First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs
Name
Numerical Methods Partial - 2025 - Nguyen - First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric.pdf
Description
Published version
Size
1.99 MB
Format
Adobe PDF
Checksum (MD5)
8e1b29aa2f947f1ceb41d17548706e9b
Author(s)
Nguyen, Ngoc Cuong
Date Issued
March 31, 2025
Journal
Numerical Methods for Partial Differential Equations
Publisher
Wiley
Citation
Nguyen, N.C. (2025), First-Order Empirical Interpolation Method for Real-Time Solution of Parametric Time-Dependent Nonlinear PDEs. Numer Methods Partial Differential Eq., 41: e70006.
Version
Final published version
Abstract
We present a model reduction approach for the real-time solution of time-dependent nonlinear partial differential equations(PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced-order models for nonlin-ear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methodsto deal with nonlinear terms. Furthermore, we introduce a first-order empirical interpolation method (EIM) to provide an effi-cient approximation of the nonlinear terms in time-dependent PDEs. We demonstrate the effectiveness of our approach on theAllen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two-phase fluid flowin porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with boththe Galerkin–Newton approach and hyper-reduced models using the standard EIM.
MIT Department
Massachusetts Institute of Technology. Center for Computational Engineering
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1002/num.70006
