Isogeometric Boundary Element Method for Acoustics

The Boundary Element Method (BEM) is an efficient numerical approach for solving an acoustical problem in the frequency domain. Due to the transformation of the differential equation onto the surface, a two-dimensional description is sufficient for the solution of a three-dimensional problem. The geometries are usually developed within CAD software that are able to represent curved shapes exactly. In the classical procedure these representations are discretized by elements based on Lagrange polynomials, in most cases by an automesh tool. This can lead to either a poor quality or manual improvement consumes a lot of time. The goal of the Isogeometric BEM is to directly incorporate the geometry description of the CAD tools, which are based on Non-Uniform Rational B-Splines (NURBS). On one hand the required mesh is easier to carry over to the BEM tool, since the underlying shape description is the same. On the other hand the surface is represented exactly in contrast to the approximation by the Lagrange polynomials. In this contribution the procedure of the new geometry description is depicted and numerical examples show the correct implementation, but also reveal the new challenges.