逆热传导问题的一种新型无网格方法  

A new meshless method for an inverse heat conduction problem

作　　者：温瑾 程秀芬 WEN Jin;CHENG Xiu-fen(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2018年第5期5-9,49,共6页Journal of Northwest Normal University(Natural Science)

基　　金：甘肃省高校大学生创新创业能力提升工程资助项目(2017-62)

摘　　要：将基本解和径向基函数相结合反演一种逆热传导问题的初值和热源.由于方程的系数矩阵是病态的,所以文中用Tikhonov正则化方法求解线性方程组,通过L-曲线方法选择正则化参数.通过几个数值例子验证了方法的有效性和精确性.An improved meshless method based on the fundamental solution and the radial basis functions is discussed for the simultaneous determination of a heat source and initial temperature.Since the coefficient matrix may be ill-conditioned,the Tikhonov regularization method is used to solve the resulted system of linear equations,and the L-curve technique is employed to choose a regularization parameter.The accuracy and efficiency of the proposed method is demonstrated by several numerical examples.

关 键 词：逆热传导问题 基本解方法 径向基函数 TIKHONOV正则化 L-曲线 

分 类 号：O241.82[理学—计算数学]