A parallel software module of FMM (fast multipole method) for three-dimensional Laplace kernel functions, JASMIN-3DLapFMM, is designed and implemented. The module is based on two phases parallel strategy of both processes and threads. A parallel software module is successfully used to solve the far field potential of electrostatic fields. With a fixed problem size of single processor,almost linear weak parallel scalability is obtained for a grand scale problem with 10¹⁰ particles on more than ten thousand processors. With a fixed size of total problem and 1024 processors, about three times speedup is obtained on four threads.

An explicit method is proposed to initiate three-layer difference scheme for two-dimensional heat problems.Stability and convergence theorem is shown with a three-layer domain decomposition parallel difference algorithm with inner boundary prediction-correction and explicit initialization.Parallel numerical experiments show that the method is numerical stable,and is more convenient in program realization compared with usual implicit initialization method.It reduces numerical errors greatly compared with existing perturbation methods.