Isogeometric boundary element method for acoustic scattering by a submarine

TL;DR

This paper investigates the application of isogeometric boundary element methods to 3D acoustic scattering problems involving submarines, introducing a new benchmark and demonstrating improved accuracy over traditional BEM.

Contribution

It presents an analysis of IGABEM's approximability for acoustic scattering, introduces an improved submarine benchmark, and compares various boundary integral formulations with enhanced integration routines.

Findings

IGABEM achieves higher accuracy than standard BEM.

The new adaptive integration routine improves numerical stability.

Benchmarking with the method of manufactured solutions validates the approach.

Abstract

Isogeometric analysis with the boundary element method (IGABEM) has recently gained interest. In this paper, the approximability of IGABEM on 3D acoustic scattering problems will be investigated and a new improved BeTSSi submarine will be presented as a benchmark example. Both Galerkin and collocation are considered in combination with several boundary integral equations (BIE). In addition to the conventional BIE, regularized versions of this BIE will be considered. Moreover, the hyper-singular BIE and the Burton--Miller formulation are also considered. A new adaptive integration routine is presented, and the numerical examples show the importance of the integration procedure in the boundary element method. The numerical examples also include comparison between standard BEM and IGABEM, which again verifies the higher accuracy obtained from the increased inter-element continuity of the spline basis functions. One of the main objectives in this paper is benchmarking acoustic scattering problems, and the method of manufactured solution will be used frequently in this regard.