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Connection and comparison between frequency shift time integration and a spectral transformation preconditioner
Author(s) -
Meerbergen Karl,
Coyette JeanPierre
Publication year - 2009
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/nla.590
Subject(s) - preconditioner , mathematics , linear system , laplace transform , transformation (genetics) , time domain , frequency domain , domain decomposition methods , finite element method , algorithm , mathematical analysis , computer science , physics , biochemistry , chemistry , computer vision , gene , thermodynamics
Abstract The numerical study of exterior acoustics problems is usually carried out in the frequency domain. Finite element analyses often require the solution of large‐scale algebraic linear systems. For very large problems, sometimes the time domain is used. Implicit time integration requires linear system solves, but these are often far easier than those from the frequency domain. This paper shows a connection between a spectral transformation preconditioner and a frequency shift time integration. This preconditioner is close to the shifted Laplace preconditioner. The preconditioned iterative method appears to be faster than time integration. Copyright © 2008 John Wiley & Sons, Ltd.