当前位置: X-MOL 学术Int. J. Numer. Methods Fluids › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A comparison of block preconditioners for isogeometric analysis discretizations of the incompressible Navier–Stokes equations
International Journal for Numerical Methods in Fluids ( IF 1.8 ) Pub Date : 2020-12-14 , DOI: 10.1002/fld.4952
Hana Horníková 1 , Cornelis Vuik 2 , Jiří Egermaier 1
Affiliation  

We deal with numerical solution of the incompressible Navier–Stokes equations discretized using the isogeometric analysis (IgA) approach. Similarly to finite elements, the discretization leads to sparse nonsymmetric saddle‐point linear systems. The IgA discretization basis has several specific properties different from standard FEM basis, most importantly a higher interelement continuity leading to denser matrices. We are interested in iterative solution of the resulting linear systems using a Krylov subspace method (GMRES) preconditioned with several state‐of‐the‐art block preconditioners. We compare the efficiency of the ideal versions of these preconditioners for three model problems (for both steady and unsteady flow in two and three dimensions) and investigate their properties with focus on the IgA specifics, that is, various degree and continuity of the discretization basis. Our experiments show that the block preconditioners can be successfully applied to the systems arising from high continuity IgA, moreover, that the high continuity can bring some benefits in this context. For example, some of the preconditioners, whose convergence is h‐dependent in the steady case, seem to be less sensitive to the mesh refinement for higher continuity discretizations. In the unsteady case, we generally get faster convergence for higher continuity than for C0 continuous discretizations of the same degree for most of the preconditioners.

中文翻译:

不可压缩的Navier–Stokes方程等几何分析离散化的块预处理器比较

我们使用等几何分析(IgA)方法处理离散化的不可压缩Navier-Stokes方程的数值解。与有限元类似,离散化导致稀疏的非对称鞍点线性系统。IgA离散化基础具有与标准FEM基础不同的几个特定属性,最重要的是,较高的元素连续性导致矩阵更密集。我们对使用Krylov子空间方法(GMRES)以及几种先进的分块预处理器进行预处理的线性系统的迭代求解感兴趣。我们针对三种模型问题(二维和三维的稳态和非稳态流动)比较了这些预处理器的理想版本的效率,并重点研究了IgA的具体情况,研究了它们的特性。离散程度的不同程度和连续性。我们的实验表明,块预处理器可以成功应用于高连续性IgA产生的系统,此外,高连续性可以在这种情况下带来一些好处。例如,一些预处理器,其收敛为在稳定情况下,h依赖性对较高连续离散化的网格细化似乎不太敏感。在不稳定情况下,对于大多数预处理器而言,与相同程度的C 0连续离散化相比,对于更高的连续性,我们通常会获得更快的收敛速度。
更新日期:2020-12-14
down
wechat
bug