xml:id='mma3416-para-0001'> This paper studies a new preconditioning technique for sparse systems arisi'/> Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software
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首页> 外文期刊>Mathematical Methods in the Applied Sciences >Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software
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Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software

机译：使用不可压缩流动和迭代求解器软件评估多级半可索收的预处理器的计算流体动力学基准问题

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xml:id="mma3416-para-0001"> 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.
机译： xml：id =“mma3416-para-0001”>本文研究了从计算流体动力学问题中由离散的部分微分方程产生的稀疏系统的新预处理技术。该预处理技术利用了系统矩阵的多级半可安装（MSSS）结构。 MSS矩阵计算提供了一种数据稀疏方式，以近似于关于问题大小的线性计算复杂度中的离散部分微分方程的稀疏矩阵的稀疏矩阵的分解。与标准块对角线和块上三角形预处理器相比，我们从离散的斯托克斯方程和线性化Navier-Stokes方程中利用了2×2块系统的全局MSSS结构。这避免了明确地逼近Schur补充，这是标准块预处理器的一个很大的优势。通过对不可压缩流动和迭代求解软件的标准计算流体动力学基准问题的数值实验，我们展示了MSS预处理器的性能。它们表明全局MSSS预处理器不仅产生网格尺寸独立收敛，还产生粘度参数和雷诺数独立收敛。与用于块预处理器的代数多缘（AMG）方法和几何多重格（GMG）方法相比，MSS预处理技术比AMG方法和GMG方法更稳健，并且比AMG方法快得多。版权？ 2015年John Wiley＆amp; SONS，LTD。

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