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To filter out these fictitious eigenfrequencies, a scheme based on the combined Helmholtz integral equation formulation (CHIEF) can be used to prevent the so-called non-uniqueness problem, although it requires additional equations and points. The BEM formulation final accuracy will, however, depend on the correct choice of these points. Here, a strategy to help in defining good approximations for the position and number of such points is proposed, based on an optimization process which maximizes the system matrix\u2019s smallest singular value. The accuracy of the method for exterior radiation problems is investigated using different examples. With low computational cost and simple implementation, the two proposed algorithms automatically circumvent the non-uniqueness problem, aiding the implementation of more stable BEM codes.<\/jats:p>","DOI":"10.3390\/app13064001","type":"journal-article","created":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:35:28Z","timestamp":1679466928000},"page":"4001","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Optimization Strategy to Position CHIEF Points in Boundary-Element Acoustic Problems"],"prefix":"10.3390","volume":"13","author":[{"given":"Kleber de Almeida","family":"Gon\u00e7alves","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, ISISE, ARISE, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coibra, Portugal"}]},{"given":"Daniela Silva","family":"Santurio","sequence":"additional","affiliation":[{"name":"Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica, Computational Modeling Department, Petr\u00f3polis 25651-075, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5756-9359","authenticated-orcid":false,"given":"Delfim","family":"Soares","sequence":"additional","affiliation":[{"name":"Structural Engineering Department, Federal University of Juiz de Fora, Juiz de Fora 36036-900, Brazil"}]},{"given":"Pedro Alves","family":"Costa","sequence":"additional","affiliation":[{"name":"CONSTRUCT, Department of Civil Engineering, Faculty of Engineering, the University of Porto (FEUP), 4099-002 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2989-375X","authenticated-orcid":false,"given":"Lu\u00eds","family":"Godinho","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, ISISE, ARISE, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coibra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"ref_1","first-page":"2908","article-title":"Acoustic Resonance Analysis of Open Cavities with the Boundary Element Method","volume":"Volume 259","author":"Wan","year":"2019","journal-title":"Proceedings of the 48th International Congress and Exposition on Noise Control Engineering (INTERNOISE 2019)"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1080\/02726349008908256","article-title":"Instabilities in Time Marching Methods for Scattering: Cause and Rectification","volume":"10","author":"Smith","year":"1990","journal-title":"Electromagnetics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1163\/156939390X00762","article-title":"Stability of Time Marching Algorithms for the Electric Field Integral Equation","volume":"4","author":"Rynne","year":"1990","journal-title":"J. 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