2023 A noniterative reconstruction method for the inverse potential problem for a time-fractional diffusion equation
Mohamed BenSalah
Topol. Methods Nonlinear Anal. 62(2): 431-454 (2023). DOI: 10.12775/TMNA.2023.004

Abstract

This paper is concerned with the reconstruction of the support of the potential term for a time-fractional diffusion equation from the final measured data. The aim of this paper is to propose an accurate approach based on the topological derivative method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing a given cost function. We derive a topological asymptotic expansion for the fractional model. The unknown support is reconstructed using the level-set curve of the topological gradient. We finally make some numerical examples proving the efficiency and accuracy of the proposed algorithm.

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Mohamed BenSalah. "A noniterative reconstruction method for the inverse potential problem for a time-fractional diffusion equation." Topol. Methods Nonlinear Anal. 62 (2) 431 - 454, 2023. https://doi.org/10.12775/TMNA.2023.004

Information

Published: 2023
First available in Project Euclid: 19 January 2024

Digital Object Identifier: 10.12775/TMNA.2023.004

Keywords: fractional derivative , inverse problem , sensitivity analysis , topology optimization

Rights: Copyright © 2023 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.62 • No. 2 • 2023
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