IgA-BEM for 3D Helmholtz problems using conforming and non-conforming multi-patch discretizations and B-spline tailored numerical integrationDegli Esposti, Bruno (Avtor) Falini, Antonella (Avtor) Kanduč, Tadej (Avtor) Sampoli, Maria Lucia (Avtor) Sestini, Alessandra (Avtor) Helmholtz equationIsogeometric AnalysisIgABoundary Element MethodBEMnon-conforming discretizationsingular integralnearly singular integralnumerical integrationB-spline quasi-interpolationAn 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.20232024-01-03 13:52:43Članek v reviji153400sl