A two-stage method for reconstruction of parameters in diffusion equations
Numerical Analysis
2022-06-28 v1 Numerical Analysis
Optimization and Control
Abstract
Parameter reconstruction for diffusion equations has a wide range of applications. In this paper, we proposed a two-stage scheme to efficiently solve conductivity reconstruction problems for steady-state diffusion equations with solution data measured inside the domain. The first stage is based on total variation regularization of the log diffusivity and the split Bregman iteration method. In the second stage, we apply the K-means clustering for the reconstruction of ``blocky'' conductivity functions. The convergence of the scheme is theoretically proved and extensive numerical examples are shown to demonstrate the performance of the scheme.
Cite
@article{arxiv.2206.12750,
title = {A two-stage method for reconstruction of parameters in diffusion equations},
author = {Xuesong Bai and Elena Cherkaev and Dong Wang},
journal= {arXiv preprint arXiv:2206.12750},
year = {2022}
}