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An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem
Univ Sao Paulo Sao Carlos, Dept Appl Math & Stat, Inst Math & Comp Sci, POB 668, BR-13560970 Sao Paulo, Brazil..
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.ORCID iD: 0000-0002-8318-1251
Univ Sao Paulo Sao Carlos, Dept Appl Math & Stat, Inst Math & Comp Sci, POB 668, BR-13560970 Sao Paulo, Brazil..
2019 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 349, p. 21-40Article in journal (Refereed) Published
Abstract [en]

In this exposition, a simple practical adaptive algorithm is developed for efficient and accurate reconstruction of Neumann boundary data in the inverse Stefan problem, which is a highly nontrivial task. Primarily, this algorithm detects the satisfactory location of the source points from the boundary in reconstructing the boundary data in the inverse Stefan problem efficiently. To deal with the ill-conditioning of the matrix generated by the MFS, we use Tikhonov regularization and the algorithm is designed in such a way that the optimal regularization parameter is detected automatically without any use of traditional methods like the discrepancy principle, the L-curve criterion or the generalized cross-validation (GCV) technique. Furthermore, this algorithm can be thought of as an alternative to the concept of Beck's future temperatures for obtaining stable and accurate fluxes, but without it being necessary to specify data on any future time interval. A MATLAB code for the algorithm is discussed in more-than-usual detail. We have studied the effects of accuracy and measurement error (random noise) on both optimal location and number of source points. The effectiveness of the proposed algorithm is shown through several test problems, and numerical experiments indicate promising results.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2019. Vol. 349, p. 21-40
Keywords [en]
Inverse Stefan problem, Method of fundamental solutions, Tikhonov regularization, Neumann data, Adaptive algorithm
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-241297DOI: 10.1016/j.cam.2018.09.004ISI: 000454969100002Scopus ID: 2-s2.0-85054454052OAI: oai:DiVA.org:kth-241297DiVA, id: diva2:1291061
Note

QC 20190222

Available from: 2019-02-22 Created: 2019-02-22 Last updated: 2019-02-22Bibliographically approved

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Vynnycky, Michael

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