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Analysis of matrix‐dependent multigrid algorithms
Author(s) -
Shapira Yair
Publication year - 1998
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199805/06)5:3<165::aid-nla132>3.0.co;2-n
Subject(s) - multigrid method , mathematics , matrix (chemical analysis) , convergence (economics) , separable space , algorithm , grid , class (philosophy) , mathematical optimization , symbolic convergence theory , computer science , partial differential equation , key (lock) , mathematical analysis , geometry , materials science , computer security , artificial intelligence , economics , composite material , economic growth
Convergence theory for a multigrid method with matrix‐dependent restriction, prolongation and coarse‐grid operators is developed for a class of SPD problems. It motivates the construction of improved multigrid versions for diffusion problems with discontinuous coefficients. A computational two‐level analysis method for a class of separable problems is also available. It motivates the design of matrix‐dependent multigrid algorithms and, in particular, multiple coarse‐grid correction algorithms for highly indefinite equations. Numerical experiments show the advantage of the present methods for several examples. © 1998 John Wiley & Sons, Ltd.