Differential operator acting on accelerated Cartesian expansion algorithm

Abstract

The multilevel accelerated Cartesian expansion algorithm (MLACEA) and its incorporation with multilevel fast multipole algorithm (MLFMA) have been studied and used for solving practical problems. The algorithms are successful, but the authors found the truncation error of accelerated Cartesian expansion (ACE) is sensitive with the differential operator. Integral equations in electromagnetics always contain differential operators, so the precision will be influenced when trying to accelerate the method of moments with MLACE algorithm. The reason of why differential operator can influence the precision of the ACE is given, and also proved by numerical experimentation. To meet the requirements of piratical application, electric field integral equation is deeply investigated. The studies also extend to the hybrid algorithm MLFMA-MLACEA and performances are tested on different implementation.