Meshless Schemes for Solving Volume Integral Equations in Electromagnetics
Prof. Meisong Tong
Department of Electronic Science and Technology
Tongji University, Shanghai, China
Volume integral equations (VIEs) are indispensable for solving inhomogeneous or anisotropic electromagnetic (EM) problems by integral equation approach. The solution of VIEs strongly relies on an appropriate discretization for volume integral domains, and tetrahedral discretization is usually preferred for arbitrary geometric shapes. Unlike discretizing a surface domain, discretizing a volume domain is very inconvenient in practice, and special commercial software is needed in general even for a simple and regular geometry. To reduce the cost of descretizing volume domains, especially remove the constraint of mesh conformity in the traditional method of moments (MoM), we proposed a novel meshless scheme for solving the VIEs recently. The scheme is based on the transformation of volume integrals into boundary integrals through the Green-Gauss theorem when integral kernels are regularized by excluding a small cylinder enclosing an observation node. The original integral domain represented by the object is also expanded to a cylindrical domain circumscribing the object to facilitate the evaluation of boundary integrals. The singular integrals over the small cylinder are specially handled with singularity subtraction techniques. Several numerical examples for solving EM scattering problems are presented to illustrate the scheme and good results can be observed.
Mei Song Tong received the Ph. D. degree in electrical engineering from Arizona State University, Tempe, Arizona, USA, in 2004. He is currently a Distinguished Professor and the Head of the Department of Electronic Science and Technology, School of Electronics and Information Engineering, Tongji University, Shanghai, China. Before he joined Tongji University, he was a Research Scientist at the Center for Computational Electromagnetics and Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA. His research interests include electromagnetic field theory, antenna theory and technology, design of RF/microwave circuits and devices, interconnect and packaging analysis, inverse scattering for microwave imaging, multiphysics electromagnetics, and numerical techniques. He has authored or co-authored more than 100 papers published in refereed journals and conference proceedings, and co-authored a book: Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan & Claypool, San Rafael, CA, 2008. Prof. Tong is a fellow of Electromagnetics Academy, a senior member of IEEE, a full member (Commission B) of USNC/URSI, and a member of AAAS, ACES, Sigma Xi Society, etc. He is serving as an associate editor or guest editor for several well-known international journals, including IEEE Transactions on Antennas and Propagation, IEEE Transactions on Components, Packaging and Manufacturing Technology, Progress in Electromagnetics Research, Journal of Electromagnetic Waves and Applications, International Journal of Numerical Modeling: Electronic Networks, Devices and Fields, etc. Prof. Tong is currently a visiting professor at the University of Illinois at Urbana-Champaign and an honorary professor at the University of Hong Kong, Hong Kong, China. He won a visiting professor award from Kyoto University, Kyoto, Japan, in 2012.