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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.16711 |
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| _version_ | 1866916410821705728 |
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| author | Li, Xinyan |
| author_facet | Li, Xinyan |
| contents | In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calderón problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian, and the parameter reconstruction is formulated into a variational problem based on Tikhonov regularization to obtain a stable and accurate solution. Conjugate gradient method is utilized to solve the variational problem. Moreover, we also provide a suggestion to choose the regularization parameter. Numerical experiments are performed to illustrate the efficiency and effectiveness of the developed method and verify the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A numerical method for reconstructing the potential in fractional Calderón problem with a single measurement Li, Xinyan Numerical Analysis In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calderón problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian, and the parameter reconstruction is formulated into a variational problem based on Tikhonov regularization to obtain a stable and accurate solution. Conjugate gradient method is utilized to solve the variational problem. Moreover, we also provide a suggestion to choose the regularization parameter. Numerical experiments are performed to illustrate the efficiency and effectiveness of the developed method and verify the theoretical results. |
| title | A numerical method for reconstructing the potential in fractional Calderón problem with a single measurement |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.16711 |