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A ( T , ψ )‐ ψ e decoupled scheme for a time‐dependent multiply‐connected eddy current problem
Author(s) -
Chen Tao,
Kang Tong,
Lu Guizhen,
Wu Liyun
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2795
Subject(s) - mathematics , saddle point , norm (philosophy) , scheme (mathematics) , uniqueness , eddy current , current (fluid) , finite element method , domain (mathematical analysis) , mathematical analysis , control theory (sociology) , computer science , geometry , control (management) , physics , quantum mechanics , political science , law , thermodynamics , artificial intelligence
The aim of this paper is to develop a fully discrete ( T , ψ )‐ ψ e finite element decoupled scheme to solve time‐dependent eddy current problems with multiply‐connected conductors. By making ‘cuts’ and setting jumps of ψ e across the cuts in nonconductive domain, the uniqueness of ψ e is guaranteed. Distinguished from the traditional T ‐ ψ method, our decoupled scheme solves the potentials T and ψ ‐ ψ e separately in two different simple equation systems, which avoids solving a saddle‐point equation system and leads to a remarkable reduction in computational efforts. The energy‐norm error estimate of the fully discrete decoupled scheme is provided. Finally, the scheme is applied to solve two benchmark problems—TEAM Workshop Problems 7 and IEEJ model. Copyright © 2013 John Wiley & Sons, Ltd.