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Spectral properties of primal-based penalty preconditioners for saddle point problems

✍ Scribed by Shu-Qian Shen; Ting-Zhu Huang; Er-Jie Zhong

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
603 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

For large and sparse saddle point linear systems, this paper gives further spectral properties of the primal-based penalty preconditioners introduced in [C.R. Dohrmann, R.B. Lehoucq, A primal-based penalty preconditioner for elliptic saddle point systems, SIAM J. Numer. Anal. 44 (2006) 270-282]. The regions containing the real and non-real eigenvalues of the preconditioned matrix are obtained. The model of the Stokes problem is supplemented to illustrate the theoretical results and to test the quality of the primal-based penalty preconditioner.

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A comparison of overlapping Schwarz meth
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Three domain decomposition methods for saddle point problems are introduced and compared. The first two are blockdiagonal and block-triangular preconditioners with diagonal blocks approximated by an overlapping Schwarz technique with positive definite local and coarse problems. The third is an overl