| Finite element method(FEM)is the most widely used method in the electrical electromagnetic field simulation of electromagnetic devices.However,the efficiency of FEM is low,and its application in engineering is limited.Benefit from the increasing abundance of multi-core computing resources,large-scale parallel finite element computing become a hot research direction.As a device with large amount of arithmetic and logic unit(ALU),GPU has attracted extensive attention in the field of computational electromagnetics in recent years.Nodal domain decomposition with relaxation(NDDR)is a finite element algorithm suitable for GPU parallel computation.It has been applied in the static characteristic calculation of electromagnetic field.However,it has not been applied to the calculation of dynamic characteristics of electromagnetic devices yet.In order to improve the efficiency of FEM in static and transient electromagnetic field,we study the NDDR algorithm and GPU heterogeneous programming.Firstly,we study the Newton-Raphson based parallel FEM algorithm to calculate the static magnetic field of 2D axisymmetric electromagnetic model.Aiming at the typical axisymmetric electromagnetic mechanism,the control equation of the static magnetic field is established,the nonlinear discrete system is formed by Galerkin method,and the discrete process is verified.In order to improve the solving efficiency and reduce memory consumption,we study the storage and assembly of sparse matrices,and studied the finite element parallelization scheme based on OpenMP and the parallelized matrix solver Super LU＿MT.Through C++ programming,the FEM parallel calculation of twodimensional axisymmetric electromagnetic field is realized,which lays the theoretical foundation and engineering foundation for the research of the NDDR algorithm.Secondly,we study the NDDR based parallel FEM algorithm and GPU heterogeneous programming.The advantages of the NDDR method over the traditional finite element method are demonstrated.The mathematical modeling of NDDR subdomain analysis process is carried out.On this basis,we implement the NDDR algorithm through CPU parallel programming,and verify the accuracy of the NDDR algorithm.Furthermore,we study the GPU architecture and GPU heterogeneous programming,realize the NDDR algorithm on the GPU platform.Then,we compare the solution efficiency of traditional Newton-Raphson iteration,CPU version of NDDR algorithm and GPU version of NDDR algorithm.After that,the influence of different hardware architectures and hardware performance on the solution efficiency of NDDR algorithm is discussed.Then,we study the NDDR algorithm to calculate the transient electromagnetic field of 2D axisymmetric electromagnetic model.The dynamic characteristic calculation process is decomposed into electromagnetic force calculation,electromagnetic-circuit coupling calculation and mechanical motion calculation.To obtain the governing equation of dynamic characteristic,the mathematical modeling of the above processes are carried out.Aiming at the deformation of the mesh during the calculation of dynamic characteristics,we study the local re-mesh technology to realize the calculation of electromagnetic field and the processing of the armature moving.On this basis,NewtonRaphson algorithm and NDDR algorithm are used to realize the dynamic characteristics of electromagnetic device respectively.The solution accuracy and solution efficiency of the two algorithms are compared,and the advantages of NDDR algorithm in the calculation of dynamic characteristics and its optimization scheme are discussed.Finally,we develop a 2D axisymmetric electromagnetic FEM solver on the basis on FEM algorithm research.We analyze the demand of the solver,design the function module and call time sequence of the solver.Furthermore,through the integration of open source software for pre-processing and post-processing,the complete finite element analysis process is realized. |
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