{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:27:50Z","timestamp":1790710070567,"version":"4.1.0"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,2,28]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Fast multipole methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from boundary integral equations (BIEs) in acoustics or electromagnetics. However, their cost strongly increases in the high-frequency regime. This paper introduces a new directional FMM for oscillatory kernels ( defmm: directional equispaced interpolation-based fmm), whose precomputation and application are FFT-accelerated due to polynomial interpolations on equispaced grids. We demonstrate the consistency of our FFT approach and show how symmetries can be exploited in the Fourier domain. We also describe the algorithmic design of defmm, well-suited for the BIE nonuniform particle distributions, and present performance optimizations on one CPU core. Finally, we exhibit important performance gains on all test cases for defmm over a state-of-the-art FMM library for oscillatory kernels.<\/jats:p>","DOI":"10.1137\/22m1472930","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T13:15:52Z","timestamp":1677071752000},"page":"C20-C48","source":"Crossref","is-referenced-by-count":2,"title":["A Directional Equispaced Interpolation-Based Fast Multipole Method for Oscillatory Kernels"],"prefix":"10.1137","volume":"45","author":[{"given":"Igor","family":"Chollet","sequence":"first","affiliation":[{"name":"Institut des Sciences du Calcul et des Donn\u00e9es (ISCD), INRIA Alpines, Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0826-6244","authenticated-orcid":true,"given":"Xavier","family":"Claeys","sequence":"additional","affiliation":[{"name":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9, Inria \u00e9quipe ALPINES, F-75005 Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Fortin","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, LIP6, F-75005 Paris, France, and Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Grigori","sequence":"additional","affiliation":[{"name":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9, Inria \u00e9quipe ALPINES, F-75005 Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,2,23]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1173599"},{"key":"ref2","unstructured":"E. Agullo , \nB. Bramas , \nO. Coulaud , \nE. Darve , \nM. Messner , and \nT. Takahashi , Pipelining the Fast Multipole Method over a Runtime System, Research report RR-7981, INRIA, https:\/\/hal.inria.fr\/hal-00703130\/file\/RR-7981.pdf, 2012."},{"key":"ref3","volume-title":"Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable","author":"Ahlfors L. 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Kremenliev , Porting and Verification of ExaFMM Library in MIC Architecture, 2014, https:\/\/doi.org\/10.5281\/zenodo.822725."},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/090774707"},{"key":"ref30","doi-asserted-by":"crossref","unstructured":"D. Schobert  and \nT. Eibert , A multilevel interpolating fast integral solver with fast Fourier transform acceleration, in Proceedings of the 20th URSI International Symposium on Electromagnetic Theory, 2010, pp. 520\u2013523.","DOI":"10.1109\/URSI-EMTS.2010.5637194"},{"key":"ref31","first-page":"109","volume":"33","author":"Smith S.","year":"2006","journal-title":"Ann. Math. Inform."},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.11.021"},{"key":"ref33","volume":"7","author":"Yokota R.","year":"2012","journal-title":"J. Algorithms Comput. 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