An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems

Fuente: arXiv
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Main Authors: Jin, Bangti, Wang, Fengru, Zou, Jun
Format: Preprint
Published: 2025
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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