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arXiv · 1604.00883

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

Elena Beretta·Andrea Manzoni·Luca Ratti
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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.

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Elena Beretta, Andrea Manzoni, Luca Ratti. 2016-04-04. A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem. https://doi.org/10.1088/1361-6420/aa5c0a

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