A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem. (15th February 2017) - Beretta, Elena; Manzoni, Andrea; Ratti, Luca
Abstract: In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomogeneities located inside a domain Ω, where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary ∂ Ω . Exploiting theoretical results recently achieved in [013 ], we implement a reconstruction procedure based on the computation of the topological gradient of a suitable cost functional. Numerical results obtained for several test cases finally assess the feasibility and the accuracy of the proposed technique.