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.

- A. Kaypmaz, Y. Tokad, and O. Usta, “Diakoptics – a parallel processing approach for the analysis of large scale power systems”, in:
*Melecon.**Proc. 7th Mediterranean Electrotechnical Conference*, vol. 3, pp. 1069-1072, 1994. - P. Bjorstad and W. Gropp,
*Domain decomposition: Parallel multilevel methods for elliptic partial differential equations*, Cambridge University Press, 2004. - Y.Boubendir, X. Antoine, and C. Geuzaine, “A non-overlapping quasi-optimal optimized Schwarz domain decomposition algorithm for the Helmholtz equation”, in
*Proc**.**20*, p. 547-554, 2011. Available at: http://www.ddm.org/DD20/ proceedings/articles/Boubendir.pdf^{th}International Conference on Domain Decomposition Methods - S.Guttel, “A parallel overlapping time-domain decomposition method for ODEs”, in
*Proc**.**20*, pp. 483-490, 2011. Available at^ http://www.ddm.org/DD20/ proceedings/articles/Guettel.pdf^{th}International Conference on Domain Decomposition Methods - R.Filc, “Discrete analogy of Hamilton’s operator”,
*Mathematical Methods and Physical-Mechanics Fields,*no. 24, pp. 20-25, 1986. (in Russian)