International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

For Online Access

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2008, Volume6

Issue 1

114 pages

DOI: 10.1615/IntJMultCompEng.v6.i1

Issue price - $150.00

J. M. Tang
Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, J. M. Burgerscentrum, Mekelweg 4,2628 CD Delft, The Netherlands

C. Vuik
Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, J. M. Burgerscentrum, Mekelweg 4,2628 CD Delft, The Netherlands

Traditional Krylov iterative solvers, such as the preconditioned conjugate gradient method, can be accelerated by incorporating a second-level preconditioner. We use deflation as a second-level preconditioner, which is very efficient in many applications. In this paper, we give some theoretical results for the general deflation method applied to singular matrices, which provides us more insight into the properties and the behavior of the method. Moreover, we discuss stability issues of the deflation method and consider some ideas for a more stable method. In the numerical experiments, we apply the deflation method and its stabilized variant to singular linear systems derived from two-phase bubbly flow problems. Because of the appearance of bubbles, those linear systems are ill-conditioned, and therefore, they are usually hard to solve using traditional preconditioned Krylov iterative methods. We show that our deflation methods can be very efficient to solve the linear systems. Finally, we also investigate numerically the stability of these methods by examining the corresponding inner-outer iterations in more detail.

DOI: 10.1615/IntJMultCompEng.v6.i1.20 Download article, 13-24 pages

Article price - $12.00

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