Location search techniques for a grounded conductor

This paper deals with the inverse problem of inferring the position of an electrically grounded conductor D from a single measurement of electric field (Cauchy data) on the boundary of a smooth domain Ω ⊂ Rⁿ, n = 2,3, that contains D̄. We present new simple and real time algorithms for locating D with a rigorous mathematical verification. These location search techniques use a special property of the surface charge density of the electrically grounded conductor. The computations in these location search methods are very simple, so that the location of a moving grounded conductor can be detected in a instant even in three dimensions.