Börm, Steffen and Le Borne, Sabine (2012) H-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems. International Journal for Numerical Methods in Fluids, 68 (1). pp. 83-98. DOI 10.1002/fld.2495.

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Abstract

The (mixed finite element) discretization of the linearized Navier–Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as ‘grad-div’ (GD) stabilization, as well as on the discrete side where it is known as an ‘augmented Lagrangian’ (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ℋ-LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ℋ-LU factorization in the preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.

Document Type:	Article
Keywords:	saddle point problems Oseen problem grad‐div stabilization augmented Lagrangian method hierarchical matrices ℋ︁‐LU
Research affiliation:	Kiel University > Kiel Marine Science OceanRep > The Future Ocean - Cluster of Excellence Kiel University
Refereed:	Yes
Open Access Journal?:	Yes
Publisher:	American Medical Association
Projects:	Future Ocean
Date Deposited:	14 May 2014 10:21
Last Modified:	05 Aug 2019 09:55
URI:	https://oceanrep.geomar.de/id/eprint/23842

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