地震波数值模拟的非规则网格PML吸收边界

以格子法为基础，以声波方程为例研究非规则网格PML(Perfectly Matched Layer)方法.本方法的核心是建立局部坐标系下的分裂方程和基于积分近似的微分方程弱形式.该非规则网格模拟方法允许在计算域内设置任意形状的人工边界.对于二维半空间问题，与采用矩形人工边界相比，采用半圆形人工边界可减少计算量20%以上.采用光滑的曲边界，不仅可减少计算区域，还可避免常规的PML吸收边界在吸收带角点区域的特殊处理.本方法事先计算和存储边界单元的局部几何参数，在计算的每一时间步查表调用这些参数，与常规的直边界PML方法相比，不增加任何计算量.

An irregular-grid perfectly matched layer absorbing boundary for seismic wave modeling

The perfectly matched layer(PML)absorbing boundary condition is incorporated into the acoustic grid method,thus resulting in an irregular-grid PML method.The proposed scheme is developed using the local coordinate system based PML splitting equations and integral approaches of the PML equations under a discretization of triangular grid cells.The irregular-grid PML method allows the artificial boundaries to be constructed with arbitrary geometries only if the interested zones are enclosed.We can take a semi-circle rather than a rectangle as the artificial boundary in simulating the 2-D half-space using the proposed scheme.This results in an over 20% reduction of the nodes in the numerical discretization.By using a smoothed artificial boundary,the irregular-grid PML method can also avoid the special treatments for the corners,which lead to complex computer implementations in the conventional PML method.Owing to that the local geometrical coefficients are computed and stored in a table in advance,no extra computational costs arise when we use the irregular-grid PML method rather than the conventional PML method.The 2-D acoustic cases are considered here.