光滑最低阶虚元法的Schwarz预条件

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-08-12 DOI:10.1016/j.camwa.2025.08.006

Luis F. Amey , Juan G. Calvo , Josué Padilla-Torres

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引用次数: 0

摘要

本文介绍了一种谱等效于虚元法的虚平滑方法。此外，我们设计了一种针对不规则子域的鲁棒两级Schwarz预调节器，适用于扩展光滑有限元方法、光滑应变单元方法和所提出的光滑虚拟单元方法。给出了新方法的理论证明，包括预条件系统的谱估计。数值实验验证了该方法在求解不规则子域中的有效性、可扩展性和实用性。

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A Schwarz preconditioner for the smoothed lowest-order virtual element method

In this paper we introduce a novel virtual smoothed method that is spectrally equivalent to the virtual element method. Furthermore, we design a robust two-level Schwarz preconditioner tailored for irregular subdomains, applicable to extended smoothed finite element methods, smoothed strain element methods, and the proposed smoothed virtual element method. Theoretical proofs are provided for the new method, including spectral estimates of the preconditioned system. Numerical experiments validate the effectiveness, scalability, and practical applicability of the approach in addressing irregular subdomains.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).