Natural element method
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Euclidean_Voronoi_diagram.svg/220px-Euclidean_Voronoi_diagram.svg.png)
20 points and their Voronoi cells
The natural element method (NEM)[1][2][3] is a meshless method to solve partial differential equation, where the elements do not have a predefined shape as in the finite element method, but depend on the geometry.[4][5][6]
A Voronoi diagram partitioning the space is used to create each of these elements.
Natural neighbor interpolation functions are then used to model the unknown function within each element.
Applications[]
When the simulation is dynamic, this method prevents the elements to be ill-formed, having the possibility to easily redefine them at each time step depending on the geometry.
References[]
- ^ Sukumar, N.; Moran, B.; Belytschko, T. (21 June 1998). "The natural element method in solid mechanics". International Journal for Numerical Methods in Engineering. 43 (5): 839–887. Bibcode:1998IJNME..43..839S. doi:10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R.
- ^ J. Yvonnet; D. Ryckelynck; P. Lorong; F. Chinesta. "A new extension of the natural element method for non‐convex and discontinuous problems: the constrained natural element method (C‐NEM)". International Journal for Numerical Methods in Engineering: 1451–1474. Cite journal requires
|journal=
(help) - ^ "Large deformation analysis of elastic bodies by nonlinear Petrov–Galerkin natural element method". Advances in Mechanical Engineering. April 2019.
- ^ Lu, Ping; Shu, Yang; Lu, Dahai; Jiang, Kaiyong; Liu, Bin; Huang, Changbiao (2017-01-01). "Research on Natural Element Method and the application to simulate metal forming processes". Procedia Engineering. International Conference on the Technology of Plasticity, ICTP 2017, 17-22 September 2017, Cambridge, United Kingdom. ScienceDirect. 207: 1087–1092. doi:10.1016/j.proeng.2017.10.1135.
- ^ "What is the difference between nem (natural element method) and cnem (constrained natural element method)?". ResearchGate. Retrieved 2019-07-15.
- ^ Botelho, D. P.; Marechal, Y.; Ramdane, B. (November 2016). "Vector interpolation on natural element method: Mesh sensitivity analysis". 2016 IEEE Conference on Electromagnetic Field Computation (CEFC). Institute of Electrical and Electronics Engineers. p. 1. doi:10.1109/CEFC.2016.7816353. ISBN 978-1-5090-1032-5. S2CID 27851390.
Categories:
- Numerical differential equations
- Numerical analysis
- Computational fluid dynamics
- Computational mathematics
- Simulation