The paper discusses versatile constraint equations used for providing compatibility between the solutions obtained for separate sub-domains of electromagnetic field which are analyzed simultaneously. The mathematical model of the task has been developed using invariant approximation technique for finite-difference method. Different techniques for domain decomposition are considered. The discussed constraint equations and domain decomposition techniques have been applied to solving a test problem, and namely the problem of magnetic skin-effect. On the basis of obtained computational results some recommendations regarding the scope of overlapping and applicability of different constraint equations have been formulated.
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