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Simul."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an [Formula: see text]-like hierarchical factorization of the dense system matrix, permitting application of the inverse in [Formula: see text] time, where [Formula: see text] is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted adaptive octree data structure, and therefore, it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nystr\u00f6m quadrature methods to integrate the singular and weakly-singular Green\u2019s functions used in the integral representations. Our method has immediate applications to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies, and provide rigorous justification for compression of submatrices via proxy surfaces.<\/jats:p>","DOI":"10.1137\/22m1514040","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T04:32:33Z","timestamp":1698985953000},"page":"1570-1601","source":"Crossref","is-referenced-by-count":15,"title":["FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions"],"prefix":"10.1137","volume":"21","author":[{"given":"Daria","family":"Sushnikova","sequence":"first","affiliation":[{"name":"King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leslie","family":"Greengard","sequence":"additional","affiliation":[{"name":"Courant Institute, NYU, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2724-215X","authenticated-orcid":true,"given":"Michael","family":"O\u2019Neil","sequence":"additional","affiliation":[{"name":"Courant Institute, NYU, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manas","family":"Rachh","sequence":"additional","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, New York, NY 10010 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,11,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-013-9714-z"},{"key":"ref2","unstructured":"S. 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