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In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems.<\/jats:p>","DOI":"10.1145\/3368618","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T10:23:08Z","timestamp":1584699788000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Product Algebras for Galerkin Discretisations of Boundary Integral Operators and their Applications"],"prefix":"10.1145","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3323-2110","authenticated-orcid":false,"given":"Timo","family":"Betcke","sequence":"first","affiliation":[{"name":"University College London, London, UK"}]},{"given":"Matthew W.","family":"Scroggs","sequence":"additional","affiliation":[{"name":"University of Cambridge, Trumpington Street, Cambridge, UK"}]},{"given":"Wojciech","family":"\u015amigaj","sequence":"additional","affiliation":[{"name":"Met Office, FitzRoy Road, Exeter, UK"}]}],"member":"320","published-online":{"date-parts":[[2020,3,20]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"SciPy. 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