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Global‐basis two‐level method for indefinite systems. Part 1: convergence studies
Author(s) -
Fish Jacob,
Qu Yong
Publication year - 2000
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 - 10.1002/1097-0207(20000930)49:3<439::aid-nme981>3.0.co;2-a
Subject(s) - convergence (economics) , smoothing , discretization , solver , mathematics , finite element method , operator (biology) , sensitivity (control systems) , basis (linear algebra) , matrix (chemical analysis) , mathematical optimization , mathematical analysis , geometry , engineering , biochemistry , statistics , chemistry , materials science , structural engineering , repressor , electronic engineering , transcription factor , economics , composite material , gene , economic growth
A robust two‐level solver for high indefinite system of equations arising from the finite element discretization is developed. It is shown that the optimal coarse model is spanned by the spectrum of the highest eigenmodes of the smoothing iteration matrix. Convergence studies conducted on a model prolongation operator reveal pathological sensitivity to any deviation from the optimal coarse model. Copyright © 2000 John Wiley & Sons, Ltd.