2024 Volume 10 Issue 35 Pages 1317-1321
Numerical methods with high accuracy and low computational cost are needed to predict the dynamic response of the ground during earthquakes. Conventional dynamic analysis methods include explicit and implicit methods, whereas explicit methods are often numerically unstable and have large errors, and implicit methods require a large cost to solve the simultaneous equations. We propose a new method that is explicit but more accurate than the implicit method and can allow for large time increments based on the analytical solution to the semi-discretized finite element equations. The wave kernel function (WKF) is known as a spectral representation of the exact solution of the one-dimensional wave equation. The proposed method combines WKF and digital filtering techniques for time semi-discretized finite element equations. Since the WKF amplifies spurious high frequencies due to spatial discretization errors, a low-pass filter is incorporated into the WKF. This new method is referred to as the time-spectral finite element method (T-S FEM) in this work. The numerical solution of the 1D wave equation was obtained by T-S FEM; even a numerical solution in close agreement with the exact ones was obtained even when a large time increment corresponding to Courant number 2.0 was employed. Furthermore, the results suggest that the optimal cutoff frequency of the low-pass filter is approximately equal to the time update frequency
