基于区域分解求解磁暴感应地电场的广义极小残量迭代算法

doi:10.19595/j.cnki.1000-6753.tces.170829

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Abstract To solve the multi-scale model of geoelectric field induced by geomagnetic storms, the domain decomposition method is put to use in this paper. As for each decomposed domain, modeling and solving can be worked out by means of finite element method (FEM). In order to simplify the iterative process and avoid the processing of the boundary conditions on the interface generated by the non-overlapping domain decomposition, the overlapping domain decomposition method is adopted. The potential function on the virtual boundary is chosen as the unknown variable, based on the linear relationship in computation of FEM, the problem of multi-scale induced geoelectric field is finally transformed into an asymmetric complex linear equation. In order to save computational memory, the GMRES iterative algorithm of domain decomposition is deduced without directly solving the specific coefficient matrix of the equations according to the mathematical principles of Arnoldi's orthogonalization algorithm and generalized minimal residue (GMRES) method. In this paper, a small scale model is derived from the whole model of the large scale induced geoelectric field, and a multi-scale solution model is formed. For 2D and 3D cases, the iterative variable selection and the derivation of the iterative process are described. Taken the results of FEM direct solution as benchmark, the correctness is verified. Besides, the efficiency of the proposed algorithm is verified by comparing with direct iteration and relaxation iteration in 2D case. The proposed algorithm is used to calculate a numerical example of multi-scale geoelectric field, which provides a new method for the calculation of multi-scale alternating electromagnetic field.

Key words： Finite element method domain decomposition geomagnetic storms geoelectric field generalized minimal residual (GMRES) method

Received: 09 June 2017 Published: 28 March 2018

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TM152

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	Wang Zezhong
	Tao Ruixiang

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Wang Zezhong,Tao Ruixiang. Generalized Minimal Residual Iterative Algorithm for Solving Induced Geoelectric Field During Geomagnetic Storms Based on Domain Decomposition[J]. Transactions of China Electrotechnical Society, 2018, 33(6): 1265-1275.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.170829 OR https://dgjsxb.ces-transaction.com/EN/Y2018/V33/I6/1265

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