Research On Parallel FEM Technique Of Apparatus' Nonlinear Magnetic Field Based On Transmission Line Method

Finite element method plays an important role in scientific computation of nonlinear partial differential equations for electromagnetic devices.It is an indispensable tool for electromagnetic devices in single or multi-physics field's simulation and optimization,such as electromagnetic,thermal,and mechanic.With the increasing of the solution task's scale and complexity,the computation burden required for electromagnetic simulation has increased sharply.The key to break through the computational bottleneck is to realize the repetitive solution of large nonlinear sparse matrix systems in the electromagnetic field's finite element analysis quickly,efficiently,and accurately.The transmission line method is gradually adopted in parallel finite element analysis due to its superiority in computational efficiency improvements,such as the separation of nonlinear element,invariant coefficients matrix,and unconditional convergence.However,there are still many problems associated with transmission line method and its applications in electromagnetic problems are still in research,such as the equivalent circuit modeling of finite element global matrices,the optimization of finite element solving speed based on direct solvers,and the generalizability and the universality,and convergence of transmission line model in electromagnetic field's finite element computation,etc.It is not yet fully exploited in parallel computation and need to be studied in depth.In this paper,we will study the improvement method of the transmission line model in depth to solve the above-mentioned issues,taking electromagnetic devices such as electromagnetic relays,contactors as examples,based on the existing research at home and abroad.From a physical point of view,we will establish parallel computational methods for 2D/3D nonlinear problems,including magnetostatic fields,transient magnetic fields,and dynamic coupling of electromagnetic,circuit,and mechanical motion.Firstly,we will study the parallel FEM algorithm based on transmission line method to calculate 2D axisymmetric magnetostatic field.Aiming at the typical axisymmetric electromagnetic devices,the governing equation of the magnetostatic field is established,the nonlinear discrete system is formed by the principle of variational method,and the system's equivalent nonlinear circuit network modeling method is studied.On this basis,the transmission line method is introduced into the calculation of the magnetostatic field,and the shortcomings of the traditional transmission line method in nonlinear calculations and improved methods are studied.Furthermore,we study the transmission line method's ability to solve multiple large sub-domains,establish a domain decomposition calculation method,and study the parallel acceleration effect of the method in magnetostatic field finite element solution.Secondly,we will study the parallel FEM algorithm based on transmission line method to calculate the 2D axisymmetric transient magnetic field of electromagnetic devices.According to Maxwell's equations,the dynamic process of common electromagnetic devices is mathematically modeled and the governing equations are obtained.The traditional transmission line method requires a more complex equivalent circuit,and has a poor ability to adapt different finite elements.Therefore,we research on a more general black-box circuit model to improve it,and study the convergence and calculation accuracy of the method.Using Galerkin method,the strong field-circuit coupling partial differential equation is numerically discretized,and the black-box transmission line method is used to solve it.The calculation of dynamic characteristics involves deformation of the mesh,thus 2D remeshing technology is studied.Then,the calculation results are compared and verified.Then,we will study the parallel FEM algorithm based on transmission line method to calculate the magnetostatic field of 3D electromagnetic devices.Aiming at the typical3 D electromagnetic devices,the governing equation of its magnetostatic field is studied.Based on the vector edge element and Galerkin method,the discrete process of the governing equation is studied.The magnetic vector potential cannot meet the Coulomb gauge in the 3D edge element,therefore,the treatment of the gauge problem in the edge element is studied.After that,an equivalent circuit model is established according to the special element matrix form of the 3D finite element.The iterative speed of the traditional transmission line method is greatly affected by the admittance.In order to avoid the use of pre-processing methods,the quasi multiconductor transmission line method is studied to improve the convergence speed.Using virtual work method,the parallel calculation method of electromagnetic force and torque in the edge element is derived.Then,the transmission line method is applied to the 3D magnetostatic field finite element calculation,and the results are compared with commercial software.Finally,we will study the parallel FEM algorithm based on transmission line method to calculate the transient magnetic field of 3D electromagnetic devices.The dynamic characteristics of the 3D electromagnetic devices are modeled and analyzed,and its timestepping finite element model based on the field-circuit-mechanic coupling is established.For the Coulomb gauge problem,the governing equation formed with divergence gauge is considered.Galerkin method and edge element are used to obtain the nonlinear equations that need to be solved for transient field-circuit coupling.Thus,the equivalent circuit of the finite element tetrahedral element in the transient electromagnetic field can be established.Due to the deformation of the mesh caused by the moving parts,the 3D remeshing technology and the storage method of the edge element variables are studied.Finally,the method of parallel calculation of dynamic characteristics is proposed,and its results are compared with the commercial software and the measured results.