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A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation

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  • Bai, Feng
  • Wang, Yi

Abstract

This paper presents a method to embed the Gauss–Newton approximated tensor (GNAT) reduced order model (ROM) into the hybrid snapshot simulation to enhance generation speed and representation of snapshot data for constructing GNAT ROMs. The snapshot simulation is divided into multiple temporal intervals, each of which is simulated by one of three numerical models: the full order model (FOM), the local ROM based on Petrov–Galerkin projection (ROM-PG), or the local ROM based on GNAT (ROM-GNAT). New model switch criteria are proposed to determine alternation among FOM, ROM-PG and ROM-GNAT in the simulation on-the-fly, which not only expedites snapshot data generation, but also preserves its underlying subspace representation. In contrast to existing GNAT approaches, the proper orthogonal decomposition (POD) modes of the residual and the column-reduced Jacobian in our local ROM-GNATs are continuously updated by the incremental singular value decomposition (iSVD) of the snapshot data generated by both the FOM and the local ROM-PG in the preceding intervals. The GNAT-embedded snapshot simulation is implemented for the recently proposed finite volume discretization of the 2D Burgers equation, and demonstrated for flow with weak divergence (Re≤100). Compared with its traditional counterparts, the proposed method accelerates the snapshot simulation by 33% while keeping the numerical error (RMSE) around 10−3. In online simulation, the ROM-GNAT constructed using the proposed hybrid snapshot method is compared with the high fidelity FOM. It is found that the ROM-GNAT is 70% faster and the numerical error (RMSE) is less than 10−2 relative to the FOM in the online simulation.

Suggested Citation

  • Bai, Feng & Wang, Yi, 2022. "A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 100-132.
    • Handle: RePEc:eee:matcom:v:199:y:2022:i:c:p:100-132
    DOI: 10.1016/j.matcom.2022.03.006
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    References listed on IDEAS

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    1. Sheng, Ying & Zhang, Tie & Jiang, Zhong-Zhong, 2016. "A stabilized finite volume method for the stationary Navier–Stokes equations," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 363-372.
    2. Luo, Zhendong & Li, Hong & Sun, Ping & An, Jing & Navon, Ionel Michael, 2013. "A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 50-68.
    3. Antil, Harbir & Heinkenschloss, Matthias & Hoppe, Ronald H.W. & Linsenmann, Christopher & Wixforth, Achim, 2012. "Reduced order modeling based shape optimization of surface acoustic wave driven microfluidic biochips," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1986-2003.
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