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Domain decomposition methods are used for approximate solving boundaryproblems for partial differential equations on parallel computing systems.Specific features of unsteady problems are taken into account in the mostcomplete way in iteration-free schemes of domain decomposition.Regionally-additive schemes are based on different classes of splittingschemes. In this paper we highlight a class of domain decomposition schemeswhich is based on the partition of the initial domain into subdomains withcommon boundary nodes. Using the partition of unit we have constructed andstudied unconditionally stable schemes of domain decomposition based ontwo-component splitting: the problem within subdomain and the problem at theirboundaries. As an example there is considered the Cauchy problem forevolutionary equations of first and second order with non-negative self-adjointoperator in a finite Hilbert space. The theoretical consideration issupplemented with numerical solving a model problem for the two-dimensionalparabolic equation.

Substructuring domain decomposition scheme for unsteady problems