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
刘源 1张永富1
作者信息
- 1. 内蒙古民族大学数学科学学院,内蒙古 通辽 028000
- 折叠
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.
Abstract
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 paral-lelogram 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Key words
inverse heat conduction problem/basic solution method/radial basis function/singular value decomposition regularization method/GCV method引用本文复制引用
出版年
2024
NETL
NSTL
万方数据