Frequency domain analysis of time integration algorithms

✍ Scribed by Ata Muğan

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 273 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00197-9

✦ Synopsis

In this paper, the discrete generalized Bode's theorem is derived and applied to the transfer functions of time integration algorithms for semidiscrete ®nite element equations. An integral equation is obtained that has to be satis®ed by discrete-time transfer functions of time integration algorithms. Subsequently, the frequency response of temporally discretized ®nite element equations and the achievable accuracy cannot be manipulated independently in dierent frequency ranges. However, there is a tradeo in low and high frequency behavior of time integration algorithms. A characteristic gain that complements the role of the spectral radius of the ampli®cation matrix is derived to quantify the asymptotic mode annihilation capability of the algorithms. As shown, the characteristic gain helps to compare dierent time integration algorithms. Numerical examples are presented to demonstrate the role of the proposed characteristic gain.