Analysis of non-overlapping domain decomposition algorithms with inexact solves

In this paper we construct and analyze new non-overlapping domain decomposition preconditioners for the solution of second-order elliptic and parabolic boundary value problems. The preconditioners are developed using uniform preconditioners on the subdomains instead of exact solves. They exhibit the same asymptotic condition number growth as the corresponding preconditioners with exact subdomain solves and are much more e cient computationally. Moreover, this asymptotic condition number growth is bounded independently of jumps in the operator coe cients across subdomain boundaries. We also show that our preconditioners t into the additive Schwarz framework with appropriately chosen subspace decompositions. Condition numbers associated with the new algorithms are computed numerically in several cases and compared with those of the corresponding algorithms in which exact subdomain solves are used.

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: James H. Bramble, Joseph E. Pasciak, Apostol T. Vassilev
• Keywords: Asymptotic Condition Number, Condition Number Growth, MOC 1998, Subdomain