# Computational Mathematics and Scientific Computing Seminar

## Low-frequency Electromagnetic Scattering in Multiply-connected Geometries

**Speaker:**
Michael O'Neil, CIMS

**Location:**
Warren Weaver Hall 1302

**Date:**
March 23, 2012, 10 a.m.

**Synopsis:**

A classical problem in electromagnetics concerns the solution of the time-harmonic Maxwell equations in the low-frequency and static regimes. When solving scattering problems from a simply connected body, standard integral equation methods provide sufficient means with which to calculate the scattered field. However, when the scatterer is multiply connected, topology plays a fundamental role and calculating the scattered field is not so straightforward. In fact, for multiply connected conductors, at zero frequency the standard boundary conditions on the tangential components of the incoming magnetic field do not uniquely determine the induced surface current, and thus do not uniquely determine the scattered field. With this in mind, we will describe a new consistency condition (independent of gauge) on the vector potential that overcomes this non-uniqueness and resolves a long-standing difficulty in inverting the Magnetic Field Integral Equation (MFIE). Numerical examples of this stabilizing consistency condition in axisymmetric geometries will be shown.