Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
- Univ. of Utah, Salt Lake City, UT (United States)
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
- Research Organization:
- Front Range Scientific Computations, Inc., Boulder, CO (United States); US Department of Energy (USDOE), Washington DC (United States); National Science Foundation, Washington, DC (United States)
- OSTI ID:
- 223829
- Report Number(s):
- CONF-9404305-Vol.1; ON: DE96005735; TRN: 96:002320-0001
- Resource Relation:
- Journal Volume: 180; Conference: Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994; Other Information: PBD: [1994]; Related Information: Is Part Of Colorado Conference on iterative methods. Volume 1; PB: 203 p.
- Country of Publication:
- United States
- Language:
- English
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