Modeling Magnetic Diffusion

Kevin O'Neill

Adjunct Professor, Thayer School of Engineering

This talk treats computational methods applied to certain electromagnetic phenomena in underground remote sensing. The research is undertaken to help address the long term environmental cleanup problem posed by unexploded ordnance (UXO) on lands where military activities or conflicts have taken place. UXO pose dangers in the event that they are disturbed such that they may explode; or they may leak contaminants into the surrounding environment.
Currently our sensors cannot detect explosive encased in metal underground, thus we must detect and characterize the metal shells. The requisite surveying and remote sensing must employ electromagnetic devices operating at low frequencies in order to penetrate the ground. Together with the constraint that we must survey only from above ground, this means that resolution is quite limited - no visual images of the sort available in medical settings are possible. Instead, one must analyze the characteristics of complex electromagnetic responses to infer information that might be useful in discriminating harmful materials from innocuous objects.
Our numerical modeling and analysis have been applied to coupled Laplace and Helmholtz equations. While the latter is frequently regarded as a wave equation, in fact in this context it supports only diffusion. Computational results have been vital for understanding the underlying low frequency electromagnetic phenomena, for knowing what to expect and what might be useful, and for specific discrimination processing of signals. This talk summarizes some of the progress we have achieved by applying integral equation approaches, "thin skin" approximations, the method of auxiliary sources, the standardized excitations approach, and other methods. A recurrent theme is the achievement of leaps in computational efficiency by avoiding computing. That is, we bring to bear sagacious changes of basis, limitations on the spectrum of operators, or specially applicable approximations and manipulations of governing relations. These avoid tangling with intractable or at least daunting calculations that would be required by more obvious, straight-ahead approaches and thus lead more directly to the desired results.

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