三维可压缩Navier-Stokes方程DPG格式的自适应双网格求解器

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2023-07-12 DOI:10.1515/cmam-2022-0206
W. Rachowicz, W. Cecot, A. Zdunek
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引用次数: 0

摘要

摘要我们提出了一个三维可压缩粘性流离散化线性系统的重叠域分解迭代求解器。它是一个双网格求解器,利用辅助粗网格上的解和由粗网格基本形状函数的支持定义的元素块上的标准块Jacobi迭代。以这种方式定义的简单迭代被用作共轭梯度过程的预处理器。理论分析表明,预处理系统的条件数应独立于实际有限元网格和辅助粗网格,前提是它们是拟均匀的。数值试验证实了这一结果。此外,它们表明,强扁平或细长元件的存在不会减缓收敛。有限元网格具有自适应性,即划分具有大误差的单元,直到达到所需的精度。辅助粗网格正在根据不均匀的实际网格进行调整。
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An Adaptive Two-Grid Solver for DPG Formulation of Compressible Navier–Stokes Equations in 3D
Abstract We present an overlapping domain decomposition iterative solver for linear systems resulting from the discretization of compressible viscous flows with the Discontinuous Petrov–Galerkin (DPG) method in three dimensions. It is a two-grid solver utilizing the solution on the auxiliary coarse grid and the standard block-Jacobi iteration on patches of elements defined by supports of the coarse mesh base shape functions. The simple iteration defined in this way is used as a preconditioner for the conjugate gradient procedure. Theoretical analysis indicates that the condition number of the preconditioned system should be independent of the actual finite element mesh and the auxiliary coarse mesh, provided that they are quasiuniform. Numerical tests confirm this result. Moreover, they show that presence of strongly flattened or elongated elements does not slow the convergence. The finite element mesh is subject to adaptivity, i.e. dividing the elements with large errors until a required accuracy is reached. The auxiliary coarse mesh is adjusting to the nonuniform actual mesh.
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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