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Volume 14, Issue 1
Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem

Yixin Tan & Shengfeng Zhu

East Asian J. Appl. Math., 14 (2024), pp. 147-178.

Published online: 2024-01

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  • 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.

  • AMS Subject Headings

49M41, 49N45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-147, author = {Tan , Yixin and Zhu , Shengfeng}, title = {Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-075.010623 }, url = {http://global-sci.org/intro/article_detail/eajam/22323.html} }
TY - JOUR T1 - Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem AU - Tan , Yixin AU - Zhu , Shengfeng JO - East Asian Journal on Applied Mathematics VL - 1 SP - 147 EP - 178 PY - 2024 DA - 2024/01 SN - 14 DO - http://doi.org/10.4208/eajam.2023-075.010623 UR - https://global-sci.org/intro/article_detail/eajam/22323.html KW - Shape reconstruction, distributed shape gradient, interface problem, semi-linear elliptic, level set method. AB -

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.

Yixin Tan & Shengfeng Zhu. (2024). Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem. East Asian Journal on Applied Mathematics. 14 (1). 147-178. doi:10.4208/eajam.2023-075.010623
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