Year: 2024
Author: Yixin Tan, Shengfeng Zhu
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 1 : pp. 147–178
Abstract
We consider a shape reconstruction inverse problem constrained by a semi-linear elliptic interface problem in reaction diffusion. The existence of the model is shown. We perform shape sensitivity analysis and propose two numerical optimization algorithms based on the distributed shape gradient. The first algorithm allows shape changes and the second algorithm uses a level set method allowing shape and topological changes. Numerical results are presented to verify effectiveness of the algorithms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-075.010623
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 1 : pp. 147–178
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Shape reconstruction distributed shape gradient interface problem semi-linear elliptic level set method.