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Conservation properties of a time FE method. Part I: time‐stepping schemes for N ‐body problems

Conservation properties of a time FE method. Part I: time‐stepping schemes for N ‐body problems In the present paper one‐step implicit integration algorithms for the N‐body problem are developed. The time‐stepping schemes are based on a Petrov–Galerkin finite element method applied to the Hamiltonian formulation of the N‐body problem. The approach furnishes algorithmic energy conservation in a natural way. The proposed time finite element method facilitates a systematic implementation of a family of time‐stepping schemes. A particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals. The influence of various standard as well as non‐standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements. Copyright © 2000 John Wiley & Sons, Ltd. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

Conservation properties of a time FE method. Part I: time‐stepping schemes for N ‐body problems

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References (27)

Publisher
Wiley
Copyright
Copyright © 2000 John Wiley & Sons, Ltd.
ISSN
0029-5981
eISSN
1097-0207
DOI
10.1002/1097-0207(20001020)49:5<599::AID-NME960>3.0.CO;2-9
Publisher site
See Article on Publisher Site

Abstract

In the present paper one‐step implicit integration algorithms for the N‐body problem are developed. The time‐stepping schemes are based on a Petrov–Galerkin finite element method applied to the Hamiltonian formulation of the N‐body problem. The approach furnishes algorithmic energy conservation in a natural way. The proposed time finite element method facilitates a systematic implementation of a family of time‐stepping schemes. A particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals. The influence of various standard as well as non‐standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements. Copyright © 2000 John Wiley & Sons, Ltd.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: Oct 20, 2000

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