{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T16:09:57Z","timestamp":1786118997289,"version":"build-2736575974"},"reference-count":32,"publisher":"American Mathematical Society (AMS)","issue":"362","license":[{"start":{"date-parts":[[2026,11,24]],"date-time":"2026-11-24T00:00:00Z","timestamp":1795478400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>This paper proposes a new multiple-scattering frequency-time hybrid (FTH-MS) integral equation solver for problems of wave scattering by obstacles in two dimensional space, including interior problems in closed cavities and problems exterior to a set of disconnected open or closed scattering obstacles. The multiple-scattering FTH-MS method is based on a partition of the domain boundary into a user-prescribed set of overlapping open arcs, along with a corresponding sequence of multiple-scattering problems that effectively decompose the interior problem into a series of open-arc wave equation subproblems. The new strategy provides a significant extension of the original FTH-MS algorithm originally presented by Bruno and Yin [Math. Comp. 93 (2024), pp. 551\u2013587], in that (1)\u00a0By allowing for use of an arbitrary of number of component arcs, and not just two as in the previous contribution, the new approach affords (1a) A significantly increased geometric flexibility, as well as (1b)\u00a0The use of partitions for which each open arc leads to small numbers of iterations if iterative linear-algebra solvers are employed; and (2)\u00a0It facilitates parallelization\u2014as the subproblem solutions that are needed at each multiple scattering step can be evaluated in an embarrassingly parallel fashion. Utilizing a suitably-implemented Fourier transformation, each sub-problem is reduced to a Helmholtz frequency-domain problem that is tackled via a uniquely-solvable boundary integral equation. Similar FTH-MS methods are also presented for problems exterior to a number of bounded obstacles. All of the algorithms considered incorporate the previously introduced \u201ctime-windowing and recentering\u201d methodology (that enables both treatment of incident signals of long duration and long time simulation), as well as a high-frequency Fourier transform algorithm that delivers numerically dispersionless, spectrally-accurate time evolution for arbitrarily long times.<\/p>","DOI":"10.1090\/mcom\/4164","type":"journal-article","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T16:37:50Z","timestamp":1764002270000},"page":"2817-2848","source":"Crossref","is-referenced-by-count":2,"title":["Multi-patch\/multiple-scattering frequency-time hybrid solver for interior and exterior wave equation problems"],"prefix":"10.1090","volume":"95","author":[{"given":"Shuai","family":"Pan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Bao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Yin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oscar","family":"Bruno","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2025,11,24]]},"reference":[{"issue":"7","key":"1","doi-asserted-by":"publisher","first-page":"1746","DOI":"10.1016\/j.cam.2010.02.011","article-title":"On the energetic Galerkin boundary element method applied to interior wave propagation problems","volume":"235","author":"Aimi, A.","year":"2011","journal-title":"J. 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