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Title: An Optimization Strategy to Position CHIEF Points in Boundary-Element Acoustic Problems
Authors: Gonçalves, Kleber de Almeida 
Santurio, Daniela Silva
Soares, Delfim
Costa, Pedro Alves
Godinho, Luís 
Keywords: boundary elements; CHIEF points; smallest singular value; exterior acoustics
Issue Date: 2023
Publisher: MDPI
Project: This research was partially funded by FCT—Fundação para a Ciência e a Tecnologia, I.P., by Base Funding (UIDB/04029/2020) and Programmatic Funding (UIDP/04029/2020) of the research unit “Institute for sustainability and innovation in structural engineering—ISISE”, and by Base Funding (UIDB/04708/2020) and Programmatic Funding (UIDP/04708/2020) of the research unit “CONSTRUCT—Instituto de ID em Estruturas e Construções”. This work was also funded by FEDER funds through the COMPETE 2020, Portugal 2020, under the projects POCI-01-0247-FEDER- 033990 (iNBrail) and POCI-01-0247-FEDER-046111 (FERROVIA 4.0), and by national funds (PIDDAC) through FCT/MCTES under the project PTDC/ECI-EGC/3352/2021 (IntRAIL). It was also partially funded by “Conselho Nacional de Desenvolvimento Científico e Tecnológico” (CNPq) and “Fundação de Amparo à Pesquisa do Estado de Minas Gerais” (FAPEMIG). 
Serial title, monograph or event: Applied Sciences (Switzerland)
Volume: 13
Issue: 6
Abstract: The use of boundary elements in the analysis of exterior acoustic problems poses challenges at specific frequencies, since fictitious eigenfrequencies may arise at the internal resonances of cavities, leading to inaccurate results or even unstable behavior. 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’s 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.
ISSN: 2076-3417
DOI: 10.3390/app13064001
Rights: openAccess
Appears in Collections:I&D ISISE - Artigos em Revistas Internacionais
FCTUC Eng.Civil - Artigos em Revistas Internacionais

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