Uncertainty quantification for the 3D half-space sound scattering problem of IGABEM based on the Catmull–Clark subdivision surfaces

The generalized $n$th-order perturbation method for the quantitative uncertainty analysis in half-space acoustic problems proposed in this study is based on the isogeometric boundary element method, where the acoustic wave frequency is defined as a stochastic variable. We derive the Taylor series expansion and the kernel function formulation of the acoustic boundary integral equation for the half-space acoustic problem, and obtain the sound pressure’s $n$th-order derivative with respect to the acoustic wave frequency. In addition, we employ Burton–Miller method to deal with the fictitious frequency problem of external sound field and apply fast multipole method to accelerate the matrix–vector product computation. The statistical characterization of the acoustic state function is obtained based on the $n$th-order perturbation theory. Finally, the accuracy and efficacy of the uncertainty quantization algorithm is confirmed by three numerical examples.