Natural element method

The Natural Element Method (NEM) ^[1]^[2]^[3] is a meshless method to solve partial differential equation, where the elements don't have a predefined shape like 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. doi:10.1002/(SICI)1097-0207(19981115)43:53.0.CO;2-R. Retrieved 21 June 2019 – via Wiley Online Library.
^ 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}}: 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. pp. 1087–1092. doi:10.1016/j.proeng.2017.10.1135. Retrieved 2019-07-15.
^ "What is the difference between nem (natural element method) and cnem (constrained natural element method)?". ResearchGate. ResearchGate. Retrieved 2019-07-15.
^ Botelho, D. P.; Marechal, Y.; Ramdane, B. (November 2016). "Vector interpolation on natural element method: Mesh sensitivity analysis". Institute of Electrical and Electronics Engineers. pp. 1–1. doi:10.1109/CEFC.2016.7816353. Retrieved 15 July 2019.

Category:Numerical analysis Category:Numerical differential equations Category:Computational fluid dynamics Category:Computational mathematics Category:Simulation

[1] 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. doi:10.1002/(SICI)1097-0207(19981115)43:53.0.CO;2-R. Retrieved 21 June 2019 – via Wiley Online Library.

[2] 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}}: Cite journal requires |journal= (help)

[3] "Large deformation analysis of elastic bodies by nonlinear Petrov–Galerkin natural element method". Advances in Mechanical Engineering. April 2019.

[4] 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. pp. 1087–1092. doi:10.1016/j.proeng.2017.10.1135. Retrieved 2019-07-15.

[5] "What is the difference between nem (natural element method) and cnem (constrained natural element method)?". ResearchGate. ResearchGate. Retrieved 2019-07-15.

[6] Botelho, D. P.; Marechal, Y.; Ramdane, B. (November 2016). "Vector interpolation on natural element method: Mesh sensitivity analysis". Institute of Electrical and Electronics Engineers. pp. 1–1. doi:10.1109/CEFC.2016.7816353. Retrieved 15 July 2019.

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