The finite element square reduced (FE2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations
The finite element square reduced (FE2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations
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DOI：
10.1002/nme.5188
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发表时间：
2016-09
影响因子：
2.9
通讯作者：
F. Fritzen;M. Hodapp
中科院分区：
文献类型：
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作者：
F. Fritzen;M. Hodapp
FE 2方法是一种用于具有细尺度微观结构的固体材料的著名计算多尺度模拟技术。它允许准确预测的非均匀材料的非线性材料行为的结构的力学行为。然而，FE 2方法导致过多的CPU时间和存储需求，即使是学术二维问题。为了实现逼真的三维双尺度模拟，需要显著减少CPU和内存使用。为此，作者最近提出了一个减少基均匀化计划的基础上的混合增量变分原理。该方法利用了广义标准材料的潜在结构。因此，可以实现重要的速度提升和内存节省。使用高性能GPU，可以进一步加速缩减基方法。在本文中，我们将以前的工作结合起来，并扩展形成FE 2-约化方法：FE 2 R。FE 2 R可用于以可接受的计算成本模拟三维结构问题，并考虑底层材料的非线性和微观结构。因此，它允许在非线性多尺度模拟的复杂性的新水平。数值例子说明了所选择的方法的能力。版权所有© 2016约翰威利父子有限公司.
The FE2 method is a renown computational multiscale simulation technique for solid materials with fine‐scale microstructure. It allows for the accurate prediction of the mechanical behavior of structures made of heterogeneous materials with nonlinear material behavior. However, the FE2 method leads to excessive CPU time and storage requirements, even for academic two‐dimensional problems. In order to allow for realistic three‐dimensional two‐scale simulations, a significant reduction of the CPU and memory usage is required. For this purpose, the authors have recently proposed a reduced basis homogenization scheme based on a mixed incremental variational principle. The approach exploits the potential structure of generalized standard materials. Thereby, important speed‐ups and memory savings can be achieved. Using high‐performance GPUs, the reduced‐basis method can be further accelerated. In the present contribution, our previous works are combined and extended to form the FE2‐reduced method: the FE2R. The FE2R can be used to simulate three‐dimensional structural problems with consideration of the nonlinearity and microstructure of the underlying material at acceptable computational cost. Thereby, it allows for a new level of complexity in nonlinear multiscale simulations. Numerical examples illustrate the capabilities of the chosen approach. Copyright © 2016 John Wiley & Sons, Ltd.