Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of certain partial differential equations (PDEs) using conventional techniques where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the "plug-and-play" integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multi-scale coupling of finite element FOMs in solid mechanics, we present a new extension of the Schwarz formulation that enables ROM-FOM and ROM-ROM coupling in nonlinear solid mechanics. In order to maintain efficiency, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting approach. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.
翻译:以投影为基础的降序模型(ROMs)可以实现大量的计算速度,这在实时或多盘分析中特别有用。投影式的ROM的一个已知缺陷是,它们可能缺乏强健、稳定和准确性,特别是在预测性制度中,这最终限制了它们的有用应用。另一个妨碍在建模和模拟界广泛采用ROM的研究差距是,由于这种更为紧凑的代表性,因此,投影式降序模型(ROMs)可以实现大量的计算速度,这在实时或多盘分析中特别有用。投影式的ROM(FMs)是一个已知的缺陷,即它们可能因缺乏稳健、稳定性和准确性,特别是在预测性制度中,而最终限制了其实用性应用。另一个妨碍在建模和模拟界广泛采用ROM(ROM)中广泛采用ROM(ROM)的仪表)的模型,其理论基础和算法是,将这些模型的“插图”纳入现有的多制和多盘框架。本文描述了一种新的方法,通过Schwarz(S-ROM)的不断变动的变压式变压式模型,将我们目前的S-ROM(Sch-RO)系统的系统升级的系统,使目前的Sch-Sch-roal-romod-ro)系统能够使目前不断调整一个不断的系统变动的系统成为新的系统。