等效原理算法在不同等效面下的误差分析

等效原理算法(EPA)借鉴了区域分解的思想,并基于惠更斯等效原理实现了对大规模散射问题的计算.本文对EPA中的等效原理算子(EPO)进行了误差分析,选取了立方体、球体和进行了光滑处理的立方体等作为等效面寻找误差来源,并提出了误差改进的建议.根据计算结果,等效磁流在等效面上描述的误差一般集中在等效面表面的几何不连续处,且主要受等效面上的法向向量不连续性和基函数的选取的影响.故在选取等效面时应尽量考虑使用平滑的等效面,而不是直接使用立方体等效面.

Error analysis of equivalence principle algorithm on different equivalence surfaces

Equivalence principle algorithm (EPA) is a domain decomposition algorithm based on the Huygens' equivalence principle to solve large scale scattering problems. The errors of the equivalence principle operator (EPO) in EPA using cubic, spherical and smooth cubic equivalence surfaces were analyzed to find the source of errors. The sources of the error were investigated and a simple scheme to improve its accuracy was developed. From the numerical examples, it shows that the error of equivalent magnetic current is mainly concentrated on geometrical discontinuity of the equivalence surface, and affected by both the discontinuity of the normal vector on the equivalence surface and the choice of basis functions. Therefore it is suggested to choose smooth equivalence surfaces if possible rather than to use cubic ones directly.