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An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).ORCID iD: 0000-0002-7123-2066
Orebrov Univ, Sch Sci & Technol, Dept Math, Orebro, Sweden.
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2018 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 26, no 10, p. 1464-1489Article in journal (Refereed) Published
Abstract [en]

We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique, we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the a posteriori error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA.

Place, publisher, year, edition, pages
Oxon, UK: Taylor & Francis, 2018. Vol. 26, no 10, p. 1464-1489
Keywords [en]
Rate constant distribution, inverse problem, regularization, adaptive finite element, a posteriori error estimation
National Category
Computational Mathematics Geophysics Chemical Engineering
Research subject
Chemistry
Identifiers
URN: urn:nbn:se:kau:diva-68754DOI: 10.1080/17415977.2017.1411912ISI: 000438638300005OAI: oai:DiVA.org:kau-68754DiVA, id: diva2:1239464
Note

Zhang, Yue saknar cas! 20181018

Available from: 2018-08-16 Created: 2018-08-16 Last updated: 2019-03-28Bibliographically approved

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Forssén, PatrikFornstedt, Torgny

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