A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Abstract

Communicated by M. CostabelThe aim of this paper is to develop a fully discrete .T, /-e finite element decoupled scheme to solve time-dependent eddy current problems with multiply-connected conductors. By making 'cuts' and setting jumps of e across the cuts in nonconductive domain, the uniqueness of e is guaranteed. Distinguished from the traditional T-method, our decoupled scheme solves the potentials T and -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.

Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations

“…Numerical schemes with backward Euler discretization in time and mixed conforming finite elements in space were discussed for nonlinear conductivity problems in [5,6]. A fully-discrete (T, ψ) − ψ e finite element decoupled scheme was developed to solve time-dependent eddy current problem with multipleconnected conductors [2]. Subsequently, an improved convergence rate analysis was presented in [15].…”