This paper presents a newly developed stochastic version of spectral finite element method (StSFEM) for analysis of wave propagation in random domain. The StSFEM provides some merits for numerical analysis of elasto-dynamic problems, which includes accuracy, suitable computational cost, fast solver for eigensolution of Fredholm integral equation in Karhunen–Loève expansion, diagonal mass matrix, etc. This method utilizes desirable domain discretization, higher-order interpolation functions and quadrature scheme. Here, material definition of the mathematical model is assumed as random field. Numerical results demonstrate the efficiency, accuracy and suitable compatibility of the StSFEM as a pioneer rival for the time-consuming Monte Carlo simulation, particularly for large domains. Although large matrices are inevitable in such domains, the StSFEM needs much smaller temporary storage space and is faster than standard stochastic finite element method. Also, due to existence of uncertainties in computational earthquake engineering, the StSFEM can be used for reliability assessment of seismic wave propagation.
