Generalized isogeometric boundary element method for uncertainty analysis of time-harmonic wave propagation in infinite domains

Abstract

This paper proposes a novel generalized nth order perturbation isogeometric fast multipole boundary element method for time harmonic wave propagation in infinite domains. The non-uniform rational B-splines are employed to construct structural geometries and discretize boundary integral equations. The randomness of wave number for incident plane wave is considered as the source of system uncertainty. The generalized nth order perturbation method is employed to model the physical field depending on the input random variable. The nth order derivatives of field functions and kernel functions in the boundary integral equations are derived by generalized nth order Taylor series expansions with a small perturbation parameter. The subtraction of singularity technique is used to evaluate the singular integrals and the fast multipole method is applied to accelerate the solution. The Monte Carlo simulations are conducted in numerical examples to demonstrate the validity and correctness of the proposed algorithm.