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Title: A Combined Preconditioning Strategy for Nonsymmetric Systems

Here, we present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typically arise in finite element discretizations. An example of the additive Schwarz method applied to nonsymmetric but definite matrices is presented for which the abstract assumptions are verified. Variable preconditioner, which combines the original nonsymmetric one and a weighted least-squares version of it, and it is shown to be convergent and provides a viable strategy for using nonsymmetric preconditioners in practice. Numerical results are included to assess the theory and the performance of the proposed preconditioners.
 [1] ;  [2] ;  [2]
  1. Univ. of Bologna (Italy). Dept. of Mathematics; King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1064-8275
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 36; Journal Issue: 6
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE preconditioning; nonsymmetric matrices; normal matrix form; additive Schwarz method