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Acoustic shape optimization using cut finite elements
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0001-8329-8348
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0003-0473-3263
2018 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 113, no 3, p. 432-449Article in journal (Refereed) Published
Abstract [en]

Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.

Place, publisher, year, edition, pages
Hoboken: John Wiley & Sons, 2018. Vol. 113, no 3, p. 432-449
Keywords [en]
shape optimization, level set, CutFEM, sensitivity analysis, acoustic horn, Helmholtz equation
National Category
Computational Mathematics Computer Sciences
Identifiers
URN: urn:nbn:se:umu:diva-143623DOI: 10.1002/nme.5621ISI: 000418346200004OAI: oai:DiVA.org:umu-143623DiVA, id: diva2:1178547
Funder
Swedish Research Council, 621-2013-3706Swedish Foundation for Strategic Research , AM13-0029Available from: 2018-01-30 Created: 2018-01-30 Last updated: 2018-06-09Bibliographically approved

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Bernland, AndersWadbro, EddieBerggren, Martin

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