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Subcycling first- and second-order generalizations of the trapezoidal rule

✍ Scribed by W. J. T. Daniel

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
245 KB
Volume
42
Category
Article
ISSN
0029-5981

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✦ Synopsis

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first-and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first-and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously.

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