Identifying an inaccessible electrostatic source with gradient-based inverse problem methodology and boundary elements

Identification problems are inverse problems in which an unknown part of the system is identified using some given information or data. Deterministic and/or nondeterministic methods were applied with inverse problem methodology (IPM) to solve identification problems. In this work, gradient-based inverse problem methodology (GIPM) is successfully employed with boundary elements to identify an electrostatic source using some data monitored along accessible boundaries. The boundary integral formulation is based on an integral equation, which solves only for the surface potentials due to a dielectric in the presence of an electric field. A modified version of pattern search is used at multilevels to overcome the difficulties mentioned above.