ACA-accelerated time domain BEM for 3-D elastodynamics

This paper presents the use of the adaptive cross approximation (ACA) method for the acceleration of the classic time domain boundary element method (BEM) in 3-D elastodynamics. The main advantage of using ACA is that it is based only on the knowledge of the matrix entries; therefore no special treatment of the time domain fundamental solution is required when the coefficient matrix is approximated by using this approach. In order to discretize the boundary integral equation (BIE) we use the collocation method and eight-node discontinuous quadratic element. In the numerical examples, stability of the classic time domain BEM in terms of both the degree of discontinuity of the boundary elements and the time step size is tested, and the compression ratios of the coefficient matrices by using ACA along the time steps are studied