This paper has been withdrawn by Yuxuan Huang
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Abstract:In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward solution is constructed using a Krylov sequence, while the source term is recovered via the conjugate gradient (CG) method. Under a weak regularity assumption on the solution of the parabolic partial differential equations (PDEs), we establish convergence of the forward solution and provide a rigorous error estimate for our method. Numerical results demonstrate that our approach offers substantial computational savings compared to the traditional finite element method (FEM) and retains equivalent accuracy.
From: Yuxuan Huang [view email]
[v1]
Fri, 9 Jun 2023 05:25:54 UTC (3,986 KB)
[v2]
Mon, 1 Jun 2026 17:05:37 UTC (1 KB) (withdrawn)
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