Research On The Element By Element Parallel Finite Element Method Realized By CUDA

For the analysis of large-scale engineering electromagnetic field existed multi-scale problems,such as the overall size of transformer and the small penetration depth of ferromagnetic material electromagnetic field.The nonlinearity and anisotropy of electromagnetic characteristics make the numerical calculation of electromagnetic field too large.The conventional serial finite element method will lead problems including long calculation time and the big error of calculation results.Sometimes it cannot be calculated.Therefore,the finite element parallel algorithm will become a research hotspot.GPUs are programmable stream processors designed for intensive,highly parallelized computations,and their many-core nature can support element by element computing in parallel.In this paper,the element-level parallel finite element algorithm(EBE-PFEM)is researched and implemented in parallel on CUDA platform.In this paper,the mathematical model of EBE finite element method is derived,including the implementation of boundary condition in EBE.The conjugate gradient(EBE-CG)method based on EBE strategy is researched.In order to improve the convergence of conjugate gradient method,the Jacobi preconditioned is used in this paper.The Jacobi preconditioned conjugate gradient(EBE-J-PCG)method based on EBE-FEM is derived and the concrete iteration process is given.In order to give full play to the advantage of high parallelism of EBE finite element method,the hardware structure and instruction execution characteristics of GPU based on CUDA platform are studied.Jacobi preconditioned conjugate gradient method based on EBE is researched and implemented in parallel on CUDA platform.The CPU+GPU cooperative computation model of EBE-J-PCG based on CUDA platform is proposed,and the corresponding program has been developed in C++.The validity and accuracy of the proposed method have been verified through the comparison with the analytical solution of the spatial magnetic field produced by a long straight current-carrying wire.Finally,the main magnetic field in a single-phase transformer and a three-phase induction motor are calculated by EBE-CG method and EBE-J-PCG method on the CPU platform and CUDA platform respectively.In the same calculation accuracy,Jacobi preconditioned technology can improve the convergence of the algorithm.Compared with the EBE finite element analysis on the CPU platform,the higher computational efficiency can be obtained by EBE finite element analysis on CUDA platform.In addition,the larger scale computation is involved,the higher speedup can be reached.The proposed method can be applied to electromagnetic field analysis of transformer and motor,which may refer to large scale numerical computation.