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Collocation, dissipation and [overshoot] for time integration schemes in structural dynamics
Author(s) -
Hilber Hans M.,
Hughes Thomas J. R.
Publication year - 1978
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290060111
Subject(s) - collocation (remote sensing) , overshoot (microwave communication) , dissipation , dissipative system , basis (linear algebra) , mathematics , orthogonal collocation , collocation method , dispersion (optics) , mathematical optimization , computer science , mathematical analysis , physics , differential equation , geometry , telecommunications , ordinary differential equation , quantum mechanics , machine learning , optics , thermodynamics
The concept of collocation, originally used by Wilson in the development of dissipative algorithms for structural dynamics, is systematically generalized and analysed. Optimal schemes within this class are developed and compared with a recently proposed family of dissipative algorithms, called a methods. The α methods are found to be superior on the basis of standard measures of dissipation and dispersion. It is pointed out that the tendency to overshoot is an important and independent factor which should be considered in an evaluation of an implicit scheme. The basis for studying overshoot is discussed and the optimal collocation and α methods are compared. It is found that pathological overshooting is an inherent property of collocation schemes, whereas the overshooting characteristics of the α methods are good.