Fast and Novel Computational Methods for Multi-scale and Multi-physics: FETI and POD-ROM
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ORIGINAL RESEARCH
Fast and Novel Computational Methods for Multi‑scale and Multi‑physics: FETI and POD‑ROM Si‑Hun Lee1 · Yongse Kim1 · DuHyun Gong1 · HyunShig Joo1 · Haeseong Cho2 · Haedong Kim3 · SangJoon Shin4 Received: 8 June 2020 / Revised: 3 August 2020 / Accepted: 5 September 2020 © Korean Multi-Scale Mechanics (KMSM) 2020
Abstract In this paper, the finite element tearing and interconnecting (FETI) method and proper orthogonal decomposition-based reduced order model (POD-ROM) are suggested as fast and novel computational approaches for multi-scale and multi-physics analysis. FETI is one of non-overlapping domain decomposition methods, facilitating the parallel computation. POD-ROM reduces the number of degrees of freedom (DoFs) to several representative POD modes which completely describe the behavior of the full order model. The computational time for the analyses using large number of DoFs can be decreased by using the previously mentioned methods. The present FETI-local and POD-ROM are found to reduce computational time significantly in each example. Keywords Finite element tearing and interconnecting · Reduced order model · Proper orthogonal decomposition · Computational structural dynamics · Computational fluid dynamics
Introduction
* SangJoon Shin [email protected] Si‑Hun Lee [email protected] Yongse Kim [email protected] DuHyun Gong [email protected] HyunShig Joo [email protected] Haeseong Cho [email protected] Haedong Kim [email protected] 1
Seoul National University, Seoul 08826, Republic of Korea
2
Jeonbuk National University, Jeonju 54896, Republic of Korea
3
Sejong University, Seoul 05006, Republic of Korea
4
Institute of Advanced Aerospace Technology, Seoul National University, Seoul 08826, Republic of Korea
Computational multi-scale or multi-physics require timeefficient methodologies due to required excessive number of degrees of freedom (DoFs) and iterations. An example of multi-scale computation is complex composite materials which are fabricated from various ingredients with different properties. Eulerian and Lagrangian descriptions of fluid and structural dynamics are usually involved in fluid–structure interaction (FSI) analyses. Thus, significant number of iterations needs to be conducted for at time step. In this paper, both finite element tearing and interconnecting (FETI) and proper orthogonal decomposition-based reduced order model (POD-ROM) are suggested in order for domain decomposition and fast/novel computation. FETI is one of the non-overlapping domain decomposition methods for parallel computation. Since the first introduction to the original FETI method by Farhat et al. [1], further improvements and applications have shown up [2–6]. Its recent progress revealed the scalability upto 21 billions of DoFs by using iterative reciprocal computation [7]. Consequently, FETI method is applicable for the multi-scale or multi-scale problems with large number of DoFs by parallell computing the divided subdomains. While FETI handles the complete number of DoFs ef
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