为此先推导离散格林函数的权模估计和有限元解的渐近不等式展开，然后给出公式的证明。
For this, we derive the weighted estimates for discreet Green function and the asymptotic error expansion inequalities, and then the proofs of the formulas are given.
分析了实空间离散格林函数的特点和平面声全息重构卷积计算的特殊性，推导了在重构条件下二维循环卷积与重构卷积的关系。
Characteristics of the discrete real-space Green′s function and particularities of the discrete algorithm of the planar acoustical holography reconstruction convolution are analyzed.
使用离散复镜像方法(DCIM)快速得到平面分层介质的空间域的闭式格林函数，避免了费时的索末菲尔德积分。
To avoid calculating the time-consuming Sommerfeld's integrals, the discrete complex image method (DCIM) is employed to obtain spatial domain closed-form Greens function for planar-layered media.
二级离散复镜像方法将谱域格林函数分两步近似，减少了广义函数束方法对格林函数进行指数拟合的时间。
In the two-level DCIM, the approximation is performed at two levels to reduce the time to fit the Green's functions with exponential functions so that the efficiency is improved.
数值结果表明，二级离散复镜像方法是一种快速、有效的求解闭式格林函数的方法。
Numerical results show that the two-level DCIM is an efficient method for calculating the closed-form Green's Functions.
提出了二级离散复镜像法(DCIM)与表面波处理相结合的方法对空域格林函数进行计算。
Then discrete complex images method (DCIM) is applied to obtain spatial domain Green's functions, which enhance computing efficiency.
该方法采用二级离散复镜像方法求解空间域的格林函数，与直接数值积分方法相比，提高了计算格林函数的速度。
The two-level discrete complex image method is used to compute the spatial Green's Function, and thus improves the speed to compute Green's function compared with the direct integral method.
该方法采用二级离散复镜像方法求解空间域的格林函数，与直接数值积分方法相比，提高了计算格林函数的速度。
The two-level discrete complex image method is used to compute the spatial Green's Function, and thus improves the speed to compute Green's function compared with the direct integral method.
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