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

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.