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The approach is to apply a modified fast multipole method for a boundary concentrated volume mesh. If [Formula: see text] is the meshwidth of the boundary, then the volume is discretized using nearly [Formula: see text] degrees of freedom, and the algorithm computes potentials in nearly [Formula: see text] complexity. Here nearly means that logarithmic terms of [Formula: see text] may appear. Thus the complexity of volume potential calculations is of the same asymptotic order as boundary potentials. For sources and potentials with sufficient regularity the parameters of the algorithm can be designed such that the error of the approximated potential converges at any specified rate [Formula: see text]. The accuracy and effectiveness of the proposed algorithms are demonstrated for potentials of the Poisson equation in three dimensions.<\/jats:p>","DOI":"10.1137\/21m1463008","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T03:05:11Z","timestamp":1682478311000},"page":"A480-A501","source":"Crossref","is-referenced-by-count":0,"title":["A Fast Method for Evaluating Volume Potentials in the Galerkin Boundary Element Method"],"prefix":"10.1137","volume":"45","author":[{"given":"Sasan","family":"Mohyaddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Southern Methodist University, Dallas, TX 75275 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0895-9980","authenticated-orcid":true,"given":"Johannes","family":"Tausch","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Southern Methodist University, Dallas, TX 75275 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.04.063"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/5.3.319"},{"key":"ref3","volume-title":"Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems","author":"Bebendorf M.","year":"2008"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0955-7997(02)00152-2"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/0909044"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-01970-9"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500369967"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90140-9"},{"key":"ref9","first-page":"293","volume":"32","author":"Guan W.","year":"2021","journal-title":"J. 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Mohyaddin , A Fast Method For Computing Volume Potentials in The Galerkin Boundary Element Method in 3D Geometries, Ph.D. thesis, Southern Methodist University, 2021."},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/0915046"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/080744359"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3690-7"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-68093-2"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2014.02.010"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-004-0063-5"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2022.03.030"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.10.027"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1463008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:25:41Z","timestamp":1787333141000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1463008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,26]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4,30]]}},"alternative-id":["10.1137\/21M1463008"],"URL":"https:\/\/doi.org\/10.1137\/21m1463008","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,26]]}}}