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Singularity Treatment Techniques for Solving Electromagnetic Integral Equations

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Electromagnetic (EM) problems can be described by integral equation approaches, which include surface integral equations (SIEs), volume integral equations (VIEs), and volume-surface integral equations (VSIEs). All these equations include the L operator, K operator, or both. The kernel of the L operator is the dyadic Green’s function, which includes a double gradient operation on the scalar Green’s function and results in 1/R3 hypersingular integrals (HSIs), where R is the distance between a source point and an observation point or field point. Although the HSIs could be reduced to 1/R weakly singular integrals (WSIs) in the method of moments (MoM) solution by using a divergence-conforming basis/testing function like the Rao-Wilton-Glisson (RWG) basis/testing function, we must carefully handle the HSIs in some numerical methods like Nyström method, meshless method, or boundary element method because they do not use any basis and testing functions. In the K operator, the kernel is a single gradient operator on Green's scalar function, yielding 1/R2 strongly singular integrals (SSIs). The SSIs always exist in the K operator, even in the MoM solutions. It could also exist in the L operator in the MoM when the RWG basis function is used to represent both the electric and magnetic current densities in penetrable objects. The accurate and efficient evaluation of singular integrals in matrix elements is essential for solving EM integral equations because they significantly impact the numerical solutions. In this talk, we will present some robust singularity treatment techniques we developed for those singular integrals and provide numerical examples to demonstrate their applications for solving real-world problems.
The meeting is the in-person event. However, a zoom link is given for remote attending.
Here is the Zoom link: https://montclair.zoom.us/j/2423669227
Venue: Montclair State University
Room: Center for Environmental and Life Sciences (CELS) Building, Room CELS 120
Parking: Red Hawk Deck, Montclair State University
Event Time: 6:00 PM to 7:30 PM
5:45 PM – Refreshments (Pizza) and Networking
6:00 PM-7:00 PM: Talk by Mei Song Tong
You do not have to be an IEEE Member to attend. Refreshment is free for all attendees. Please invite your friends and colleagues to take advantage of this Invited Distinguished Lecture.
Co-sponsored by: IEEE North Jersey Section and IEEE Montclaire University Student Branch
Speaker(s): Prof. Meisong Tong,
Agenda:
Venue: Montclair State University
Room: Center for Environmental and Life Sciences (CELS) Building, Room CELS 120
Parking: Red Hawk Deck, Montclair State University
Event Time: 6:00 PM to 7:30 PM
5:45 PM – Refreshments (Pizza) and Networking
6:00 PM-7:00 PM: Talk by Mei Song Tong
You do not have to be an IEEE Member to attend. Refreshment is free for all attendees. Please invite your friends and colleagues to take advantage of this Invited Distinguished Lecture.
Bldg: CELS Building, Room CELS 120, Montclair State University, Center for Environmental and Life Sciences (CELS) , Montclair, New Jersey, United States, 07043

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