Stabilized explicit peer methods with parallelism across the stages for stiff problems

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Giovanni Pagano
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引用次数: 0

Abstract

In this manuscript, we propose a new family of stabilized explicit parallelizable peer methods for the solution of stiff Initial Value Problems (IVPs). These methods are derived through the employment of a class of preconditioners proposed by Bassenne et al. (2021) [5] for the construction of a family of linearly implicit Runge-Kutta (RK) schemes.

In this paper, we combine the mentioned preconditioners with explicit two-step peer methods, obtaining a new class of linearly implicit numerical schemes that admit parallelism on the stages. Through an in-depth theoretical investigation, we set free parameters of both the preconditioners and the underlying explicit methods that allow deriving new peer schemes of order two, three and four, with good stability properties and small Local Truncation Error (LTE). Numerical experiments conducted on Partial Differential Equations (PDEs) arising from application contexts show the efficiency of the new peer methods proposed here, and highlight their competitiveness with other linearly implicit numerical schemes.

针对僵化问题的跨阶段并行稳定显式同行方法
在本手稿中,我们提出了一系列新的稳定化显式可并行同行方法,用于解决僵硬的初值问题(IVPs)。这些方法是通过使用 Bassenne 等人(2021 年)[5] 为构建线性隐式 Runge-Kutta (RK) 方案系列而提出的一类预处理器而得到的。在本文中,我们将上述预处理器与显式两步同行方法相结合,得到了一类新的允许级并行的线性隐式数值方案。通过深入的理论研究,我们设定了预处理和基础显式方法的自由参数,从而推导出具有良好稳定性和较小局部截断误差(LTE)的二阶、三阶和四阶新同级方案。在应用背景下产生的偏微分方程(PDEs)上进行的数值实验表明,这里提出的新同阶方法非常高效,并突出了它们与其他线性隐式数值方案的竞争力。
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
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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