Green's Functions In The Numerical Solution Of Some Inverse Boundary Value Problems

We use boundary elements, with least squares optimization, to solve identification problems in electrostatics and steady state heat conduction in conductive plates with simple shapes, e.g. the circular wedge. The plate has a hole in it, with a flux across the hole boundary. Voltage or heat is applied to part of the plate edge; the remainder of the plate edge is grounded or insulated. For the inverse problem, an additional voltage or heat measurement is taken on an insulated part of the plate edge; from this extra measurement we (1) determine the structure of the hole, given the flux across its boundary, or (2) given the hole, determine the flux across its boundary. Special boundary value properties of Green's functions are exploited in this numerical treatment of the identification problem.