A Preconditioned Scheme for Nonsymmetric Saddle-Point Problems

  • Abdelkader Baggag


In this paper, we present an effective preconditioning technique for solving nonsymmetric saddle-point problems. In particular, we consider those saddle-point problems that arise in the numerical simulation of particulate flows—flow of solid particles in incompressible fluids, using mixed finite element discretization of the Navier–Stokes equations.

These indefinite linear systems are solved using a preconditioned Krylov subspace method with an indefinite preconditioner. This creates an inner–outer iteration, in which the inner iteration is handled via a preconditioned Richardson scheme. We provide an analysis of our approach that relates the convergence properties of the inner to the outer iterations. Also “optimal” approaches are proposed for the implicit construction of the Richardson’s iteration preconditioner. The analysis is validated by numerical experiments that demonstrate the robustness of our scheme, its lack of sensitivity to changes in the fluid–particle system, and its “scalability”.


Outer Iteration Particulate Flow Krylov Subspace Method Conjugate Gradient Iteration Nest Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been done in collaboration with Prof. Ahmed Sameh, and the author would like to acknowledge him for his continuous support.


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Authors and Affiliations

  1. 1.College of Science and EngineeringUniversité LavalQuebec CityCanada

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