竖向成层介质中标量波传播问题的高精度人工边界条件

为了实现含竖向成层介质以及表面不规则地形场地中标量波传播问题的高效且高精度求解，该文基于连分式展开和扩展的一致边界，建立了一种频域下折线形高精度人工边界条件。通过在每个竖向地层内引入独立的斜角坐标变换，新的人工边界条件可以用于多起伏地表地形条件。新的折线形人工边界在频域下推导，仅含有连分式阶数一个待定实参数，用于调整计算精度，该参数不随外行波的频率和传播角度改变。人工边界条件可以与内域有限元方程无缝耦合，应用简单方便。由于新边界条件的高精度，内域尺寸可以取较小甚至可以直接将人工边界加在结构周围或者地表，从而极大提高计算效率。通过典型数值算例，将人工边界计算模型与有限元大模型的解进行了对比分析，验证了该文提出的折线形人工边界条件的有效性和高精度。

HIGH-PRECISION ARTIFICIAL BOUNDARY CONDITION FOR SCALAR WAVE PROPAGATION IN VERTICAL STRATIFIED MEDIA

To realize the efficient and high precision solution of the scalar wave propagation problem in the field with vertical stratified media and irregular surface topography, a high-precision artificial boundary condition is established based on continuous fraction expansion and the extension of consistent boundary. The proposed artificial boundary condition can be applied to sites with zigzag surfaces by introducing an independent oblique coordinate transformation in each vertical layer. The frequency-domain artificial boundary condition only has the continuous fraction order as an undetermined parameter, which can be used to adjust the calculation accuracy and is independent of frequency and incidence angle of outgoing propagating waves. The artificial boundary conditions can be seamlessly coupled with finite element methods for the inner finite domain, which is easy to use. Due to the high precision of the boundary condition, the size of the finite domain can be very small, or even directly added to the ground surface or around the structure, thus greatly improving the computational efficiency. The validity and accuracy of the artificial boundary condition are verified by comparing with the finite element model in typical numerical examples.