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《Journal of Harbin Engineering University》 2011-09
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Stability of numerical simulation of wave motion

LIAO Zhenpeng1,2,XIE Zhinan1(1.Institute of Engineering Mechanics,China Earthquake Administration,Harbin 150080,China;2.College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China)  
Lax-stability is first differentiated into the strong and weak categories according to different manners of convergence,techniques of the stability analysis are then classified into the strong and weak stability analysis and relationship between the two techniques is pointed out.For the former,important advances in the spectral analysis and the normal mode analysis are reviewed first,and comments on the original work by Godunov and Ryabenkii in this field are then made to reveal its value for studying the local stability.An elementary argument is presented for verifying the empirical stability criterion for numerical simulation of wave motion in an elastic bar with an interface.For the latter,its applicable premises are respectively clarified for simulation of finite differences and finite elements.In particular,its value in demonstrating the stability of the finite element simulation is stressed.Implication of the strong stability analysis and the weak one is finally discussed for further developing techniques of the numerical simulation of wave motion.
【Fund】: 国家自然科学基金资助项目(51078337 51108431);; 中国地震局工程力学研究所基本科研业务费专项基金资助项目(011800210)
【CateGory Index】: O302
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