Numerical Electromagnetic Modeling for Three-Dimensional Inspection of Ferrous Metals
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The problem that we are trying to solve is: Given an excitation source, which is known to us, and a scattered field, which we can measure (albeit somewhat inaccurately, because of noise and the like), determine the spatial distribution of the electromagnetic parameters, µ, and σ, where µ is the magnetic permeability and σ the electrical conductivity. This allows us to determine the structure of a body in free space, or the structure of an internal flaw (or anomalous region) within a given body whose properties, such as size, shape and electrical parameters, are known to us. Throughout this paper we will consider only isotropic bodies, which means that the conductivity and magnetic permeability are scalar functions of positions.