Numerical investigations with eXtended isogeometric boundary element analysis (XIBEM) for direct and inverse Helmholtz acoustic problems

Abstract

Isogeometric analysis (IGA) in the framework of the boundary element method (BEM) – known as isogeometric boundary element analysis or IGABEM – has shown recently respectable performance in the field of acoustics and handling the time harmonic wave propagation equation of Helmholtz. However, IGABEM still requires fine meshes to handle the cases of very high frequencies due to the large number of elements needed to capture the oscillatory behaviour, leading to large computational costs. IGABEM can be enriched by the partition of unity expansion of plane waves in the framework of the eXtended IGABEM (XIBEM) which can be used to simulate high frequency problems with small-scale wavelengths using coarser meshes than those used in other numerical approaches.In this paper, two numerical investigations are performed using XIBEM for two-dimensional problems. First, the number of plane waves is varied to find out the suitable enrichment scheme to achieve accurate results for higher frequency problems than those in the literature. After that, XIBEM is coupled with a non-iterative topological-shape sensitivity inverse analysis and applied for the problem of scatterer shape reconstruction. Different distributions of the receptor points are checked for this investigation with varied initial scatterer shapes.