{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T11:20:16Z","timestamp":1770895216523,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Coarse grid correction is a key ingredient in order to have scalable\ndomain decomposition methods. For smooth problems, the theory and practice of\nsuch two-level methods is well established, but this is not the case for\nproblems with complicated variation and high contrasts in the coefficients.\n\nIn a previous study, two of the authors introduced a coarse space\nadapted to highly heterogeneous coefficients using the low frequency modes of\nthe subdomain DtN maps. In this work, we present a rigorous analysis of a\ntwo-level overlapping additive Schwarz method with this coarse space,\nwhich provides an automatic criterion for the number of modes that need to be\nadded per subdomain to obtain a convergence rate of the order of the constant\ncoefficient case. Our method is suitable for parallel implementation and its\nefficiency is demonstrated by numerical examples on some challenging problems\nwith high heterogeneities for automatic partitionings.<\/jats:p>","DOI":"10.2478\/cmam-2012-0027","type":"journal-article","created":{"date-parts":[[2013,2,13]],"date-time":"2013-02-13T12:23:49Z","timestamp":1360758229000},"page":"391-414","source":"Crossref","is-referenced-by-count":79,"title":["Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps"],"prefix":"10.2478","volume":"12","author":[{"given":"Victorita","family":"Dolean","sequence":"first","affiliation":[{"name":"1Laboratoire J.-A. Dieudonn\u00e9, CNRS UMR 6621, Universit\u00e9 de Nice-Sophia Antipolis,06108 Nice Cedex 02, France."}]},{"given":"Fr\u00e9d\u00e9ric","family":"Nataf","sequence":"additional","affiliation":[{"name":"2Laboratoire J.L. Lions, CNRS UMR 7598, Universit\u00e9 Pierre et Marie Curie, 75005 Paris, France."}]},{"given":"Robert","family":"Scheichl","sequence":"additional","affiliation":[{"name":"3Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK."}]},{"given":"Nicole","family":"Spillane","sequence":"additional","affiliation":[{"name":"2Laboratoire J.L. Lions, CNRS UMR 7598, Universit\u00e9 Pierre et Marie Curie, 75005 Paris, France."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/12\/4\/article-p391.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2012-0027\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:22:31Z","timestamp":1619101351000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/12\/4\/article-p391.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2012-0027","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}