半空间格林函数的角谱平面高效计算

Efficient evaluation of half-spaces Green′s functions in angular spectrum plane

将半空间并矢格林函数的索末菲积分用角谱平面积分表示 ,将原始的索末菲积分路径变换至最陡下降路径 ,针对场源位于不同区域时的分支割线和支点分布做了讨论 ,给出了最陡下降路径方程和相应的积分公式。对于可能涉及的支点奇异性 ,通过增加一条过支点的等相位路径来计算。角谱平面的计算方法有效地简化了SDP方程的推导与积分计算过程 ;

Half-space Green' s functions was expressed in angular spectrum integrals. The original integration path was deformed into the steepest descent path. For source point and observation point located in different regions, the correspond locations of branch-cut and branch-point in the angular plane were discussed, and the SDP equation and integration representations were formulated. A constant phase path pass through branch-point was added to consider the contribution of the branch-point singularity probably existing. The proposed approach simplifies derivation of SDP equation and processing of integration evaluation. Numerical results show that the approach based on SDP can greatly enhance the efficiency of evaluation of Green's functions.