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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