{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:52Z","timestamp":1787337052068,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["258734477 - SFB 1173"],"award-info":[{"award-number":["258734477 - SFB 1173"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we propose a new spectral decomposition method to simulate waves propagating in complicated waveguides. For the numerical solutions of waveguide scattering problems, an important task is to approximate the Dirichlet-to-Neumann (DtN) map efficiently. From previous results, the physical solution can be decomposed into a family of generalized eigenfunctions, and thus we can write the DtN map explicitly by these functions. From the exponential decay of the generalized eigenfunctions, we approximate the DtN map by a finite truncation and the approximation is proved to converge exponentially. With the help of the truncated DtN map, the unbounded domain is truncated into a bounded one, and a variational formulation for the problem is set up in this bounded domain. The truncated problem is then solved by a finite element method. The error estimation is also provided for the numerical algorithm, and numerical examples are shown to illustrate the efficiency of the algorithm.<\/jats:p>","DOI":"10.1137\/22m1485425","type":"journal-article","created":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T10:21:42Z","timestamp":1684491702000},"page":"1195-1217","source":"Crossref","is-referenced-by-count":0,"title":["A Spectral Decomposition Method to Approximate Dirichlet-to-Neumann Maps in Complicated Waveguides"],"prefix":"10.1137","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2336-1020","authenticated-orcid":true,"given":"Ruming","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, 76131, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,5,19]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4338-8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-51954-8_6"},{"key":"ref3","volume-title":"Qualitative Methods in Inverse Scattering Theory. 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Zhang , Numerical Method for Scattering Problems in Periodic Waveguides, https:\/\/arxiv.org\/pdf\/1906.12283.pdf, 2019."},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/19M1290942"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1485425","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:42:32Z","timestamp":1787334152000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1485425"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,19]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,6,30]]}},"alternative-id":["10.1137\/22M1485425"],"URL":"https:\/\/doi.org\/10.1137\/22m1485425","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,19]]}}}