Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
Fast Deflation Methods with Applications to Two-Phase Flows
RÉSUMÉ
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.
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Tang J. M., Nabben R., Vuik C., Erlangga Y. A., Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods, Journal of Scientific Computing, 39, 3, 2009. Crossref
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Deb Pulok Kanti, Akter Farhana, Imtiaz Syed Ahmad, Hossain M. Enamul, Nonlinearity and solution techniques in reservoir simulation: A review, Journal of Natural Gas Science and Engineering, 46, 2017. Crossref
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Erlangga Yogi A., Nabben Reinhard, On the convergence of two-level Krylov methods for singular symmetric systems, Numerical Linear Algebra with Applications, 24, 6, 2017. Crossref