A Two-Step Sequential Hyper-Reduction Method for Efficient Concurrent Nonlinear FE 2 Analyses

Yujin So and Jaehun Lee ()
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Yujin So: Department of Mechanical, Robotics and Energy Engineering, Dongguk University, Seoul 04620, Republic of Korea
Jaehun Lee: Department of Mechanical, Robotics and Energy Engineering, Dongguk University, Seoul 04620, Republic of Korea

Mathematics, 2025, vol. 13, issue 11, 1-18

Abstract: In this paper, we propose a two-step sequential hyper-reduction method to significantly enhance computational efficiency for both macro- and micro-level analyses in concurrent nonlinear FE 2 multiscale simulations. In general, one of the major computational burdens of nonlinear FE 2 problems is the repetitive micro-level analysis, which must be performed at all integration points of the macroscopic structure. We propose adopting the discrete empirical interpolation method (DEIM) for both macroscopic and microscopic problems, achieving a significant reduction in the number of integration points in both models. The proposed two-step sequential framework aligns with reduced-order modeling, enabling an efficient multiscale procedure for concurrent nonlinear FE 2 analysis in the online stage. We verified the accuracy and efficiency of FE 2 analysis using the proposed method through a simple example.

Keywords: multiscale finite element method; FE 2 analysis; reduced-order model; hyper-reduction; discrete empirical interpolation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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