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Frequency‐domain analysis of time‐integration methods for semidiscrete finite element equations—part II: Hyperbolic and parabolic–hyperbolic problems
Author(s) -
Muğan Ata,
Hulbert Gregory M.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.135
Subject(s) - frequency domain , mathematics , mathematical analysis , finite element method , hyperbolic partial differential equation , time domain , parabolic partial differential equation , domain (mathematical analysis) , transfer function , hyperbolic function , partial differential equation , computer science , engineering , structural engineering , electrical engineering , computer vision
Time‐integration methods for semidiscrete finite element equations of hyperbolic and parabolic– hyperbolic types are analysed in the frequency domain. The discrete‐time transfer functions of six popular methods are derived, and subsequently the forced response characteristics of single modes are studied in the frequency domain. Three characteristic numbers are derived which eliminate the parameter dependence of the frequency responses. Frequency responses and L 2 ‐norms of the phase and magnitude errors are calculated, and comparisons are given of the methods. As shown; the frequency‐domain analysis explains all time‐domain properties of the methods, and gives more insight into the subject. Copyright © 2001 John Wiley & Sons, Ltd.