Wave propagation model by time series hybrid element method

Abstract

In this study, a time domain boundary-finite element method is developed for solving wave propagation problems. By applying the weighted residual approach and using the static fundamental solutions as the weight function, the wave propagation equation is converted to simple boundary integral. In addition, the effects of domain integral related to inertia term are considered by applying the finite element method to the solution. Furthermore, after deriving the boundary-finite element (Hybrid) formulations, the solvable matrix of the equations in the discretized form is presented. In a novel approach, by estimating the temporal variations of the element nodes using Taylor and Fourier series, a time series discrete matrix is introduced for solving the equations which provides a higher degree of accuracy in compare to other time discretization approaches. Finally, the formulations and method are implemented into a computer algorithm and various examples are solved. The results demonstrated that the proposed time series hybrid approach (TSHEM) accurately models wave propagation problems with lower computational cost in compare to other numerical solutions, making it a preferable choice for solving complex problems with higher accuracy.