The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model

Gülden Mülayim

doi:10.33187/jmsm.1650309

EN

The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model

Abstract

This work investigates reduced-order modelling (ROM) strategies for the Brusselator system, a linear cross-diffusion framework with applications in chemical and biological systems. Spatial discretization is performed via the symmetric interior penalty discontinuous Galerkin (SIPG) method, and time-stepping is handled via the backward Euler scheme to derive the full-order model (FOM). To construct reduced-order bases, singular value decomposition (SVD) is applied to a snapshot matrix of FOM solutions, followed by proper orthogonal decomposition (POD) to generate low-dimensional approximations. However, the nonlinear terms in the ROM retain the original high-dimensional structure of the FOM. To mitigate this computational burden, the discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) are integrated to approximate nonlinearities efficiently. Numerical experiments conducted on a 2D Brusselator system validate the accuracy and efficiency of the proposed POD-DEIM and POD-DMD frameworks, with both methods achieving close agreement with the FOM.

Keywords

Brusselator model, Discrete empirical interpolation method, Dynamic mode decomposition, Proper orthogonal decomposition method

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Gülden Mülayim ^*
0000-0001-8952-7658
Türkiye

Early Pub Date

August 18, 2025

Publication Date

September 11, 2025

Submission Date

March 3, 2025

Acceptance Date

July 30, 2025

Published in Issue

Year 2025 Volume: 8 Number: 3

DOI

https://doi.org/10.33187/jmsm.1650309

IZ

https://izlik.org/JA28JL88XJ

APA

Mülayim, G. (2025). The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model. Journal of Mathematical Sciences and Modelling, 8(3), 121-128. https://doi.org/10.33187/jmsm.1650309

AMA

1.Mülayim G. The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model. Journal of Mathematical Sciences and Modelling. 2025;8(3):121-128. doi:10.33187/jmsm.1650309

Chicago

Mülayim, Gülden. 2025. “The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model”. Journal of Mathematical Sciences and Modelling 8 (3): 121-28. https://doi.org/10.33187/jmsm.1650309.

EndNote

Mülayim G (September 1, 2025) The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model. Journal of Mathematical Sciences and Modelling 8 3 121–128.

IEEE

[1]G. Mülayim, “The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 3, pp. 121–128, Sept. 2025, doi: 10.33187/jmsm.1650309.

ISNAD

Mülayim, Gülden. “The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model”. Journal of Mathematical Sciences and Modelling 8/3 (September 1, 2025): 121-128. https://doi.org/10.33187/jmsm.1650309.

JAMA

1.Mülayim G. The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model. Journal of Mathematical Sciences and Modelling. 2025;8:121–128.

MLA

Mülayim, Gülden. “The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 3, Sept. 2025, pp. 121-8, doi:10.33187/jmsm.1650309.

Vancouver

1.Gülden Mülayim. The Application of Model Order Reduction Methods to a Linear Cross-Diffusion Model. Journal of Mathematical Sciences and Modelling. 2025 Sep. 1;8(3):121-8. doi:10.33187/jmsm.1650309