### The Method of Auxiliary Sources (MAS): theory and application to
various inverse scattering problems

* *Fridon Shubitidze

Thayer School, Dartmouth College

The MAS is a numerical technique, originally designed for solving various
electromagnetic radiation and scattering problems. MAS is a robust, easy to
implement, and accurate method for studying a wide range of electromagnetic
problems, such as the investigation of waveguide structures, antennas,
scattering, electromagnetic wave propagation in complex media, etc.
Recently, the MAS has also been used successfully for the analysis of low
frequency electromagnetic induction (EMI) scattering phenomena for detection
and discrimination subsurface metallic objects particularly unexploded
ordnances (UXO). For EMI electromagnetic induction, boundary value problems
are solved numerically by representing the electromagnetic fields in each
domain of the structure under investigation by a finite linear combination
of analytical solutions of the relevant field equations, corresponding to
sources situated at some distance away from the boundaries of each domain.
These "auxiliary sources" producing these analytical solutions are chosen to
be elementary currents/charges located on fictitious auxiliary surface(s),
usually conforming to the actual surface(s) of the structure. The method
only requires points on the auxiliary and actual surfaces, without resorting
to the detailed mesh structures as required by other methods (finite element
method (FEM), boundary element method (BEM) etc).

In this talk, the mathematical bases of the MAS will be presented and the
scattered field singularities will be discussed in order to illustrate
relation between the method's numerical stability and field's singularities.
Finally, applicability of the MAS technique to various boundary value
electromagnetic problems such as UXO detection and discrimination, EMI
scattering from photonic band gap structures will be demonstrated.

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