An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912701911924736 |
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| author | Jin, Bangti Wang, Fengru Zou, Jun |
| author_facet | Jin, Bangti Wang, Fengru Zou, Jun |
| contents | We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very limited data are available, even with only one pair of lateral Cauchy data, and enjoys remarkable numerical stability for noisy data and over an extended time horizon. The method is formulated in an abstract framework, and is applicable to linear and nonlinear parabolic problems, including linear, nonlinear, and mixed-type inhomogeneities. Numerical experiments across diverse scenarios show its effectiveness and robustness against the data noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08197 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems Jin, Bangti Wang, Fengru Zou, Jun Numerical Analysis We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very limited data are available, even with only one pair of lateral Cauchy data, and enjoys remarkable numerical stability for noisy data and over an extended time horizon. The method is formulated in an abstract framework, and is applicable to linear and nonlinear parabolic problems, including linear, nonlinear, and mixed-type inhomogeneities. Numerical experiments across diverse scenarios show its effectiveness and robustness against the data noise. |
| title | An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.08197 |