Local and Parallel Mixed-Precision Finite Element Methods for the Time-Dependent Incompressible Flows

IF 1.8 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2025-02-27 DOI:10.1002/fld.5388

Qingfang Liu, Jian Su, Baotong Li

引用次数: 0

Abstract

In this article, a local and parallel mixed-precision finite element method is applied for solving the time-dependent incompressible flows. We decompose the solution into the large eddy components and small eddy components based on two-grid method. The analysis shows that the small eddy components carry little part of the total energy compared with the large eddy components. In view of this character, we first obtain the large eddy components by solving the standard nonlinear equation using the high-precision solvers globally in the coarse mesh space, then get the small eddy components by solving a series of local linearized residual equation using the low-precision solvers locally and parallel based on the partition of unity. The performance advantages of the mixed-precision methods are tested with respect to speedups over a high-precision implementation in time and less storage requirements in space.

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时变不可压缩流的局部与并行混合精度有限元方法

本文采用局部并行混合精度有限元法求解时变不可压缩流。基于双网格法，将解分解为大涡流分量和小涡流分量。分析表明，与大涡流分量相比，小涡流分量携带的总能量较少。针对这一特点，首先在粗网格空间中采用高精度全局解算方法求解标准非线性方程得到大的涡流分量，然后采用低精度局部解算方法求解一系列局部线性化残差方程得到小的涡流分量。测试了混合精度方法的性能优势，即相对于高精度实现在时间上的加速和在空间上更少的存储需求。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.