Model Reduction for Partial Differential Equations

Abstract

This research project considersModel Order Reduction (MOR) techniques known as Proper Orthogonal Decomposition (POD) method and Discrete Empirical Interpolation Method (DEIM) for Partial Differential Equations (PDEs). First, Proper Orthogonal Decomposition is used to formulate a low dimensional basis that can preserve the dynamics of the system. Then, POD-Galerkin approach is employed to obtain a reduced-order model. However, POD method is not efficient when dealing with nonlinear systems and therefore DEIM is used to minimize the computational complexity of the nonlinear term. We will apply POD and DEIM to estimate solutions of high dimensional dynamical systems that arise from finite difference discretization of PDEs. Practically, we will apply POD-DEIM approach to Fisher’s equation and POD method to Diffusion-advection equation.