An abstract theory for the domain reduction method

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1992 English Publisher:Springer Science and Business Media LLCJournal:Computing, volume 48, pages 73-96 (issn: 0010-485X, eissn: 1436-5057,

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Authors: Craig C. Douglas; Jan Mandel;

doi: 10.1007/bf02241707

An abstract theory for the domain reduction method

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Abstract

Theoretical foundations of the domain reduction method based on known results from group representation theory and algebras of finite groups are investigated. The main result is that if an initial system of linear equations arising by discretization of partial differential equations splits into subproblems based on isomorphic subdomains, then the group of symmetries must be commutative.

Related Organizations

University of Colorado Denver
United States
IBM (United States)
United States
IBM Research – Thomas J. Watson Research Center
United States

Keywords

Finite difference methods for boundary value problems involving PDEs, Representation theory for linear algebraic groups, Multigrid methods; domain decomposition for boundary value problems involving PDEs, algebras of finite groups, group of symmetries, domain reduction method, group representation theory

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