A Substructuring Domain Decomposition Scheme for Unsteady Problems

Abstract: Domain decomposition methods are used for the approximate solution of boundary-value problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are fully taken into account in iteration-free domain decomposition schemes. Regionally-additive schemes are based on various classes of splitting schemes. In this paper we highlight a class of domain decomposition schemes which are based on the partition of the initial domain into subdomains with common boundary nodes. Using a partition of unity we construct and analyze unconditionally stable schemes for domain decomposition based on a two-component splitting: the problem within each subdomain and the problem at their boundaries. As an example we consider a Cauchy problem of first or second order in time with a non-negative self-adjoint second order operator in space. The theoretical discussion is supplemented with the numerical solution of a model problem for a two-dimensional parabolic equation.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: A Substructuring Domain Decomposition Scheme for Unsteady Problems ; volume:11 ; number:2 ; year:2011 ; pages:241-268 ; Computational methods in applied mathematics ; 11, Heft 2 (2011), 241-268

Contributors, Places and Time

• Creator: Vabishchevich, Petr

Further information

• DOI: 10.2478/cmam-2011-0013
• URN: urn:nbn:de:101:1-2410261627520.274274258649
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:37 AM CEST