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Abstract <p>A noniterative domain decomposition method with overlapping subdomains is considered as applied to multidimensional parabolic problems. The method is similar in structure to dimensional splitting with a smooth partition of unity. The method has been known for a long time, but a number of important technical details related to the design of domain decomposition ensuring a smooth partition of unity have not been published before. These details are presented as a set of statements with proofs. An error estimation procedure is described, the details of which have also not been published before.</p>

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On Some Approaches in Domain Decomposition Methods for Solving Parabolic Problems

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Yu. M. Laevsky

摘要

Abstract

A noniterative domain decomposition method with overlapping subdomains is considered as applied to multidimensional parabolic problems. The method is similar in structure to dimensional splitting with a smooth partition of unity. The method has been known for a long time, but a number of important technical details related to the design of domain decomposition ensuring a smooth partition of unity have not been published before. These details are presented as a set of statements with proofs. An error estimation procedure is described, the details of which have also not been published before.