Research on application of LU decomposition and CG method in nonlinear iteration of transmission line finite element method
ISSN: 0332-1649
Article publication date: 28 September 2022
Issue publication date: 12 January 2023
Abstract
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.
Keywords
Acknowledgements
This work is supported in part by the National Natural Science Foundation under Grant 51777128.
Citation
Ren, X., Yan, X., Xu, C., Zhang, Y. and Xie, D. (2023), "Research on application of LU decomposition and CG method in nonlinear iteration of transmission line finite element method", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 1, pp. 230-240. https://doi.org/10.1108/COMPEL-01-2022-0058
Publisher
:Emerald Publishing Limited
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