Uncertainty analysis in acoustics: perturbation methods and isogeometric boundary element methods

This study proposes a generalized nth-order perturbation method based on (isogeometric) boundary element methods for uncertainty analysis in 3D acoustic scattering problems. In this paper, for the first time, we derive nth-order Taylor expansions of 3D acoustic boundary integral equations, taking incident wave frequency as a random input variable. In addition, subdivision surface basis functions used in geometric modeling are employed to discretize the generalized nth-order derivative boundary integral equations, in order to avoid cumbersome meshing procedure and retain geometric accuracy. Moreover, the fast multipole method is introduced to accelerate the stochastic perturbation analysis with boundary element methods. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed uncertainty quantification algorithm.