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

Authors
  • Beretta, Elena
  • Manzoni, Andrea
  • Ratti, Luca
Type
Preprint
Publication Date
Apr 04, 2016
Submission Date
Apr 04, 2016
Identifiers
arXiv ID: 1604.00883
Source
arXiv
License
Yellow
External links

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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