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Journals / Journal of Mathematical Sciences and Modelling / 2023 / Cilt: 6 Sayı: 2

Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems

Gülden MÜLAYİM
Pages
42–48
Publication Date
2023-08-07
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Numerical simulations show the accuracy and efficiency of the POD and POD-DEIM reduced solutions for the SKT system.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Shigesada-Kawasaki-Teramoto (SKT) is the most known equation in population ecology for nonlinear cross-diffusion systems.
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Key Findings & Data:The full order model (FOM) of the SKT system is constructed using symmetric interior penalty discontinuous Galerkin method (SIPG) in space and the semi-implicit Euler method in time.
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Conclusion & Impact:Numerical simulations show the accuracy and efficiency of the POD and POD-DEIM reduced solutions for the SKT system.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:discontinuous Galerkin method · discrete empirical interpolation method · proper orthogonal decomposition

Abstract

Shigesada-Kawasaki-Teramoto (SKT) is the most known equation in population ecology for nonlinear cross-diffusion systems. The full order model (FOM) of the SKT system is constructed using symmetric interior penalty discontinuous Galerkin method (SIPG) in space and the semi-implicit Euler method in time. The reduced order models (ROMs) are solved using proper orthogonal decomposition (POD) Galerkin projection. Discrete empirical interpolation method (DEIM) is used to solve the nonlinearities of the SKT system. Numerical simulations show the accuracy and efficiency of the POD and POD-DEIM reduced solutions for the SKT system.

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Cite This Article

MÜLAYİM, G. (2023). Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems. Journal of Mathematical Sciences and Modelling, Cilt: 6 Sayı: 2, 42–48. https://ajindex.com/articles/957517

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