Title: First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

Journal Article · · Numerical Methods for Partial Differential Equations
DOI: https://doi.org/10.1002/num.70006 · OSTI ID:2545099
 [1]
  1. Center for Computational Engineering, Department of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge Massachusetts USA
+ Show Author Affiliations

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 nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Sponsoring Organization:
USDOE
Grant/Contract Number:
NA0003965
OSTI ID:
2545099
Journal Information:
Numerical Methods for Partial Differential Equations, Journal Name: Numerical Methods for Partial Differential Equations Journal Issue: 3 Vol. 41; ISSN 0749-159X
Publisher:
Wiley Blackwell (John Wiley & Sons)Copyright Statement
Country of Publication:
United States
Language:
English

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