Reduced-Order Modeling of a Local Discontinuous Galerkin Method for Burgers-Poisson Equations

Nattapol Ploymaklam, Saifon Chaturantabut

Abstract

In this work, we apply model reduction techniques to efficiently approximate the solution of the Burgers-Poisson equation. The proper orthogonal decomposition (POD) framework is first used with the Galerkin projection to reduce the number of unknowns in the discretized system obtained from  a local Discontinuous Galerkin (LDG) method. Due to nonlinearity of Burgers-Poisson equation, the complexity in computing the resulting POD reduced system may still depend on the original discretized dimension. The discrete empirical interpolation method (DEIM) is therefore used to solve this complexity issue. Numerical experiments demonstrate that the combination of POD and DEIM approaches  can provide accurate approximate solution of  the Burgers-Poisson equation with much less computational cost.