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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 18, Issue 2

Issues

Domain Decomposition Methods for Recovering Robin Coefficients in Elliptic and Parabolic Systems

Daijun Jiang
  • Corresponding author
  • School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, P. R. China
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/ Hui Feng
Published Online: 2017-06-02 | DOI: https://doi.org/10.1515/cmam-2017-0007

Abstract

We shall derive and propose several efficient domain decomposition methods for solving the nonlinear inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The highly ill-posed inverse problems are transformed into output least-squares nonlinear and non-convex minimizations with classical Tikhonov regularization. The Levenberg–Marquardt method is applied to transform the non-convex minimizations into convex minimizations, which will be solved by several efficient domain decomposition methods. The methods are completely local and the local minimizers have explicit expressions within the subdomains. Several numerical experiments are presented to show the accuracy and efficiency of the methods; in particular, the convergence seems nearly optimal in the sense that the iteration number of the methods is nearly independent of mesh sizes.

Keywords: Robin Inverse Problems; Domain Decomposition Method; Levenberg–Marquardt Method, Explicit Subdomain Minimizer

MSC 2010: 31A25; 65M55; 90C25

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About the article

Received: 2017-03-28

Revised: 2017-04-05

Accepted: 2017-04-06

Published Online: 2017-06-02

Published in Print: 2018-04-01


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11401241

Award identifier / Grant number: 11571265

Award identifier / Grant number: 11661161017

Award identifier / Grant number: 91130022

Award identifier / Grant number: 10971159

Award identifier / Grant number: 11161130003

Funding Source: China Postdoctoral Science Foundation

Award identifier / Grant number: 20130141110026

The first author was financially supported by National Natural Science Foundation of China (nos. 11401241 and 11571265) and NSFC-RGC (China-Hong Kong, no. 11661161017). The second author was supported by National Natural Science Foundation of China (nos. 91130022, 10971159 and 11161130003), and the Doctoral Fund of Ministry of Education of China (no. 20130141110026).


Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 2, Pages 257–274, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0007.

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