IgA-BEM for 3D Helmholtz problems using conforming and non-conforming multi-patch discretizations and B-spline tailored numerical integration

Degli Esposti, Bruno (author), Falini, Antonella (author), Kanduč, Tadej (author), Sampoli, Maria Lucia (author), Sestini, Alessandra (author)

An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth multi-patch representation of their finite boundary surface. The discretization spaces are formed by $C^0$ inter-patch continuous functional spaces whose restriction to a patch simplifies to the span of tensor product B-splines composed with the given patch NURBS parameterization. Both conforming and non-conforming spaces are allowed, so that local refinement is possible at the patch level. For regular and singular integration, the proposed model utilizes a numerical procedure defined on the support of each trial B-spline function, which makes possible a function-by-function implementation of the matrix assembly phase. Spline quasi-interpolation is the common ingredient of all the considered quadrature rules; in the singular case it is combined with a B-spline recursion over the spline degree and with a singularity extraction technique, extended to the multi-patch setting for the first time. A threshold selection strategy is proposed to automatically distinguish between nearly singular and regular integrals. The non-conforming $C^0$ joints between spline spaces on different patches are implemented as linear constraints based on knot removal conditions, and do not require a hierarchical master-slave relation between neighbouring patches. Numerical examples on relevant benchmarks show that the expected convergence orders are achieved with uniform discretization and a small number of uniformly spaced quadrature nodes.

• Language: English
• Keywords: Helmholtz equation, Isogeometric Analysis, IgA, Boundary Element Method, BEM, non-conforming discretization, singular integral, nearly singular integral, numerical integration, B-spline quasi-interpolation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics; FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 164-184
• Numbering: Vol. 147
• PID: 20.500.12556/RUL-153400
• UDC: 519.6
• ISSN on article: 0898-1221
• DOI: 10.1016/j.camwa.2023.07.012
• COBISS.SI-ID: 178695171
• Publication date in RUL: 03.01.2024

Record is a part of a journal

• Title: Computers & mathematics with applications
• Shortened title: Comput. math. appl.
• Publisher: Elsevier
• ISSN: 0898-1221
• COBISS.SI-ID: 15336965

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
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