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The generalized global basis (GGB) method
Author(s) -
Waisman H.,
Fish J.,
Tuminaro R. S.,
Shadid J.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1107
Subject(s) - generalized minimal residual method , convergence (economics) , basis (linear algebra) , krylov subspace , eigenvalues and eigenvectors , subspace topology , computer science , matrix (chemical analysis) , mathematics , algorithm , iterative method , chemistry , geometry , artificial intelligence , physics , quantum mechanics , chromatography , economics , economic growth
In this work, we present the generalized global basis (GGB) method aimed at enhancing performance of multilevel solvers for difficult systems such as those arising from indefinite and non‐symmetric matrices. The GGB method is based on the global basis (GB) method ( Int J Numer Methods Eng 2000; 49 :439–460, 461–478), which constructs an auxiliary coarse model from the largest eigenvalues of the iteration matrix. The GGB method projects these modes which would cause slow convergence to a coarse problem which is then used to eliminate these modes. Numerical examples show that best performance is obtained when GGB is accelerated by GMRES and used for problems with multiple right‐hand sides. In addition, it is demonstrated that GGB method can enhance restarted GMRES strategies by retention of subspace information. Copyright © 2004 John Wiley & Sons, Ltd.