Abstract
We study a recovery problem for unknown boundary data in static electromagnetism. One part of the boundary is over-determined, i.e., boundary conditions of two kinds are simultaneously imposed thereon. The other part of the boundary is unreachable, i.e., the boundary data are unknown and it has to be determined as a part of the problem. This type of problem occurs, e.g., in passive electromagnetic shielding. We design a constructive algorithm for the solution of this problem. The numerical scheme is based on the steepest descent method for the minimization of a regularized cost functional, having its derivative determined via an adjoint method. We analyse the properties of the cost functional and we prove the convergence of the minimization process. The method is supported by numerical experiments.
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