Fast convergence of SPH numerical solutions using robust algebraic multilevel

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science Pub Date : 2024-06-27 DOI:10.1016/j.jocs.2024.102369

L.P. da Silva , C.H. Marchi , M. Meneguette , R. Suero

引用次数: 0

Abstract

In our study we solve 2D equations that model the mathematical phenomenon of steady state heat diffusion. The discretization of the equations is performed with the smoothed particle hydrodynamics (SPH) method and the resolution of the associated system of linear equations is determined with a modified solver that we call the Gauss–Seidel–Silva (G–S–S). The single level parallel G–S–S solver is compared to the algebraic multilevel (AML) with serial G–S–S smoother which has the ability to smooth the error of the numerical solutions and accelerate convergence due to its iterative formulation. The AML with serial G–S–S smoother is responsible for determining speed-ups of 4084 times for uniform and 5136 times for non-uniform particle discretization. We estimate a speed-up of 41082 times for the AML with parallel G–S–S smoother.

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使用鲁棒代数多级法快速收敛 SPH 数值解法

在我们的研究中，我们求解了模拟稳态热扩散数学现象的二维方程。方程的离散化采用平滑粒子流体力学（SPH）方法，相关线性方程组的分辨率采用我们称之为高斯-赛德尔-席尔瓦（G-S-S）的改进求解器确定。单级并行 G-S-S 求解器与带串行 G-S-S 平滑器的代数多级 (AML) 求解器进行了比较。带串行 G-S-S 平滑器的代数多级 (AML) 可以将均匀粒子离散化的速度提高 4084 倍，将非均匀粒子离散化的速度提高 5136 倍。我们估计，采用并行 G-S-S 平滑器的 AML 的速度提高了 41082 倍。

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

Journal of Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS

CiteScore

5.50

自引率

3.00%

发文量

227

审稿时长

41 days

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