A new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFs

被引：32
作者：
Amirfakhrian, M. [1 ]
Arghand, M. [1 ]
Kansa, E. J. [2 ]
机构：
[1] Islamic Azad Univ, Cent Tehran Branch, Dept Math, Tehran, Iran
[2] Convergent Solut LLC, Livermore, CA USA
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2016年 / 64卷
关键词：
Meshless methods; Radial basis functions; Method of fundamental solutions; Inverse heat source problem; Time-dependent heat source problems; Tikhonov regularization (TR); Ill-posed problems; PARTIAL-DIFFERENTIAL-EQUATIONS; SINGULAR BOUNDARY METHOD; UNKNOWN SOURCE-TERM; CONDUCTION PROBLEMS; NUMERICAL-SOLUTION; SHAPE-PARAMETERS; CONDITION NUMBER; MESHLESS METHOD; ERROR ANALYSIS; CAUCHY-PROBLEM;
D O I：
10.1016/j.enganabound.2015.12.016
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This paper presents a meshless numerical scheme to solve the inverse heat source time dependent problem. Fundamental solutions of heat equations and radial basis functions (RBFs) are used to obtain a numerical solution. Since the coefficient matrix may be ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulting system of linear equations. Therefore, the generalized cross validation (GCV) criterion is applied to choose a regularization parameter. The accuracy and efficiency of the proposed method is illustrated by some numerical examples. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：278 / 289
页数：12
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