A new modified conjugate gradient method to identify thermal conductivity of transient non-homogeneous problems based on radial integration boundary element method

Abstract

In order to analyze the heat conduction problem of composite materials in aerospace engineering, a modified conjugate gradient method is proposed to identify the physical parameters of transient heat conduction problems in this paper. In the positive problem, the boundary element method based on radial integration method is used to obtain the measured point temperature of the transient heat conduction problem with varying thermal conductivity. In the inverse problem, based on the advantages of high accuracy and fast convergence rate of the conjugate gradient method, a modified conjugate gradient method is used. On the one hand, the complex variable derivative method is introduced into the traditional conjugate gradient method, and then the sensitivity coefficient matrix can be accurately calculated. On the other hand, based on the linear convergence property of the conjugate gradient method, a restart factor is introduced in this paper. For an inverse problem containing n unknown parameters, the algorithm restarts from the steepest descent method after every n + 1 iterations to identify physical properties of transient non-homogeneous thermal conduction. The complex variable derivation method overcomes the problem that the traditional conjugate gradient method needs differential processing and low derivative accuracy in solving the inverse transient heat conduction problem. When solving the complicated inverse problems, conjugate gradient method, which includes restart factor, solves the problem of slow convergence in traditional conjugate gradient methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the present method in identifying the parameters of transient non-homogeneous thermal conductivity.