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The scaled boundary finite-element method, a semi-analytical method based on finite element technology, is well suited to model unbounded domains. Only the boundary is discretized. No fundamental solution is necessary. General anisotropic material is analyzed without any increase in computational effort. The goal of this paper is to increase the computational efficiency of the scaled boundary finite-element analysis of large-scale problems. A reduced set of weighted block-orthogonal base functions is introduced. The scaled boundary finite-element equation is reformulated in generalized coordinates reducing the number of degrees of freedom on boundary. The solution procedure in frequency domain is presented. To enforce the radiation condition at infinity, an asymptotic expansion for displacement at high frequency is developed. Numerical examples have demonstrated that the computational time is reduced by more than an order of magnitude. © 2005 Elsevier B.V. All rights reserved.