笛卡尔展开算法高效求解增广电场积分方程

Efficient solution of augmented electric field integral equation using accelerated cartesian expansion algorithm

摘要:
将多层快速笛卡尔展开算法(Multilevel Accelerated Cartesian Expansion Algorithm, MLACEA)用于求解理想导体目标的增广电场积分方程(Augmented Electric Field Integral Equation, AEFIE),详细推导了基于AEFIE矩量法(Method of Moments,MoM)的MLACEA算法的具体实现过程. 计算实例表明,在求解低频电磁散射问题及电路问题时基于AEFIE-MoM矩量法的MLACEA算法既具有非常高的计算精度、又可大幅度降低MoM的计算复杂度,使得其计算量和计算机内存需求可由原来MoM的O(N2)量级降低至MLACEA算法的O(N)量级.

Abstract:
The multilevel accelerated Cartesian expansion algorithm is used to solve augmented electric field integral equation for perfect electric conduct target. The multilevel accelerated Cartesian expansion algorithm based on augmented electric field integral equation is derived in detail. The numerical results are proposed to show that the accuracy of the algorithm is very high when solving low frequency electromagnetic scattering problems and circuit problems. While computational complexity can be reduced. The time consumption and memory consumption can be reduced from the original method of moment O(N²) level to this fast algorithm O(N) level.