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

Authors : Gülden MÜLAYİM

Pages : 42-48

Doi:10.33187/jmsm.1234247

View : 73 | Download : 89

Publication Date : 2023-08-07

Article Type : Research Paper

Abstract :Shigesada-Kawasaki-Teramoto insert ignore into journalissuearticles values(SKT); is the most known equation in population ecology for nonlinear cross-diffusion systems. The full order model insert ignore into journalissuearticles values(FOM); of the SKT system is constructed using symmetric interior penalty discontinuous Galerkin method insert ignore into journalissuearticles values(SIPG); in space and the semi-implicit Euler method in time. The reduced order models insert ignore into journalissuearticles values(ROMs); are solved using proper orthogonal decomposition insert ignore into journalissuearticles values(POD); Galerkin projection. Discrete empirical interpolation method insert ignore into journalissuearticles values(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