高效计算用于二阶微分方程积分的 sinc 矩阵函数

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED Advances in Computational Mathematics Pub Date : 2024-10-28 DOI:10.1007/s10444-024-10202-y
Lidia Aceto, Fabio Durastante
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引用次数: 0

摘要

这项工作涉及振荡二阶微分方程系统的数值求解,这些系统通常产生于偏微分方程的空间半离散化。由于这些微分方程表现出(明显或高度)振荡行为,标准数值方法的性能很差。我们的方法是通过基于 sinc 矩阵函数的 Gautschi-type 积分器直接将问题离散化。这里的新颖之处在于,使用 sinc 矩阵函数的合适有理近似公式,在适当选择极点的情况下,应用类似克雷洛夫的有理近似方法。我们特别讨论了整个策略在波方程有限元离散化中的应用。
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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Efficient computation of the sinc matrix function for the integration of second-order differential equations

This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit (pronounced or highly) oscillatory behavior, standard numerical methods are known to perform poorly. Our approach consists in directly discretizing the problem by means of Gautschi-type integrators based on sinc matrix functions. The novelty contained here is that of using a suitable rational approximation formula for the sinc matrix function to apply a rational Krylov-like approximation method with suitable choices of poles. In particular, we discuss the application of the whole strategy to a finite element discretization of the wave equation.

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来源期刊
CiteScore
3.00
自引率
5.90%
发文量
68
审稿时长
3 months
期刊介绍: Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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