The Helmholtz equation is an elliptic partial differential equation which is a time-harmonic solution of the wave equation . Obtaining an efficient and more accurate numerical solution for the Helmholtz equation has been the subject of many studies .

亥姆霍兹方程是一个 波方程的 时间 调和解答，寻求高精度的数值解一直是 计算 力学界研究的主题。

For incident plane time-harmonic and elastic SH waves the effect of the frequency the direction of the wave incidence and the distance between neighboring cracks on the dynamic stress intensity factors is analyzed .

对于入射平面 SH弹性谐波，分析了 波的频率、入射方向以及相邻裂纹间距离对动应力强度因子的影响。

In addition taking the single-pole and two-pole Debye model for example the composite EM scattering from 1-D dispersive sea water and soil with and without a target are analyzed and the results are also verified by those of the time-harmonic wave incidence . 5 .

另外以单极和双极 Debye模型为例，分析了一维色散海水、土壤及其与二维目标的复合电磁散射 特性，并与 时 谐 场 源 激励 下的结果进行了验证。

Firstly probing the medium with a time-harmonic homogeneous plane wave gives the Christoffel equation . Then the formulas for slowness and complex velocities of the longitudinal wave and the slow and quick shear waves may be obtained from Christoffel equation .

使用平面均匀 简谐 波的方法，得到了Christoffel方程，利用此方程推导出纵波及快、慢横波的慢度和复速度方程。