{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:24:30Z","timestamp":1787336670919,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Optimized transmission conditions in domain decomposition methods have been the focus of intensive research efforts over the past decade. Traditionally, transmission conditions are optimized for two subdomains model configurations, and then used in practice for many subdomains. We optimizetransmission conditions here for the first time directly for many subdomains for a class of complex diffusion problems. Our asymptotic analysis leads to closed form optimized transmission conditions for many subdomains, and shows that the asymptotic best choice in the mesh size only differs from the two subdomain best choice in the constants, for which we derive the dependence on the number of subdomains explicitly, including the limiting case of an infinite number of subdomains, leading to new insight into scalability. Our results include both Robin and Ventcell transmission conditions, and we also optimize for the first time a two-sided Ventcell condition. We illustrate our results with numerical experiments, both for situations covered by our analysis and situations that go beyond.<\/jats:p>","DOI":"10.1137\/22m1492386","type":"journal-article","created":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T05:49:52Z","timestamp":1682574592000},"page":"A829-A848","source":"Crossref","is-referenced-by-count":1,"title":["Closed Form Optimized Transmission Conditions for Complex Diffusion with Many Subdomains"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5885-1903","authenticated-orcid":true,"given":"Victorita","family":"Dolean","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK, and Laboratoire J A Dieudonn\u00e9, CNRS, University C\u00f4te d\u2019Azur, Nice, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8450-9223","authenticated-orcid":true,"given":"Martin J.","family":"Gander","sequence":"additional","affiliation":[{"name":"Section de Math\u00e9matiques, University of Geneva, Geneva, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandros","family":"Kyriakis","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,27]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-015-0784-8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol55s112"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/19M125858X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1063\/1.4816767"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10013-018-0316-9"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-020-01394-8"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/218\/03035"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/16M1065215"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/17M1115885"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol49s210"},{"key":"ref11","first-page":"313","volume":"1","author":"Despr\u00e9s B.","year":"1990","journal-title":"C.R. Acad. Sci. Paris"},{"key":"ref12","first-page":"44","volume-title":"Mathematical and Numerical Aspects of Wave Propagation Phenomena","author":"Despr\u00e9s B.","year":"1991"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"V. Dolean , \nM. J. Gander , and \nA. Kyriakis , Optimizing Transmission Conditions for Multiple Subdomains in the Magnetotelluric Approximation of Maxwell\u2019s Equations, https:\/\/arxiv.org\/abs\/2103.07879, accepted for publication in DD26 proceedings (2022).","DOI":"10.1007\/978-3-030-95025-5_22"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2018041"},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"F. Donzelli , \nM. J. Gander , and \nR. D. 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