Rational square-root approximations for parabolic equation algorithms
Rational square-root approximations for parabolic equation algorithms
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DOI：
10.1121/1.418038
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发表时间：
1997-02
影响因子：
2.4
通讯作者：
F. Milinazzo;C. Zala;G. Brooke
中科院分区：
文献类型：
--
作者：
F. Milinazzo;C. Zala;G. Brooke
在本文中，通过在负半平面中选择分支切割来导出函数 1+z 的稳定 Pade 近似。 Pade系数是复数并且可以从与由z<-1、I(z)=0定义的主分支相关联的对应实数系数解析地推导出任意阶[I(z)表示z的虚部]。针对复平面的各个部分示出了相应平方根近似的特征。特别地，对于波导问题，表明可以获得声学情况的模式谱的倏逝部分和弹性情况的复模式谱两者的越来越精确的表示。使用弹性抛物线方程算法来说明新的帕德近似在现实海洋环境中的应用，包括海底的弹性。
In this article, stable Pade approximations to the function 1+z are derived by choosing a branch cut in the negative half-plane. The Pade coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z<−1, I(z)=0 [I(z) denotes the imaginary part of z]. The characteristics of the corresponding square-root approximation are illustrated for various segments of the complex plane. In particular, for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part of the mode spectrum for the acoustic case and the complex mode spectrum for the elastic case. An elastic parabolic equation algorithm is used to illustrate the application of the new Pade approximations to a realistic ocean environment, including elasticity in the ocean bottom.