A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem. (15th February 2017)

• Record Type: Journal Article
• Authors: Beretta, Elena; Manzoni, Andrea; Ratti, Luca
• Is Part Of: Inverse problems. Volume 33:Number 3(2017:Mar.)
• Publication Date: 2017-02-15
• Subjects: nonlinear elliptic equation -- inverse problem -- reconstruction algorithm; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa5c0a
• Languages: English
• ISSNs: 0266-5611

Abstract

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.