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Subcycling first‐ and second‐order generalizations of the trapezoidal rule
Author(s) -
Daniel W. J. T.
Publication year - 1998
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/(sici)1097-0207(19980730)42:6<1091::aid-nme401>3.0.co;2-a
Subject(s) - trapezoidal rule , partition (number theory) , finite element method , stability (learning theory) , algorithm , numerical integration , simple (philosophy) , newmark beta method , mathematics , computer science , first order , calculus (dental) , mathematical analysis , medicine , philosophy , physics , dentistry , epistemology , combinatorics , machine learning , thermodynamics
Abstract 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. © 1998 John Wiley & Sons, Ltd.