Simulation of heat flow in welding using hybrid restarting FDM-SVR-Lanczos

This paper discusses the numerical simulations of heat transfer problem, particularly during the welding materials processing. This process highly depends on the temperature to determine the metallurgical properties, the strength, and the sureness of the joint during welding; hence it is desirable to study its heat flow. Finite difference method (FDM) is used to discretize partial differential equations (PDEs) to obtain the systems of linear equations (SLEs), which can be solved by an iterative method. Here, we used a variant of Lanczos based methods, called Restarting-FDM-SVR-Lanczos to solve two-dimensional heat flow in welding. The proposed method is a combination of Lanczos method and machine learning under the support vector regression (SVR) method, where the SVR plays important role in predicting the non-existing solutions of the Lanczos iterates, due to the breakdown issue in Lanczos method. Numerical results were presented and showed that Hybrid Restarting FDM-SVR-Lanczos performed better in solving the heat flow in welding problem compared with the single FDM and Lanczos methods, with small residual norms.