Time Domain Spectral Element Method for Simulation of Guided Wave: Analysis of Calculation Accuracy and Efficiency

Ultrasonic guided wave is currently under extensive research and application in the field of nondestructive testing and structural health monitoring. Numerical simulation of wave propagation and the interaction between wave and defect/discontinuity helps guide the damage detection. However, the small temporal increment, together with dense mesh discretization to satisfy the calculation in the ultrasonic range, significantly hinders the modeling of wave propagation. The time domain spectral element method (SEM), a finite element method (FEM) of high order with specialized Gauss-Lobatto-Legendre node distribution and Lobatto quadrature algorithm, is frequently used in the domain of wave propagation. This paper quantitatively compares the calculation accuracy and efficiency of SEM over conventional FEM. A 2-D plane strain model of Lamb wave propagation is built with both SEM and conventional FEM, in which the speeds of fundamental symmetric mode (S0) and anti-symmetric mode (A0) are calculated to be compared with analytical result as the indicator of accuracy. When the mesh size is restricted within 20 nodes per wavelength, SEM exhibits a trend of quicker convergence speed and higher calculation accuracy, presenting the error less than 0.1%, while FEM can only reach an error larger than 1%. In addition, with the formed diagonalized mass matrix, the avoidance of complex inverse of mass matrix and less matrix multiplication in every temporal increment step of the explicit algorithm endows SEM with much higher calculation efficiency over conventional FEM.