- Journal of Mathematical Sciences and Modelling
- Vol: 6 Issue: 2
- Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems
Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems
Authors : Gülden Mülayim
Pages : 42-48
Doi:10.33187/jmsm.1234247
View : 70 | Download : 84
Publication Date : 2023-08-07
Article Type : Research Article
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.Keywords : discontinuous Galerkin method, discrete empirical interpolation method, proper orthogonal decomposition, Shigesada-Kawasaki-Teramoto equation