A method of fundamental solutions for the one-dimensional inverse Stefan problem

被引：74

作者：

Johansson, B. T. ^{[1
]}

Lesnic, D. ^{[2
]}

Reeve, T. ^{[1
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[2] Univ Leeds, Dept Appl Math, Leeds LS2 9JT, W Yorkshire, England

来源：

APPLIED MATHEMATICAL MODELLING | 2011年 / 35卷 / 09期

基金：

英国工程与自然科学研究理事会;

关键词：

Heat conduction; Method of fundamental solutions (MFS); Inverse Stefan problem; HEAT-CONDUCTION; NUMERICAL-SOLUTION; BOUNDARY; RECONSTRUCTION; MOLLIFICATION; FLUX;

D O I：

10.1016/j.apm.2011.03.005

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T,T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：4367 / 4378

页数：12

共 46 条

[1] On the choice of source points in the method of fundamental solutions [J].

Alves, Carlos J. S. .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (12) :1348-1361

[2] An inverse Stefan problem: Identification of boundary value [J].

Ang, DD ;

Dinh, APN ;

Thanh, DN .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 66 (1-2) :75-84

[3] The method of fundamental solutions for linear diffusion-reaction equations [J].

Balakrishnan, K ;

Ramachandran, PA .

MATHEMATICAL AND COMPUTER MODELLING, 2000, 31 (2-3) :221-237

[4]

Beck J.V., 1985, Inverse Heat Conduction: Ill-Posed Problems

[5] Reconstruction of time-dependent boundary heat flux by a BEM-based inverse algorithm [J].

Bialecki, Ryszard ;

Divo, Eduardo ;

Kassab, Alain .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2006, 30 (09) :767-773

[6] FUNDAMENTAL-SOLUTIONS METHOD FOR ELLIPTIC BOUNDARY-VALUE PROBLEMS [J].

BOGOMOLNY, A .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1985, 22 (04) :644-669

[7] THE ONE PHASE STEFAN PROBLEM SUBJECT TO THE SPECIFICATION OF ENERGY [J].

CANNON, JR ;

VANDERHOEK, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1982, 86 (01) :281-291

[8] REMARKS ON ONE-PHASE STEFAN PROBLEM FOR HEAT EQUATION WITH FLUX PRESCRIBED ON FIXED BOUNDARY [J].

CANNON, JR ;

PRIMICER.M .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1971, 35 (02) :361-&

[9]

CANNON JR, 1967, J MATH MECH, V17, P1

[10] Methods of fundamental solutions for time-dependent heat conduction problems [J].

Chantasiriwan, S .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2006, 66 (01) :147-165

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