A T-ψ decoupled scheme with C-N difference for a multiply connected eddy current problem

The aim of this paper is to present a new T-ψ finite element decoupled scheme with Crank-Nicholson difference format for time-dependent eddy current problem, which avoids solving a saddle-point equations system and is more economical than the traditional scheme. The holes of multiply connected conductors are stemmed by making "cuts" and jumps of the function value ψ across the "cuts" are enforced. The construction of the finite element space with discontinuities at the "cuts" are given. The superior performance of the decoupled scheme is demonstrated by numerical experiment of the benchmark problem-TEAM Workshop Problem 7.