Long-time dynamic analysis of damped wave propagation using a time-spectral BEM with discontinuous triangular elements

In this work, a time-spectral boundary element method (TSBEM) with discontinuous triangular elements is proposed for long-time dynamic analysis of damped wave propagation in two dimension. Within this framework, the first- and second-order time derivatives of displacement in the governing equations are treated as nonhomogeneous terms and incorporated into the kernel functions of the domain integrals in the boundary integral equation using Green’s second identity. These time derivatives are approximated as weighted linear combinations of displacements values at Gaussian nodes within each temporal interval, following an inverse spectral integration technique. To evaluate domain integrals whose kernels involve unknown or non-functional physical quantities, discontinuous quadratic triangular elements are introduced to accurately approximate these quantities. Consequently, the developed approach accommodates large time steps while maintaining stability in long-time dynamic simulations. Notably, the coefficient matrix generated in the TSBEM is independent of the time variable, meaning it only needs to be computed once throughout the entire time marching process. To validate the accuracy and computational efficiency of the proposed approach, several numerical experiments are conducted. The numerical results obtained using the TSBEM are compared with those from traditional approaches.