A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

作者：Luo Zhendong^*; Ou Qiulan; Wu Jiarong; Xie Zhenghui

来源：Acta Mathematica Scientia, 2012, 32(5): 1997-2009.

• proper orthogonal decomposition
• finite element formulation
• error estimate
• hyperbolic equations

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.

• 出版日期2012-9
• 单位中国科学院大气物理研究所; 华北电力大学