A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics. I: Formulation. II: Algorithms and analysis
type: Item
instance of: scholarly article
title: A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics. I: Formulation. II: Algorithms and analysis
zbMATH Open document ID: 0892.73059
DOI: 10.1016/S0045-7825(96)01191-7
author: J. Ning
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1998-08-03T00:00:00Z
review text: A new class of time integration algorithms for dynamics is presented. The algorithms are based on finite element in time. The equations of motion are expressed in first-order form and the variables are interpolated via time polynomials. The unknown nodal variables are solved by the generalized Galerkin method. Algorithms of any desired order of time accuracy can be achieved by proper choice of the finite element interpolation in time. The salient feature of the algorithms is that it can be either asymptotic annihilating or non-dissipative. Besides, any desired algorithmic damping between these two extreme cases could be obtained. The spectral characteristics equivalent to the upper diagonal, diagonal of the Padé approximations, and other rational approximations are given. In part II, we present details of four lower-order algorithms using parametrized temporal finite elements, together with the analyses of numerial stability, dissipation and dispersion.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1079181
zbMATH Keywords: time integration algorithms
zbMATH Keywords: generalized Galerkin method
zbMATH Keywords: spectral characteristics
zbMATH Keywords: lower-order algorithms
zbMATH Keywords: parametrized temporal finite elements
zbMATH Keywords: numerial stability
zbMATH Keywords: dissipation
zbMATH Keywords: dispersion
MaRDI profile type: Publication
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full work available at URL: s0045-7825(96)01191-7
OpenAlex ID: W1993342384
Wikidata QID: Q127807457
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description: scientific article; zbMATH DE number 1079181