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 , where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary . Exploiting theoretical results recently achieved in [13], 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.

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

BERETTA, ELENA;Manzoni Andrea;
2017-01-01

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 , where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary . Exploiting theoretical results recently achieved in [13], 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.
2017
nonlinear elliptic equation, inverse problem, reconstruction algorithm
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1028174
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