Parallel Implementation And Optimization Of EBE-FEM Based On CUDA Platform

When the finite element method(FEM)is used to analyze the electromagnetic field of large electrical equipment,a large number of elements are required to obtain more accurate results,which will lead to large-scale calculation.However,due to the limitation of computer memory,software and hardware,traditional FEM and existing commercial software cannot achieve fast and accurate calculation for such problems.Therefore,the element-level finite element parallel method and optimization technology of the parallel computing process based on the CPU + GPU heterogeneous computing system CUDA(Compute Unified Device Architecture)platform are researched in this paper.In this paper,the mathematical model of 2-D and 3-D EBE(element-by-element)-FEM is derived,and the correctness of the algorithms and programs is verified through analyzing the examples with accurate solution.The heterogeneous architecture and thread model based on CUDA platform are researched.The CPU + GPU heterogeneous computing model of EBE-FEM combined with Jacobi preprocessing conjugate gradient method(EBE-J-PCG)is established,and the concrete iterative process of 2-D and 3-D parallel EBE-J-PCG method is given.The thread branches in reduction operations and the loops in programs are researched.Instruction-level thread-data remapping method and loop unrolling method are proposed,which are used to optimize the addressing process of reduction operation and the loops in program,respectively.In addition,a mathematical model for calculating unrolling factors is proposed and applied to 2-D serial EBE-FEM program.All corresponding programs are developed in C ++language.Finally,the algorithm and programs are applied to calculate the main magnetic field of a single-phase power transformer.The analysis of the results shows that compared with the 2-D serial EBE-J-PCG method,parallel EBE-J-PCG can significantly improve the calculation efficiency.In the same calculation accuracy,the two instruction-level optimization methods proposed in this paper can achieve further acceleration on the basis of parallelism,and the larger the calculation scale involved,the more obvious the acceleration effect.