Differential operator acting on accelerated Cartesian expansion algorithm

• Published in: IET microwaves, antennas & propagation Vol. 11; no. 4; pp. 570 - 576
• Main Authors: Zheng, Yuteng, Zhao, Yanwen, Cai, Qiangming, Jia, Miaomiao, Nie, Zaiping
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 18.03.2017
• Subjects: accelerated Cartesian expansion; ACE; Algorithms; Cartesian; Differential equations; differential operator; differential operators; electric field integral equation; Integral equations; Microwave antennas; MLACEA; MLFMA; Multilevel; multilevel accelerated Cartesian expansion algorithm; multilevel fast multipole algorithm; Operators; Research Article; truncation error; Truncation errors; integral equations; ACE; multilevel accelerated Cartesian expansion algorithm; electric field integral equation; multilevel fast multipole algorithm; accelerated Cartesian expansion; truncation error; differential operators; differential operator; MLFMA; MLACEA
• ISSN: 1751-8725; 1751-8733; 1751-8733
• DOI: 10.1049/iet-map.2016.0592

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.