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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

An adaptive boundary algorithm for the reconstruction of boundary and initial data using the method of fundamental solutions for the inverse Cauchy-Stefan problem

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Author(s):
Reddy, G. M. M. [1] ; Nanda, P. [1] ; Vynnycky, M. [2] ; Cuminato, J. A. [3]
Total Authors: 4
Affiliation:
[1] Birla Inst Technol & Sci, Dept Math, Hyderabad Campus, Pilani 500078, Telangana - India
[2] Univ Limerick, Dept Math & Stat, Limerick V94 T9PX - Ireland
[3] Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, POB 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: COMPUTATIONAL & APPLIED MATHEMATICS; v. 40, n. 3 APR 2021.
Web of Science Citations: 0
Abstract

In this paper, a recent algorithm, based around the method of fundamental solutions (MFS), for reconstructing boundary data in inverse Stefan problems is extended and applied to inverse Cauchy-Stefan problems, wherein initial data must also be reconstructed. A key feature of the algorithm is that it is adaptive and iterates to find the optimal locations of the source points that are required by the method. Tikhonov regularization is used to take care of the ill-conditioned matrix that the MFS generates, with the algorithm being able to determine the optimal regularization parameter automatically. The effects of accuracy and random noise on the optimal location and number of source points are also evaluated. In addition, we consider a nonlinear variant of the inverse problem where one has to identify the moving boundary along with the missing initial data. Numerical experiments, carried out on five different benchmark examples, show promising results. (AU)

FAPESP's process: 16/19648-9 - Efficient numerical solution of the inverse Stefan problems using the method of fundamental solutions
Grantee:Gujji Murali Mohan Reddy
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 18/07643-8 - Industrial mathematics and practical asymptotics
Grantee:José Alberto Cuminato
Support type: Research Grants - Visiting Researcher Grant - International