辅助微分方程完全匹配层在声波方程数值模拟中的应用

在地震波数值模拟中，为提高算法精度，需要使用高阶时间更新格式，而普通的非分裂完全匹配层（PML）吸收边界局限于低阶时间格式。辅助微分方程完全匹配层（ADE PML）是一种可以适应任意阶时间格式的非分裂完全匹配层技术，且可以直接应用复频移拉伸算子以提高PML在高角度入射时的效果。作者将ADE PML应用于声波方程四阶Runge Kutta时间格式的数值模拟中，对其吸收效能进行了检验。数值模拟表明，复频移ADE PML在高角度入射时表现优于非复频移ADE PML。另外，不同辅助变量更新格式的吸收效果存在微小差异，显格式下计算结果与解析解吻合较好。长时间能量衰减计算表明ADE PML可以稳定至2 × 10⁵时间步。

Application of Auxiliary Differential Equation Perfectly Matched Layer for Numerical Modeling of Acoustic Wave Equations

In seismic wave modeling, a high-order time marching scheme is required in order to increase the accuracy of the algorithm. However, ordinary unsplit perfectly matched layer(PML) absorbing boundaries are constrained to low-order time schemes. The auxiliary differential equation PML (ADE-PML) is a kind of unsplit PMLs that can be applied to arbitrary-order time schemes, and also can implement complex-frequency-shifted (CFS) coordinate tensor to enhance the performance of PML at high-angle incidence.We introduce the ADE-PML in the numerical modeling in fourth-order Runge-order time scheme for acoustic wave equations, and validate the efficiency. The numerical experiments demonstrate that CFS ADE-PML preforms better than non-CFS ADE-PML at high-angle incidence. Besides, there are minor distinctions among the absorbing efficiency of different update schemes for auxiliary variable, and the solution calculated by explicit scheme better agree with the analytical one. The long-time computation of energy decay shows that ADE-PML is stable up to 2 × 10⁵ steps.