A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

Abstract EN

We propose a new meshless method to solve a backward inverse heat conduction problem.

The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution.

Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations.

Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter.

A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.