2628 CD Delft , Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9310-8533","authenticated-orcid":false,"given":"Oliver","family":"Rheinbach","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Zentrum f\u00fcr effiziente Hochtemperatur-Stoffwandlung (ZeHS); and Universit\u00e4tsrechenzentrum (URZ) , Technische Universit\u00e4t Bergakademie Freiberg , 09596 Freiberg , Germany"}]},{"given":"Friederike","family":"R\u00f6ver","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Zentrum f\u00fcr effiziente Hochtemperatur-Stoffwandlung (ZeHS); and Universit\u00e4tsrechenzentrum (URZ) , Technische Universit\u00e4t Bergakademie Freiberg , 09596 Freiberg , Germany"}]}],"member":"374","published-online":{"date-parts":[[2023,7,12]]},"reference":[{"key":"2023100411150439040_j_cmam-2022-0168_ref_001","doi-asserted-by":"crossref","unstructured":"C. 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