𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Energy dissipative time finite elements for classical mechanics

✍ Scribed by Q.V. Bui

Book ID
104267286
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
521 KB
Volume
192
Category
Article
ISSN
0045-7825

No coin nor oath required. For personal study only.

✦ Synopsis

Based upon the temporal discretisation of HamiltonΓ•s canonical equations by means of the continuous Galerkin method, a Petrov-Galerkin time finite element formulation is presented to analyse non-linear mechanical systems for long time integration with the presence of dissipation. The time-stepping scheme features a correct estimation of physical dissipative energy for mechanical systems with weak dissipation. This enables to introduce a moderate numerical dissipation to damp out undesired spurious high frequency modes in a controllable manner. Numerical examples are performed to demonstrate that the proposed scheme allows us to obtain a correct amount by which the energy changes over the integration run.

πŸ“œ SIMILAR VOLUMES

Inherently Energy Conserving Time Finite
Inherently Energy Conserving Time Finite Elements for Classical Mechanics
✍ P. Betsch; P. Steinmann πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 189 KB

In this paper, we develop a finite element method for the temporal discretization of the equations of motion. The continuous Galerkin method is based upon a weighted-residual statement of Hamilton's canonical equations. We show that the proposed finite element formulation is energy conserving in a n

Finite element interpolation for combine
Finite element interpolation for combined classical/quantum mechanical molecular dynamics simulations
✍ Berweger, Christian D.; van Gunsteren, Wilfred F.; MοΏ½ller-Plathe, Florian πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 187 KB πŸ‘ 1 views

A method is presented to interpolate the potential energy function for a part of a system consisting of a few degrees of freedom, such as a molecule Ε½ . in solution. The method is based on a modified finite element FE interpolation scheme. The aim is to save computer time when expensive methods such