Difference Decomposition Schemes Based on Splitting the Solution and Operator of the Problemстатья
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Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:Domain decomposition methods are used for the approximate solution of boundary valueproblems for partial differential equations on parallel computing systems. The specifics ofnonstationary problems is most completely taken into account when using noniterative domaindecomposition schemes. Regionally additive schemes are constructed on the basis of variousclasses of splitting schemes. A new class of domain decomposition schemes with an additiverepresentation of the solution on a new time level is distinguished that is based on splitting thedomain into subdomains based on a partition of unity. An example of the Cauchy problem forfirst-order evolution equations with a positive self-adjoint operator in a finite-dimensional Hilbertspace is considered. Unconditionally stable two- and three-level splitting schemes are constructedfor the corresponding system of equations.