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On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems
Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, Sao Carlos, SP, Brazil..
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.ORCID iD: 0000-0002-8318-1251
Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, Sao Carlos, SP, Brazil..
2018 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 26, no 9, p. 1249-1279Article in journal (Refereed) Published
Abstract [en]

Current practice in the use of the method of fundamental solutions (MFS) for inverse Stefan problems typically involves setting the source and collocation points at some distance, h, from the boundaries of the domain in which the solution is required, and then varying their number, N, so that the obtained solution fulfils a desired tolerance, Tol, when a random noise level d is added to the boundary conditions. This leads to an open question: can h andN be chosen simultaneously so that N is minimized, thereby leading to a lower computational expense in the solution of the inverse problem? Here, we develop a novel, simple and practical algorithm to help answer this question. The algorithm is used to study the effect of Tol and d on both h andN. Its effectiveness is shown through three test problems and numerical experiments show promising results: for example, even with d as high as 5% and Tol as low as 10-3, we are able to find satisfactory solutions for N as low as 8.

Place, publisher, year, edition, pages
Taylor & Francis, 2018. Vol. 26, no 9, p. 1249-1279
Keywords [en]
Inverse Stefan problem, method of fundamental solutions, algorithm, source points, noise
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-240248DOI: 10.1080/17415977.2017.1391244ISI: 000435684700002Scopus ID: 2-s2.0-85032383483OAI: oai:DiVA.org:kth-240248DiVA, id: diva2:1270566
Note

QC 20181213

Available from: 2018-12-13 Created: 2018-12-13 Last updated: 2018-12-13Bibliographically approved

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Vynnycky, Michael

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