Nonintrusive model order reduction for cross-diffusion systems

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KARASÖZEN B., Mülayim G., Uzunca M.

Communications in Nonlinear Science and Numerical Simulation, vol.115, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 115
  • Publication Date: 2022
  • Doi Number: 10.1016/j.cnsns.2022.106734
  • Journal Name: Communications in Nonlinear Science and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Implicit-explicit methods, Matrix differential equations, Reduced-order modeling, Tensor algebra, APPROXIMATION
  • Middle East Technical University Affiliated: Yes

Abstract

© 2022 Elsevier B.V.In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting from finite difference discretization of the differential operators by taking the advantage of Kronecker structure. The matrix/tensor differential equations are integrated in time with the implicit–explicit (IMEX) Euler method. The reduced bases, relying on a finite sample set of parameter values, are constructed in form of a two-level approach by applying higher-order singular value decomposition (HOSVD) to the space–time snapshots in tensor form, which leads to a large amount of computational and memory savings. The nonintrusive reduced approximation for an arbitrary parameter value is obtained through tensor product of the reduced basis by the parameter dependent core tensor that contains the reduced coefficients. The reduced coefficients for new parameter values are computed with the radial basis functions. The efficiency of the proposed method is illustrated through numerical experiments for two-dimensional Schnakenberg and three-dimensional Brusselator cross-diffusion equations. The spatiotemporal patterns are accurately predicted by the reduced-order models with speedup factors of orders two and three over the full-order models.