A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

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 $\Omega$, where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary $\partial \Omega$. Exploiting theoretical results recently achieved in [11], 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.

Cited by in corpus (5)

• Quasi-Newton Methods for Topology Optimization Using a Level-Set Method
• Adjoint based methods to compute higher order topological derivatives with an application to elasticity
• Topological derivative for PDEs on surfaces
• On a nonlinear model in domains with cavities arising from cardiac electrophysiology
• Adaptive Approximations of Inclusions in a Semilinear Elliptic Problem Related to Cardiac Electrophysiology