Natural element method
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The Natural Element Method (NEM) [1][2] 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.
A Voronoi diagram partitioning the space is used to create each of these elements.
Laplace 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 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.
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