Abstract
In this paper, the discrete generalized Bode's theorem is derived and applied to the transfer functions of time integration algorithms for semidiscrete finite element equations. An integral equation is obtained that has to be satisfied by discrete-time transfer functions of time integration algorithms. Subsequently, the frequency response of temporally discretized finite element equations and the achievable accuracy cannot be manipulated independently in different frequency ranges. However, there is a tradeoff in low and high frequency behavior of time integration algorithms. A characteristic gain that complements the role of the spectral radius of the amplification matrix is derived to quantify the asymptotic mode annihilation capability of the algorithms. As shown, the characteristic gain helps to compare different time integration algorithms. Numerical examples are presented to demonstrate the role of the proposed characteristic gain.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Computer Methods in Applied Mechanics and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
