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

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

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.

• Jezik: Angleški jezik
• Ključne besede: Helmholtz equation, Isogeometric Analysis, IgA, Boundary Element Method, BEM, non-conforming discretization, singular integral, nearly singular integral, numerical integration, B-spline quasi-interpolation
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko ; FS - Fakulteta za strojništvo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: Str. 164-184
• Številčenje: Vol. 147
• PID: 20.500.12556/RUL-153400
• UDK: 519.6
• ISSN pri članku: 0898-1221
• DOI: 10.1016/j.camwa.2023.07.012
• COBISS.SI-ID: 178695171
• Datum objave v RUL: 03.01.2024

Gradivo je del revije

• Naslov: Computers & mathematics with applications
• Skrajšan naslov: Comput. math. appl.
• Založnik: Elsevier
• ISSN: 0898-1221
• COBISS.SI-ID: 15336965

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.