Determine the point source of the heat equation with sparse boundary measurements
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915138684059648 |
|---|---|
| author | Gu, Qiling Zhang, Wenlong Zhang, Zhidong |
| author_facet | Gu, Qiling Zhang, Wenlong Zhang, Zhidong |
| contents | In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is considered. We propose a numerical method to reconstruct the location of a Dirac point source by reformulating the inverse problem as a least-squares optimization problem, which is efficiently solved using a gradient descent algorithm. Numerical experiments confirm the accuracy of the proposed method and demonstrate its robustness to noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determine the point source of the heat equation with sparse boundary measurements Gu, Qiling Zhang, Wenlong Zhang, Zhidong Numerical Analysis In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is considered. We propose a numerical method to reconstruct the location of a Dirac point source by reformulating the inverse problem as a least-squares optimization problem, which is efficiently solved using a gradient descent algorithm. Numerical experiments confirm the accuracy of the proposed method and demonstrate its robustness to noise. |
| title | Determine the point source of the heat equation with sparse boundary measurements |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.03018 |