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通过将谱域Green函数在复平面上进行局部小宗量Taylor级数展开,提出了一种将谱域Green函数全部模式快速、精确定位的方法(FLAM),并将其应用到基于全模提取的最陡下降路径方法中,简称SDP-FLAM,实现了分层媒质Green函数的精确计算.基于复变函数理论,严格分析了谱域Green函数极点和支点奇异性与黎曼面之间的关系.在将谱域Green函数反演到空域时,对非近场区采用SDP-FLAM计算,而对近场区则采用离散复镜像方法来获得,最终得到与精确解相吻合的空域Green函数.SDP-FLAM方法的优势在于它能快速计算厚层媒质和损耗媒质的分层Green函数.文中的数值算例验证了SDP-FLAM方法的正确性与有效性。
A method of fast and accurate locating all modes of Green’s function in the spectral domain (FLAM) is proposed by applying the local Green’s function of the spectral domain to the Taylor series of local minors. A new method based on full-mode extraction (SDP-FLAM), the Green function of stratified medium is accurately calculated.Based on the complex variable function theory, the relationship between the singularity of the pole and the fulcrum of the spectral Green’s function and the Riemannian surface is rigorously analyzed In the inversion of spectral Green ’s function to airspace, SDP - FLAM is used for non - near field and discrete complex image is used for near - field, and the spatial Green function which agrees well with the exact solution is obtained. The advantage of the SDP-FLAM method is that it can quickly calculate the stratified Green’s function of thick and lossy media.The numerical example in the paper verifies the correctness and validity of SDP-FLAM method.