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The procedure consists of constructing a universal operator representation through the introduction of locally singularity-resolving diffeomorphisms, thus enabling the application of wave packet--driven computation, and of constructing the associated pseudodifferential joint-partition of unity on the canonical graphs. We apply the method to a parametrix of the wave equation in the vicinity of a cusp singularity.<\/jats:p>","DOI":"10.1137\/120889642","type":"journal-article","created":{"date-parts":[[2013,5,30]],"date-time":"2013-05-30T11:20:36Z","timestamp":1369912836000},"page":"566-585","source":"Crossref","is-referenced-by-count":10,"title":["Multiscale Discrete Approximations of Fourier Integral Operators Associated with Canonical Transformations and Caustics"],"prefix":"10.1137","volume":"11","author":[{"given":"Maarten V.","family":"de Hoop","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gunther","family":"Uhlmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andr\u00e1s","family":"Vasy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Herwig","family":"Wendt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,5,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1080\/03605300701629393"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/100808174"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827593258279"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.08.001"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/040604959"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2004.05.008"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1993.1007"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(03)00095-5"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/05064182X"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/060671139"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/080734339"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2012.01.001"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/TGRS.2010.2046177"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1190\/1.3459955"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2008.06.001"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/0914081"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1995.1007"},{"key":"atypb18","unstructured":"L. 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