通过增量方法加速构建基于投影的降阶模型

IF 2 Q3 MECHANICS
Eki Agouzal, Tommaso Taddei
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引用次数: 0

摘要

我们提出了一种基于投影的参数稳定和非稳定偏微分方程减阶模型训练的加速贪婪策略。我们的方法利用分层近似正交分解加速构建最小平方 Petrov-Galerkin 公式的经验测试空间,基于非负最小平方算法的热启动逐步构建经验正交规则,以及双保真度采样策略减少昂贵的贪婪迭代次数。我们在两个测试案例中说明了我们的方法的性能:在中等马赫数下流经 LS89 叶片的二维可压缩无粘性流,以及预测核安全壳建筑标准部分在外部载荷作用下的长期结构响应的三维非线性力学问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Accelerated construction of projection-based reduced-order models via incremental approaches
We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal decomposition to speed up the construction of the empirical test space for least-square Petrov–Galerkin formulations, a progressive construction of the empirical quadrature rule based on a warm start of the non-negative least-square algorithm, and a two-fidelity sampling strategy to reduce the number of expensive greedy iterations. We illustrate the performance of our method for two test cases: a two-dimensional compressible inviscid flow past a LS89 blade at moderate Mach number, and a three-dimensional nonlinear mechanics problem to predict the long-time structural response of the standard section of a nuclear containment building under external loading.
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来源期刊
Advanced Modeling and Simulation in Engineering Sciences
Advanced Modeling and Simulation in Engineering Sciences Engineering-Engineering (miscellaneous)
CiteScore
6.80
自引率
0.00%
发文量
22
审稿时长
30 weeks
期刊介绍: The research topics addressed by Advanced Modeling and Simulation in Engineering Sciences (AMSES) cover the vast domain of the advanced modeling and simulation of materials, processes and structures governed by the laws of mechanics. The emphasis is on advanced and innovative modeling approaches and numerical strategies. The main objective is to describe the actual physics of large mechanical systems with complicated geometries as accurately as possible using complex, highly nonlinear and coupled multiphysics and multiscale models, and then to carry out simulations with these complex models as rapidly as possible. In other words, this research revolves around efficient numerical modeling along with model verification and validation. Therefore, the corresponding papers deal with advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation and simulation-based control. These challenging issues require multidisciplinary efforts – particularly in modeling, numerical analysis and computer science – which are treated in this journal.
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