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.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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