The Research And Application Of Coefficient Matrix Preconditioned Method In Element Level Parallel Algorithm

For large scale electrical equipment with large physical dimension,such as power transformer and electric motor,considering the penetration depth,huge amounts of meshes are needed to analyze the electromagnetic field in the equipment accurately using the finite element method(FEM).So the computation scale will be too large to calculate by conventional serial FEM.Therefore,the parallel algorithms has been researched by more and more researchers and applied to numerical computation.In this paper,the element level parallel algorithm EBE(element-by-element)finite element method and preconditioned technology of coefficient matrix are researched and the corresponding program has bee n developed in C++.In this paper,the EBE method is derived in detail,including the implementation of boundary condition in EBE.For solving the equations of the element-by-element finite element method(EBE-FEM),the conjugate gradient(CG)method is adopted.Meanwhile,the CG method applying to EBE-FEM is derived and the calculation process is presented.To improve the convergency,the preconditioned technology of coefficient matrix is researched.Firstly,in order to find a more effectively preconditioned method,the Gauss-Seidel preconditioned method is researched,and it is combined with the EBE-FEM.Then,the Jacobi preconditioned conjugate gradient(J-PCG)method based on EBE-FEM has been researched.Meanwhile,the Gauss-Seidel preconditioned conjugate gradient(GS-PCG)method applying to EBE-FEM and J-PCG applying to EBE-FEM are derived and the calculation process are presented in this paper.The programs corresponding to the methods has been developed in C++,which including the CG based on EBE-FEM,the GS-PCG method based on EBE-FEM,the J-PCG method based on EBE-FEM.The validity and accuracy of these methods have been verified through the applications to magnetic field analysis of a long straight current-carrying wire.Finally,these methods have been applied successfully to analyze the magnetic field in transformer and motor.With the Jacobi preconditioned method and the Gauss-Seidel precongitioned method,the convergency of CG based on EBE-FEM is improved obviously.And compared with J-PCG method applying to EBE-FEM,less computational time and cost are needed for the GS-PCG method applying to EBE-FEM with the same accuracy.The method can be applied to electromagnetic field analysis of power transformer and electric motor,which may be related to large scale numerical computation.And the larger the scale computation involved,the better converging performance can be obtaibed by the method.