Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data

Jiang, Jinhui; Shadi Mohamed, M.; Seaid, Mohammed; Li, Hongqiu

Abstract

We propose an efficient inverse solver for identifying the diffusion coefficient based on few random measurements which can be contaminated with noise. We focus mainly on problems involving solutions with steep heat gradients common with sudden changes in the temperature. Such steep gradients can be a major challenge for numerical solutions of the forward problem as they may involve intensive computations especially in the time domain. This intensity can easily render the computations prohibitive for the inverse problems that requires many repetitions of the forward solution. Compared to the literature, we propose to make such computations feasible by developing an iterative approach that is based on the partition of unity finite element method, hence, significantly reducing the computations intensity. The proposed approach inherits the flexibility of the finite element method in dealing with complicated geometries, which otherwise cannot be achieved using analytical solvers. The algorithm is evaluated using several test cases. The results show that the approach is robust and highly efficient even when the input data is contaminated with noise.

Citation

Jiang, J., Shadi Mohamed, M., Seaid, M., & Li, H. (2021). Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data. Archive of Applied Mechanics, 91(4), 1623-1639. https://doi.org/10.1007/s00419-020-01844-7

• Journal Article Type: Article
• Acceptance Date: Nov 6, 2020
• Online Publication Date: Nov 24, 2020
• Publication Date: 2021-04
• Deposit Date: Oct 26, 2021
• Journal: Archive of Applied Mechanics
• Print ISSN: 0939-1533
• Electronic ISSN: 1432-0681
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 91
• Issue: 4
• Pages: 1623-1639
• DOI: https://doi.org/10.1007/s00419-020-01844-7
• Public URL: https://durham-repository.worktribe.com/output/1225219