Fall 2015
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: October 16, 2015
Speaker: Darko Volkov
Department of Mathematical Sciences,
Worcester Polytechnic Institute
Title: "An All-Frequency Weakly-Singular Surface Integral Equation for Maxwell’s Equations in Dielectric Medi"
Abstract:
We develop and analyze a surface integral equation (SIE) whose solution pertains to numerical simulations of propagating time-harmonic electromagnetic waves in three dimensional dielectric media. This SIE is governed by an operator that is of the classical identity plus compact form. A novel feature of that second-kind SIE is that, when augmented with two stabilization equations, the corresponding reformulation does not suffer from spurious resonances or low-frequency breakdown.
This SIE formulation provides a tool for developing a new class of efficient and high-order algorithms (with numerical analysis) for simulation of the three dimensional dielectric media model from low- to high-frequencies. This was achieved in earlier work in the case of perfect conductors. We will explain the challenges (due to the stabilization constraints) in extending this to the dielectric case.
This is joint work with M. Ganesh (Colorado School of Mines).