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翻译样例: 频域格林函数计算1
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Green函数及其偏导数的数值计算在水动力学中起着重要作用,当用边界元法求解流体结构相互作用问题时,需要大量的计算Green函数及其偏导数。而格林函数中被积函数的振荡性,奇异性和积分区间为无穷使得该函数的计算较为困难,精度不易控制。因此,高效、精确的计算Green函数及其偏导数具有重要意义。

迄今为止,已出现不少成功的算法,MIT的Newman[1~4]在该问题上做了出色的工作,但其工作在算法推导的严密性,计算区域的划分,以及Green函数导数计算的实现等方面需要进一步的完善。王如森[6]在Newman的基础上用双重Chebyshev多项式对三维自由面频域Green函数及其导数的剩余函数进行数值逼近,使之达到5D精度,该方法已经相当成熟,可以完成坐标平面内任意一点Green函数及其导数的数值计算,但该方法计算过程较复杂需要非常细致的分区,循环次数较多,影响计算速度,而且在某些区域精度不是特别好。

Numerical calculation of Green's function and its partial derivative plays an important role in the water dynamics. When we use boundary element method to solve problems of fluid structure interaction, large amount of calculation of Green's function and its partial derivative is required. However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy. Therefore, efficient and accurate calculation of Green's function and its partial derivative is of great significance.

So far, there have been many successful algorithms. MIT's Newman [1 ~ 4] has done excellent work on this problem, but his work still needs further improvement on the aspects such as the tightness of derivation of algorithm zoning of calculation zone, and the calculation of the derivative of Green's function, etc. On the basis of Newman, Wang Rusen [6] conducted numerical approximation of the 3-D free surface frequency-domain Green's function and the surplus function of its derivative function with double Chebyshev polynomials, which has reached 5D accuracy. The method has been very mature and can complete numerical calculation of the Green's function and its derivative of any point within the coordinate plane. However, the computing process is complex, which requires extremely careful zoning, and more cycles, and has thus affected its computing speed. In addition, in some zones, the accuracy is not so fine.

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