Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software

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Abstract

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations in computational fluid dynamics problems. This preconditioning technique exploits the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU factorization of a sparse matrix from discretized partial differential equations in linear computational complexity with respect to the problem size. In contrast to the standard block diagonal and block upper-triangular preconditioners, we exploit the global MSSS structure of the 2×2 block system from the discretized Stokes equation and linearized Navier-Stokes equation. This avoids approximating the Schur complement explicitly, which is a big advantage over standard block preconditioners. Through numerical experiments on standard computational fluid dynamics benchmark problems in Incompressible Flow and Iterative Solver Software, we show the performance of the MSSS preconditioners. They indicate that the global MSSS preconditioner not only yields mesh size independent convergence but also gives viscosity parameter and Reynolds number independent convergence. Compared with the algebraic multigrid (AMG) method and the geometric multigrid (GMG) method for block preconditioners, the MSSS preconditioning technique is more robust than both the AMG method and GMG method, and considerably faster than the AMG method. Copyright © 2015 John Wiley & Sons, Ltd.
Original languageEnglish
Pages (from-to)888-903
JournalMathematical Methods in the Applied Sciences
Volume41
Issue number3
DOIs
Publication statusPublished - 2018

Keywords

  • partial differential equations
  • multilevel sequentially semiseparable matrices
  • preconditioners
  • computational fluid dynamics
  • multigrid method

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    A class of efficient preconditioners with multilevel sequentially semiseparable matrix structure

    Qiu, Y., van Gijzen, MB., van Wingerden, JW. & Verhaegen, M., 2013, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2013 (ICNAAM-2013). Simos, T., Psihoyios, G. & Tsitouras, CH. (eds.). Melville, NY, USA: AIP Publishing, p. 2253-2256 4 p.

    Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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