A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

doi:10.1016/S0252-9602(12)60155-6

Abstract

Abstract:

A proper orthogonal decomposition (POD) method was successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, namely, apply POD method to a classical finite element (FE) formulation for second-order hyperbolic equations with real practical applied background, establish a reduced FE formulation with lower dimensions and high enough accuracy, and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover,
it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.

Key words: proper orthogonal decomposition, finite element formulation, error estimate, hyperbolic equations

CLC Number:

65N30

LUO Zhen-Dong, OU Qiu-Lan, WU Jia-Rong, XIE Zheng-Hui. A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS[J].Acta mathematica scientia,Series B, 2012, 32(5): 1997-2009.

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