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By defining constant reference coefficients, a representation formula for the pressure field is derived. It contains a volume integral operator, related to the one in the Lippmann\u2013Schwinger equation. Besides, it features integral operators defined on<jats:inline-formula><jats:alternatives><m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><m:mrow><m:mo rspace=\"0em\">\u2202<\/m:mo><m:msup><m:mi mathvariant=\"normal\">\u03a9<\/m:mi><m:mo>\u2212<\/m:mo><\/m:msup><\/m:mrow><\/m:math><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2022-0119_ineq_0003.png\"\/><jats:tex-math>\\partial\\Omega^{-}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and closely related to boundary integral equations of single-trace formulations (STF) for transmission problems with piecewise constant coefficients. We show well-posedness of the continuous variational formulation and asymptotic convergence of Galerkin discretizations. Numerical experiments in 2D validate our expected convergence rates.<\/jats:p>","DOI":"10.1515\/cmam-2022-0119","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T11:06:20Z","timestamp":1683284780000},"page":"119-139","source":"Crossref","is-referenced-by-count":5,"title":["Volume Integral Equations and Single-Trace Formulations for Acoustic Wave Scattering in an Inhomogeneous Medium"],"prefix":"10.1515","volume":"24","author":[{"given":"Ignacio","family":"Labarca","sequence":"first","affiliation":[{"name":"Seminar for Applied Mathematics , ETH Z\u00fcrich , Z\u00fcrich , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ralf","family":"Hiptmair","sequence":"additional","affiliation":[{"name":"Seminar for Applied Mathematics , ETH Z\u00fcrich , Z\u00fcrich , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,5,6]]},"reference":[{"key":"2024010712054038776_j_cmam-2022-0119_ref_001","doi-asserted-by":"crossref","unstructured":"G. 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