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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 26, Issue 1

Issues

A modified coupled complex boundary method for an inverse chromatography problem

Xiaoliang Cheng / Guangliang Lin / Ye Zhang / Rongfang Gong / Mårten Gulliksson
Published Online: 2017-05-05 | DOI: https://doi.org/10.1515/jiip-2016-0057

Abstract

Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

Keywords: Chromatography; adsorption isotherm; inverse problem; coupled complex boundary method; Tikhonov regularization

MSC 2010: 65N21; 65F22; 65M32; 65K15; 76R50

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About the article

Received: 2016-09-10

Revised: 2017-03-03

Accepted: 2017-03-07

Published Online: 2017-05-05

Published in Print: 2018-02-01


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11571311

Award identifier / Grant number: 11401304

Funding Source: Swedish Foundation for International Cooperation in Research and Higher Education

Award identifier / Grant number: IB2015-5989

Funding Source: Knowledge Foundation

Award identifier / Grant number: 20150233

Funding Source: Vetenskapsrådet

Award identifier / Grant number: 2015-04627

The work was partially supported by NSFC (grant numbers 11571311 and 11401304), STINT (grant number IB2015-5989), KK HÖG (grant number 20150233), ÅForsk (grant number 15/497), and VR (grant number 2015-04627).


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 26, Issue 1, Pages 33–49, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2016-0057.

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