Dimension reduction for systems with parametrized boundaries for Fisher’s equation

Abstract

An application of nonlinear model reduction for Fisher’s equation with parametrized boundary conditions is proposed through the approach that combines the techniques of proper orthogonal decomposition and discrete empirical interpolation method. These techniques are extended for reducing the computational complexity in solving the systems with multiple parametrized nonlinear terms. By using this model reduction approach, the numerical solutions for Fisher’s equation with discontinuous initial condition and oscillating boundary conditions are shown to be accurately obtained from the iterative semi-implicit numerical scheme with a substantial reduction in simulation time.