Author

Feng Bai

Date of Award

Summer 2021

Document Type

Open Access Dissertation

Department

Mechanical Engineering

First Advisor

Yi Wang

Abstract

Reduced order model (ROM) is an emerging technique for rapid and efficient numerical simulation and computation in science and engineering applications. The ROM consists of two stages: (1) the offline snapshot simulation to produce high-quality snapshot data representative of model trajectories, from which the projection subspace can be extracted and used for ROM construction; and (2) the online simulation to utilize the ROM built in stage 1. The snapshot simulation is traditionally performed with full order model (FOM) and is computationally demanding, which is one of the most critical limiting factors for the development and deployment of ROM in real-world applications. In this study, a new hybrid snapshot simulation framework and algorithms are proposed to tackle this challenge by accelerating the offline snapshot simulation and reducing its computational resource usage.

In Chapter.2 of this dissertation, a hybrid snapshot simulation methodology and framework that alternates the simulation automatically between FOM and ROM is proposed, which for the first time adopts local ROMs to accelerate the snapshot data generation and demonstrates up to 50% speedup over the traditional method. In Chapter.3, the proposed hybrid snapshot simulation method is extended to construct ROM with discrete empirical interpolation method (DEIM), which enables fast reconstruction of nonlinear terms in the ROM and significantly speeds up the online simulation. In Chapter.4, a new approach to embed the DEIM into the hybrid snapshot simulation is presented, which gains additional acceleration by 10.5% ~ 27.8% relative to that developed in Chapter.2. In Chapter.5, a hyper-reduction method is introduced into the proposed hybrid simulation framework. It is based on the Gauss- Newton solver with approximated tensors(GNAT) at the level of discretized algebraic equations to realize additional system approximation of the nonlinear dynamic systems. Its potential to improve computational performance is examined thoroughly with the 2D Burgers equation. It is found that the GNAT-embedded hybrid snapshot simulation achieves 33% computational acceleration relative to the traditional FOM-based snapshot simulation for the example problem: flow of weak gradients (Re 100) while preserving ROM accuracy, viz., RMSE ~ O(10−3).

All the studies conducted in this dissertation convincingly verify the feasibility of the proposed hybrid snapshot simulation methodology. Additional system identification through DEIM or GNAT could further improve its computational efficiency.

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