求解一类平行四边形域上热传导反问题的无网格方法  

A Meshless Method for Solving a Class of Inverse Heat Conduction Problems Over a Parallelogram Domain

作　　者：刘源 张永富[1] LIU Yuan;ZHANG Yongfu(College of Mathematics Science,Inner Mongolia Minzu University,Tongliao 028000,China)

机构地区：[1]内蒙古民族大学数学科学学院,内蒙古通辽028000

出　　处：《长春师范大学学报》2024年第8期24-34,共11页Journal of Changchun Normal University

基　　金：国家自然科学基金项目“关于热传导反问题中多参数辨识的数值逼近研究”(11961053);内蒙古民族大学博士科研启动基金项目“关于一类热传导反问题数值方法的研究及应用”(BS424)。

摘　　要：基于基本解和径向基函数相结合的方法,对采用不同径向基作为近似解的基底,用平行四边形域反演一类热传导反问题的初值和热源项进行研究.因插值构造的方程系数矩阵是病态的,即系数矩阵的条件数较大,本文基于GCV准则的奇异值分解正则化方法求解线性方程组,选取不同噪声级,通过数值算例显示所给方法是稳定有效的.Based on the method of combining fundamental solution and radial basis function,the initial value and heat source term of a class of inverse heat conduction problems are studied by using different radial basis as the basis of approximate solution and using parallelogram domain.Because the coefficient matrix of the equation constructed by interpolation is ill-conditioned,which means the number of conditions of the coefficient matrix is large,the singular value decomposition regularization method based on the GCV criterion is used to solve the linear equations.The numerical examples show that the proposed method is stable and effective by selecting different noise levels.

关 键 词：热传导反问题 基本解方法 径向基函数 奇异值分解正则化方法 GCV准则 

分 类 号：O241.5[理学—计算数学]