TY - JOUR
T1 - A heat polynomial method for inverse cylindrical one-phase Stefan problems
AU - Kassabek, Samat A.
AU - Kharin, Stanislav N.
AU - Suragan, Durvudkhan
N1 - Funding Information:
The authors were supported by the Nazarbayev University Program 091019CRP2120 ?Centre for Interdisciplinary Studies in Mathematics (CISM)? and the second author was supported by the grant AP09258948 ?A free boundary problems in mathematical models of electrical contact phenomena?.
Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application of the heat polynomials method (HPM) for solving one- and two-dimensional inverse Stefan problems, where the boundary data is reconstructed on a fixed boundary. We present numerical results illustrating an application of the heat polynomials method for several benchmark examples. We study the effects of accuracy and measurement error for different degree of heat polynomials. Due to ill-conditioning of the matrix generated by HPM, optimization techniques are used to obtain regularized solution. Therefore, the sensitivity of the method to the data disturbance is discussed. Theoretical properties of the proposed method, as well as numerical experiments, demonstrate that to reach accurate results it is quite sufficient to consider only a few of the polynomials. The heat flux for two-dimensional inverse Stefan problem is reconstructed and coefficients of a solution function are found approximately.
AB - In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application of the heat polynomials method (HPM) for solving one- and two-dimensional inverse Stefan problems, where the boundary data is reconstructed on a fixed boundary. We present numerical results illustrating an application of the heat polynomials method for several benchmark examples. We study the effects of accuracy and measurement error for different degree of heat polynomials. Due to ill-conditioning of the matrix generated by HPM, optimization techniques are used to obtain regularized solution. Therefore, the sensitivity of the method to the data disturbance is discussed. Theoretical properties of the proposed method, as well as numerical experiments, demonstrate that to reach accurate results it is quite sufficient to consider only a few of the polynomials. The heat flux for two-dimensional inverse Stefan problem is reconstructed and coefficients of a solution function are found approximately.
KW - approximate solution
KW - heat flux function
KW - heat polynomials
KW - Inverse Stefan problems
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U2 - 10.1080/17415977.2021.2000977
DO - 10.1080/17415977.2021.2000977
M3 - Article
AN - SCOPUS:85119343653
SN - 1741-5977
VL - 29
SP - 3423
EP - 3450
JO - Inverse Problems in Science and Engineering
JF - Inverse Problems in Science and Engineering
IS - 13
ER -