Accession Number DE2013-1079618
Title Final Report Schwarz Proconditioners for Krylov Methods: Theory and Practice.
Publication Date 2013
Media Count 8p
Personal Author D. B. Szyld
Abstract 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 de ne the algebraic partition of the domains, with the needed overlap, as well as PDE-constraint optimization using the above-mentioned inexact Krylov subspace methods.
Keywords Algebra
Approximations
Domains
Iterative methods
Krylov methods
Linear systems
Numerical analysis
Optimization
Partial differential equations
Schwarz methods


 
Source Agency Technical Information Center Oak Ridge Tennessee
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author Temple Univ., Philadelphia, PA.
Document Type Technical report
Title Note N/A
NTIS Issue Number 1325
Contract Number DE-FG02-05ER25672

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