Print Email Facebook Twitter Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software Title Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software Author Qiu, Y. (TU Delft Team Michel Verhaegen) van Gijzen, M.B. (TU Delft Numerical Analysis) van Wingerden, J.W. (TU Delft Team Jan-Willem van Wingerden; TU Delft Team Michel Verhaegen) Verhaegen, M.H.G. (TU Delft Team Raf Van de Plas; TU Delft Team Michel Verhaegen) Vuik, Cornelis (TU Delft Numerical Analysis) Date 2018 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. Subject partial differential equationsmultilevel sequentially semiseparable matricespreconditionerscomputational fluid dynamicsmultigrid method To reference this document use: http://resolver.tudelft.nl/uuid:c15b1895-311c-4cdb-98a4-fb7c0303b391 DOI https://doi.org/10.1002/mma.3416 Embargo date 2021-11-03 ISSN 0170-4214 Source Mathematical Methods in the Applied Sciences, 41 (3), 888-903 Bibliographical note This work is an extension of the paper that has been presented in the 11th International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece, 2013 (reference 3) Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2018 Y. Qiu, M.B. van Gijzen, J.W. van Wingerden, M.H.G. Verhaegen, Cornelis Vuik Files PDF mma.3416.pdf 3.11 MB Close viewer /islandora/object/uuid:c15b1895-311c-4cdb-98a4-fb7c0303b391/datastream/OBJ/view