A stability paradox for time-stepping schemes in coupled field-circuit problems

The finite element model for the time dependent eddy current problem is coupled with mesh (loop) equations for arbitrary external circuits. Stability of the resultant system and the time-stepping scheme is analyzed. The backward difference scheme is shown to be stable, while the Crank-Nicholson method exhibits peculiar instability. Theoretical analysis is supported by numerical results for test and practical problems.<
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