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

•The generalized nth order perturbation boundary integral equation  is derived for wave propagation problems.•The isogeometric BEM base on nth order perturbation boundary integral equation is proposed.•A new formula for tackling the singularity in nth order derivative boundary integral equation is presented.•Fast multipole method is adapted to the nth order derivative boundary integral equation.