Balancing ___domain decomposition method: Difference between revisions

Revision as of 05:39, 13 March 2008

Revision as of 03:48, 14 March 2008

Line 1:

The '''Balancingbalancing Domain___domain Decompositiondecomposition method''' (BDD)''' is an [[iterative method]] to find the solution of a [[symmetric]] [[positive definite]] system of [[linear]] [[algebraic equation]]s arising from the [[finite element method]] <ref name="Mandel-1993-BDD"> J. Mandel, ''Balancing ___domain decomposition'', Comm. Numer. Methods Engrg., 9 (1993), pp. 233--241.

</ref>. In each iteration, it combines the solution of local problems on non-overlapping subdomains with a coarse problem created from the subdomain nullspaces. BDD requires only solution of subdomain problems rather than access to the matrices of those problems, so it is applicable to situations where only the solution operators are available, such as in [[oil reservoir]] [[simulation]] by [[mixed finite elements]] <ref name="Cowsar-1995-BDD"> L. C. Cowsar, J. Mandel, and M. F. Wheeler, ''Balancing ___domain decomposition for mixed finite elements'', Math. Comp., 64 (1995), pp. 989--1015.