Discussion of “development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation” by Chinmoy Kolay and James M. Ricles

Dean J. Maxam, Kumar K Tamma

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Abstract

The time integration method proposed by Kolay and Ricles, which was claimed to be both explicit and unconditionally stable, is shown to be implicit in the sense of requiring the factorization of an effective stiffness matrix where an explicit method needs no solver. Its original derivation procedure employed discrete control theory concepts, which are in fact, equivalent to conventional recurrence relation concepts aiming to match its spectral properties with those of the three-parameter optimal/generalized-α method, thus giving rise to an implicit method within the class of linear multistep methods. It is shown that the resulting method possesses several added computational drawbacks due to its derivation procedure, such as additional effective stiffness inversions and a degraded order of accuracy in general.

Original languageEnglish (US)
Pages (from-to)476-481
Number of pages6
JournalEarthquake Engineering and Structural Dynamics
Volume48
Issue number4
DOIs
StatePublished - Apr 10 2019

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Stiffness matrix
energy dissipation
Factorization
Control theory
Energy dissipation
Stiffness
stiffness
family
method
matrix

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title = "Discussion of “development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation” by Chinmoy Kolay and James M. Ricles",
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AB - The time integration method proposed by Kolay and Ricles, which was claimed to be both explicit and unconditionally stable, is shown to be implicit in the sense of requiring the factorization of an effective stiffness matrix where an explicit method needs no solver. Its original derivation procedure employed discrete control theory concepts, which are in fact, equivalent to conventional recurrence relation concepts aiming to match its spectral properties with those of the three-parameter optimal/generalized-α method, thus giving rise to an implicit method within the class of linear multistep methods. It is shown that the resulting method possesses several added computational drawbacks due to its derivation procedure, such as additional effective stiffness inversions and a degraded order of accuracy in general.

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