Scharz Preconditioners for Krylov Methods: Theory and Practice
- Temple Univ., Philadelphia, PA (United States); Temple University
Several numerical methods were produced and analyzed. The main thrust of the work relates to inexact Krylov subspace methods for the solution of linear systems of equations arising from the discretization of partial differential equations. These are iterative methods, i.e., where an approximation is obtained and at each step. Usually, a matrix-vector product is needed at each iteration. In the inexact methods, this product (or the application of a preconditioner) can be done inexactly. Schwarz methods, based on domain decompositions, are excellent preconditioners for these systems. We contributed towards their understanding from an algebraic point of view, developed new ones, and studied their performance in the inexact setting. We also worked on combinatorial problems to help define the algebraic partition of the domains, with the needed overlap, as well as PDE-constraint optimization using the above-mentioned inexact Krylov subspace methods.
- Research Organization:
- Temple Univ., Philadelphia, PA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- FG02-05ER25672
- OSTI ID:
- 1079618
- Report Number(s):
- DOE-05ER--256
- Country of Publication:
- United States
- Language:
- English
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