IgA-BEM for 3D Helmholtz problems on multi-patch domains using B-spline tailored numerical integration

Abstract

An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D domains admitting a smooth conformal multi-patch representation of the boundary surface. The discretization space is formed by C 0 inter-patch continuous basis functions whose restriction to a patch simplifies to the span of tensor product B-splines composed with the given patch parameterization. To profit by efficient function-byfunction matrix assembly, the proposed model utilizes a spline quasi-interpolation numerical integration procedure for both singular and regular integrals defined on the support of each B-spline basis function in the discretization space. In particular, in the singular case the scheme combines a singularity extraction technique with a B-spline recursion. Numerical examples on relevant benchmarks show that the expected convergence orders are achieved with a small number of quadrature nodes.