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Displaying similar documents to “An energy-preserving Discrete Element Method for elastodynamics∗”

An energy-preserving Discrete Element Method for elastodynamics

Laurent Monasse, Christian Mariotti (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations....

Integration of the EPDiff equation by particle methods

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff...