An efficient boundary-type meshfree method for analysis of two-dimensional laser heating problems

The purpose of this study is to formulate a truly and effective boundary-type meshfree method for analysis of 2D transient heat conduction problems including moving laser heat sources. Being based on the method of fundamental solutions (MFS), the present work formulates new time-dependent formulations to solve the problem directly in the time-domain. The motion path and the intensity of the laser heat source over a moving area can be arbitrary functions of time and space. In the proposed formulations, the particular solution associated to the heat source function is evaluated using a simple approach without using any internal points or cells. By solving two example problems, the efficiency and accuracy of the proposed method are demonstrated. The analyses show that the presented boundary-type meshfree method is relatively more efficient than other domain-type techniques. From the analyses, it is also observed that very accurate results can be obtained by the proposed method employing large time-step size and small number of collocation points.