Model Reduction for Fisher's Equation

Saifon Chaturantabut

Abstract


This work considers a model-order reduction (MOR) for Fisher's equation, which is generally used to describe many physical systems, such as chemical reactions and flame propagation.Due to the nonlinearity in this type of system, solving the resulting discretizedmodel for accurate solution could be time-consuming as the dimension gets large. MOR can be applied to improve the process of solving this large discretized model. In this work, a projection-based method called Proper Orthogonal Decomposition (POD) is used first to project the state variables of the system on a low dimensional subspace, which generally results in the decrease of unknowns in the systems. However, the computational complexity of the discretized nonlinear term still depends on the original large dimension. Discrete Empirical Interpolation Method (DEIM) is therefore used to eliminate this inefficiency. The numerical results show that this POD-DEIM approach can substantially decrease the computational time while provide accurate numerical solution.

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|ISSN 1686-0209|