A fully separated space-time decomposition for the simulation of viscoelastic structures

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures Pub Date : 2025-08-21 DOI:10.1016/j.compstruc.2025.107912

Hendrik Geisler , David Néron , Philipp Junker

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Abstract

A space-time decomposition based on the Proper Generalized Decomposition for viscoelastic structures is presented. The displacement field and the field of the internal variable are each represented by a sum of products of space and time modes. Due to the linearity of the evolution equation of the internal variable in the strains, the calculation of space and time modes can be fully separated. In contrast to earlier studies on the subject, this work presents a fully separated framework throughout the entire algorithm. Nevertheless, the strong coupling of balance of linear momentum equation and evolution equation is kept intact. Therefore, the resulting scheme resembles classical schemes easing the implementation. The efficiency and robustness of the method are investigated for a variety of boundary value problems. For problems with more than 20 time steps, the presented method is often more efficient. The source code is available at https://github.com/ikm-luh/SpaceTimeDecomp_SourceCode.

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粘弹性结构模拟的完全分离时空分解

针对粘弹性结构，提出了一种基于适当广义分解的空时分解方法。位移场和内变量场分别用空间模态和时间模态乘积的和表示。由于应变内变量演化方程的线性性，空间模态和时间模态的计算可以完全分离。与早期对该主题的研究相反，这项工作在整个算法中提出了一个完全分离的框架。然而，线性动量方程与演化方程的平衡保持了强耦合。因此，生成的方案类似于简化实现的经典方案。针对各种边值问题，研究了该方法的有效性和鲁棒性。对于超过20个时间步长的问题，所提出的方法通常更有效。源代码可从https://github.com/ikm-luh/SpaceTimeDecomp_SourceCode获得。

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

Computers & Structures 工程技术-工程：土木

CiteScore

8.80

自引率

6.40%

发文量

122

审稿时长

33 days

期刊介绍： Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.