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To this end, we apply the Duffy transformation to obtain singular-free integral representations, which we integrate analytically using classical calculus. In this way, we acquire closed and exact formulae for the singular cases and reduce the four-dimensional integrals to one- or two-dimensional integrals for the near singular and regular cases. We validate the correctness of the formulae in numerical experiments and report a substantial improvement in performance and efficiency compared to conventional numerical integration.<\/jats:p>","DOI":"10.1137\/22m1534857","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T04:01:02Z","timestamp":1691726462000},"page":"A2075-A2100","source":"Crossref","is-referenced-by-count":3,"title":["Almost Complete Analytical Integration in Galerkin Boundary Element Methods"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3833-2089","authenticated-orcid":true,"given":"Daniel","family":"Seibel","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Saarland University, Saarbr\u00fccken, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,8,11]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114186"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/22.563344"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/0719090"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00236-3"},{"key":"ref5","volume-title":"Differential and Integral Calculus","volume":"2","author":"Fichtenholz G. 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