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* [[symplectic integrator]]s,
* the [[leapfrog method]].
=== Software ===
There are multiple software available for DEM simulations, both open-source and commercial. Below is a list with a few examples.
* Aspherix ([https://www.aspherix-dem.com/ DCS Computing GmbH], further development from LIGGGHTS)
* Chute Maven (Hustrulid Technologies Inc.)
* EDEM des Unternehmens DEM Solutions Ltd.
* ELFEN
* GROMACS
* GROMOS 96
* LAMMPS (Open-Source)
* LIGGGHTS<ref>Models, algorithms and validation for opensource DEM and CFD-DEM", Christoph Kloss, Christoph Goniva, Alice Hager, Stefan Amberger, Stefan Pirker - Progress in Computational Fluid Dynamics, An Int. J. 2012 - Vol. 12, No.2/3 pp. 140 - 152</ref> (Open-Source, [https://www.aspherix-dem.com/ DCS Computing GmbH])
* MUSEN<ref>MUSEN: An open-source framework for GPU-accelerated DEM simulations. In: SoftwareX. Band 12, 1. Juli 2020, [[International Standard Serial Number|ISSN]] 2352-7110, S. 100618, [[Digital object identifier|doi]]:[https://doi.org/10.1016/j.softx.2020.100618 10.1016/j.softx.2020.100618]</ref> (Open-Source)
* PASIMODO Partikelsimulationspaket
* PFC2D and 3D (ITASCA)
* ROCKY DEM
* SimPARTIX (Fraunhofer IWM)
* ThreeParticle (BECKER 3D GmbH)
* Simcenter STAR-CCM+
* eXtended Particle System (XPS)
* YADE (Open-Source)
==Long-range forces==
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