A new strategy using the Proper Generalized Decomposition to model time evolving spatial domains

IF 4.8 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Max Beckermann , Ronan Scanff , Massimiliano Cremonesi , Andrea Barbarulo
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Abstract

In this paper, we propose a new approach to adapt the Proper Generalized Decomposition (PGD) to problems containing space domains that are evolving over time. PGD shines with high-order parametrized and nonlinear problems, drastically reducing their computational time. It was proven highly effective in a wide range of problems, but the space domain has always remained fixed within the parametric manifold of interest. In this work, we adapt the PGD to non-constant domains that change over time at given discrete time instances. More specifically, we focus on time evolving space domains and separate the solution along space and time. The space modes are calculated in an expanded space that comprises all the degrees of freedom throughout the simulation. To visualize the solution, the modes are then projected onto the current physical representation. The time modes are solved in a piecewise manner, dividing the time domain into intervals and initializing the time modes to zero at the beginning of each interval. This work is illustrated with an additive manufacturing-inspired example in which the hot boundary elements are sequentially activated to simulate the addition of material. This aligns perfectly with the previously described strategy as it involves an expanding boundary. The impact of the mesh division and the initialization of the new points is discussed.
一种利用适当广义分解对时间演化空间域进行建模的新策略
在本文中,我们提出了一种新的方法,使适当广义分解(PGD)适用于包含随时间变化的空间域的问题。PGD擅长处理高阶参数化和非线性问题,大大减少了它们的计算时间。它被证明在广泛的问题中是非常有效的,但空间域始终保持固定在感兴趣的参数流形内。在这项工作中,我们使PGD适应在给定离散时间实例下随时间变化的非恒定域。更具体地说,我们关注时间演化的空间域,并沿着空间和时间分离解决方案。空间模态是在包含整个仿真过程中所有自由度的扩展空间中计算的。为了可视化解决方案,然后将模式投影到当前的物理表示上。时间模式以分段方式求解,将时域划分为多个区间,并在每个区间的开始处初始化时间模式为零。这项工作用一个增材制造启发的例子来说明,其中热边界元素被依次激活以模拟材料的添加。这与前面描述的策略完全一致,因为它涉及扩展边界。讨论了网格划分和新点初始化的影响。
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
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.
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