Abstract
A new method to localize a static point source buried in a nonhomogeneous bounded domain composed of finitely many homogeneous parts separated by interfaces of arbitrary shapes was established. The source can be a simple point charge or current or a dipole of them. The method requires only the knowledge of the potential function Φ( x, y, z) at five or six points on the outermost interface depending on whether the source is simple or dipole. The new and basic feature of the method consists of determining the potential function Φ 0( x, y, z) which would be observed if the whole space was filled with a homogeneous material. Then, in the case of a simple source, the position P 0 as well as the strength s can be determined, in general, by solving a system of three linear algebraic equations. When the source consists of a dipole, its position P 0 and moment p → can be found by solving a system of six nonlinear algebraic equations. The determination of Φ 0, P 0 and s (or p → ) is achieved iteratively by solving the above-mentioned algebraic equations along with a singular integral equation satisfied by Φ 0. Some illustrative examples show the applicability and accuracy of the method. The method can have effective applications in heat conduction, matter diffusion, electrostatics, steady-state current flow, electroencephalography, electrocardiography, etc.
Published Version
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