An integral approach to the inverse electromagnetic shaping problem

An integral equation method is presented for solving the inverse shaping problem where a desired free boundary is specified in addition to the location of a number of source currents. The method results in a matrix equation which is solved for the source current magnitudes necessary to achieve the desired free boundary geometry. The integral approach described is based on the superposition integral equation for the magnetic vector potential. By limiting the sources to certain geometries, e.g. strips of surface current or line currents, analytical expressions for the vector potential due to all current sources can be used along with boundary conditions to form a system of linear equations in which the source currents are the unknowns. Surface currents are used as the predefined sources. The method is tested using a previously developed free boundary solution procedure