A RIM-based Time-domain Boundary Element Method for Three-Dimensional Non-homogeneous Wave Propagations

This paper presents a three-dimensional (3-D) boundary element method (BEM) scheme based on the Radial Integration Method (RIM) for wave propagation analysis of continuously non-homogeneous problems. The Kelvin fundamental solutions are adopted to derive the boundary-domain integral equation (B-DIE). The RIM proposed by Gao (Engineering Analysis with Boundary Elements 2002; 26(10);905-916) is implemented to treat the domain integrals in the BDIE so that only boundary discretization is required. After boundary discretization, a set of second-order ordinary differential equations with respect to time variable are derived, which are solved using the Wilson-theta method. Main advantages of the proposed method are that 1) it can treat wave propagations in non-homogeneous domains with only boundary mesh required, and that 2) coefficient matrices arising from the BEM are evaluated and stored only once so that solving large-scale problems with huge time steps is possible. In the numerical examples, the present method is tested in terms of accuracy, capacity to treat non-homogeneous problems and large-scale potentials.