2025/03/18 by Machida, Manabu, Notsu, Hirofumi, Rabago, Julius Fergy Tiongson
#49K40 #49N45 #49Q10 #65N21 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2503.14764
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. The main objective is to recover the absorption coefficient from a single boundary measurement. While conventional gradient-based methods rely on the Fréchet derivative of a cost functional with respect to the unknown parameter, we also utilize its shape derivative with respect to the unknown boundary interface for recovery. This non-conventional approach addresses the problem of parameter recovery from a single measurement, which represents the key innovation of this work. Numerical experiments confirm the effectiveness of the proposed method, even for intricate and non-convex boundary interfaces.