Purpose The purpose of this study is to develop a reliable finite element algorithm based on the transmission line method (TLM) to solve the nonlinear problem in electromagnetic field calculation. Design/methodology/approach In this paper, the TLM has been researched and applied to solve nonlinear iteration in FEM. LU decomposition method and the Jacobi preconditioned conjugate gradient method have been investigated to solve the equations in transmission line finite element method (FEM-TLM). The algorithms have been developed in C++ language. The algorithm is applied to analyze the magnetic field of a long straight current-carrying wire and a single-phase transformer. Findings FEM-TLM is more effective than traditional FEM in nonlinear iteration. The results of FEM-TLM have been compared and analyzed under different calculation scales. It is found that the LU decomposition method is more suitable for FEM-TLM because there is no need to repeatedly assemble the global coefficient matrix in the iterative solution process and it is not affected by the disturbance of the right-hand vector. Originality/value An effective algorithm is provided for solving nonlinear problems in the electromagnetic field, which can save a lot of computing costs. The efficiency of LU decomposition and CG method in FEM-TLM nonlinear iteration is investigated, which also makes a preliminary exploration for the research of FEM-TLM parallel algorithms.

No abstract

No abstract

No abstract

The element-by-element finite element method (EBE-FEM) parallel algorithm has been realized on Compute Unified Device Architecture (CUDA) platform in this paper. An improved fast color marking method (FCM) combined with tabu search algorithm is proposed to solve the problem that the elements sharing a node wait for accessing the same memory space in parallel computation. The elements in the same color can be processed at the same time without waiting. This method can get more even color grouping faster than the classical coloring method (CCM).  Combining it with the EBE parallel algorithm can achieve faster element-level operations. The validity and accuracy of the method has been verified by comparing the computed results with the analytical solution of the magnetic field produced by the solenoid. The parallel program is applied to analyze the main magnetic field of a single-phase transformer, which shows higher speedup performance.