Sentinels for the Identification of an Unknown Boundary

Abstract

A method for the identification of a part of the boundary in a diffusion problem is proposed. It is based on sentinels. A linearization scheme is used and the local convergence is proved. The method defines and proves the existence of approximate sentinels for the linearized system and builds a fixed point algorithm. To prove the existence of the linearized sentinels, the problem is reformulated as an approximate control problem and solved by a convex analysis method. The contraction property of the fixed point method follows straightforward from the definition of approximate the sentinels. Finally numerical examples are presented.