带有移动边界的热传导方程反问题基本解方法

The Method of Fundamental Solutions for Inverse Problem of Heat Conduction Equation with Moving Boundary

对带有移动边界的非齐次热传导方程反问题进行了研究,采用基本解方法求解此问题。利用积分变换将非齐次热传导方程转化成齐次方程,并应用基于奇异值分解的正则化方法对所得的不适定方程组进行求解,将方程中的未知热源项和部分初值进行了同时反演。通过数值算例显示,文中的方法对于求解此类带有移动边界的热传导方程反问题是稳定有效的。

The inverse problem of non-homogeneous heat conduction equation with moving boundary is studied.The fundamental solution method is used to solve the problem.The non-homogeneous heat transfer equation is trans-formed into homogeneous equation by integral transformation,and the ill-defined equations are solved by regulariza-tion method based on singular value decomposition.The unknown heat source term and some initial values in the equation are simultaneously retrieved.Numerical examples show that the proposed method is stable and effective for solving the inverse problem of the heat transfer equation with moving boundary.