A high-order doubly asymptotic continued-fraction solution for frequency-domain analysis of vector wave propagation in unbounded domains

The scaled boundary finite element (SBFE) equation in dynamic stiffness of unbounded domains is efficiently solved by the continued fraction expansion, which has a large convergence range and a high convergence rate. In this paper, a doubly asymptotic continued fraction solution algorithm for frequency-domain analysis of vector wave propagation in unbounded domains of arbitrary geometry is developed based on the high-frequency (singly) asymptotic approach. The exact solution over the whole frequency range can be calculated rapidly with increasing order of expansion. The coefficient matrices of the solution are determined recursively by satisfying the dynamic stiffness at both high (ω→∞) and low (ω→0) frequency limits. The solutions of out-plane motion of a semi-infinite wedge, in-plane motion of a semi-infinite wedge and a 3-D homogeneous half space in the frequency domain are presented. The results of three numerical examples demonstrate that the doubly asymptotic algorithm is more stable and superior than the high-frequency asymptotic approach.