Open Collections

Detection of conductivity inclusions in a semilinear elliptic problem via a phase field approach

Banff International Research Station for Mathematical Innovation and Discovery

Abstract: we tackle the reconstruction of discontinuous coefficients in a semilinear elliptic equation from the knowledge of the solution on the boundary of the planar bounded domain. The problem is motivated by an application in cardiac electrophysiology. We formulate a constraint minimization problem involving a quadratic mismatch functional enhanced with a phase field term which penalizes the perimeter. After computing the optimality conditions of the phase-field optimization problem and introducing a discrete finite element formulation, we propose an iterative algorithm and prove convergence properties. Several numerical results are reported, assessing the effectiveness and the robustness of the algorithm in identifying arbitrarily-shaped inclusions. (Joint work with E. Beretta and L. Ratti)

Mathematics; Functional analysis; Calculus of variations and optimal control; optimization; Numerical analysis

video/mp4

Author affiliation: Politecnico di Milano

2019-12-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73002

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/