A comparison of deflation and coarse grid correction applied to porous media flow

Report (2003)

Authors

Faculty
Electrical Engineering, Mathematics and Computer Science (EEMCS) (TU Delft)
Copyright: © 2003 Department of Applied Mathematical Analysis
Conjugate gradients Preconditioners Deflation Porous media flow Coarse grid correction Scalable parallel preconditioner
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Published Date

2003

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Source:

Reports of the Department of Applied Mathematical Analysis, 03-10

ISSN:

1389-6520

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all deflation vectors and all restrictions and prolongations, below the condition number of the system preconditioned by the coarse grid correction. This implies that the Conjugate Gradient method applied to the de ated preconditioned system converges always faster than the Conjugate Gradient method applied to the system preconditioned by the coarse grid correction. Numerical results for porous media flows emphasize the theoretical results.

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