Abstract: We considered application of pure meshfree parallel computation in  numerical simulation  of heat transfer equation. Firstly, we reserved  the Taylor expansion to the third derivative, and extended the pure mesh-free finite pointset method (FPM) to solve the three-dimensional heat conduction equation in order to improve the numerical accuracy. Secondly, we introduced massage passing interface (MPI) parallel computing technology  to improve the computational efficiency by parallel use of multiple CPUs through cyclic statements, and obtained a reliable and efficient pure grid parallel FPM algorithm for three-dimensional heat conduction problem. In the numerical example, we first solved the heat transfer problems with different boundary conditions in different regions, compared it with the analytical solutions, and analyzed the calculation efficiency and error of the proposed algorithm. Then we used  the parallel algorithm  to simulate and predict the temperature 
evolution process with time in functionally graded materials, and  compared it with other numerical results to verify the reliability of the numerical prediction.

Key words: finite pointset method, heat transfer equation, MPI parallel, calculation efficiency