{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:50:54Z","timestamp":1777449054497,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2013,7]]},"abstract":"<jats:p>We present a mathematical and numerical analysis of the stability and accuracy of the NMLA (Numerical MicroLocal Analysis) method [J. Comput. Phys. 199(2) (2004), 717\u2013741] and its discretization. We restrict to homogeneous space and focus on the two simplest cases: (1) Noisy plane wave packets, (2) Noisy point source solutions. A stability result is obtained through the introduction of a new \u201cimpedance\u201d observable. The analysis of the point source case leads to a modified second order (curvature dependent) correction of the algorithm. Since NMLA is local, this second order improved version can be applied to general data (heterogeneous media). See [J. Comput. Phys. 231(14) (2012), 4643\u20134661] for a an application to a source discovery inverse problem.<\/jats:p>","DOI":"10.3233\/asy-121157","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:27:57Z","timestamp":1575055677000},"page":"157-187","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical microlocal analysis of 2-D noisy harmonic plane and circular waves"],"prefix":"10.1177","volume":"83","author":[{"given":"J.-D.","family":"Benamou","sequence":"first","affiliation":[{"name":"INRIA, Domaine de Voluceau, Rocquencourt, France. E-mail: Jean-david.Benamou@inria.fr"}]},{"given":"F.","family":"Collino","sequence":"additional","affiliation":[{"name":"CERFACS, Toulouse, France"}]},{"given":"S.","family":"Marmorat","sequence":"additional","affiliation":[{"name":"INRIA, Domaine de Voluceau, Rocquencourt, France. E-mail: Jean-david.Benamou@inria.fr"}]}],"member":"179","published-online":{"date-parts":[[2013,1,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-121157","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-121157","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:53Z","timestamp":1777379993000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-121157"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["10.3233\/ASY-121157"],"URL":"https:\/\/doi.org\/10.3233\/asy-121157","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}