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References for Natural Neighbor Galerkin Methods
- 1.
- Belikov, V. V., V. D. Ivanov, V. K.
Kontorovich, S. A. Korytnik and A. Yu Semenov (1997).
The Non-Sibsonian Interpolation: A New Method of Interpolation
of the Values of a Function on an Arbitrary Set of Points,
Computational Mathematics and Mathematical Physics 37(1): 9-15.
- 2.
- Braun, J. and M. Sambridge (1995).
A numerical method for solving partial differential equations on
highly irregular evolving grids, Nature 376: 655-660.
- 3.
- Christ, N. H. and R. Friedberg and T. D. Lee
(1982). Weights of links and plaquettes in a random lattice,
Nuclear Physics B 210(3): 337-346.
- 4.
- Farin, G. (1990).
Surfaces over Dirichlet tessellations,
Computer Aided Geometric Design 7(1-4): 281-292.
- 5.
- Hiyoshi, H. and K. Sugihara (1999).
Two Generalizations of an Interpolant Based on Voronoi Diagrams,
International Journal of Shape Modeling 5(2): 219-231.
- 6.
- Sibson, R. (1980).
A vector identity for the Dirichlet tesselation, Mathematical
Proceedings of the Cambridge Philosophical
Society 87: 151-155.
- 7.
- Sibson, R. (1981).
A brief description of natural neighbor interpolationts, In
Interpreting Multivariate Data , Ed. V. Barnett,
Chichester, 21-36, John Wiley.
- 8.
- Sukumar, N. (June 1998).
The natural element method in solid mechanics,
Ph.D. Thesis, Theoretical and Applied Mechanics,
Northwestern University, IL, U.S.A.
[Thesis]
- 9.
- Sukumar, N., B. Moran and
T. Belytschko (1998).
The natural element method in solid mechanics,
International Journal for Numerical Methods in Engineering
43, Number 5: 839-887.
![[PDF]](Gifs/pdf.gif)
- 10.
- Sukumar, N. and B. Moran
(July, 1999).
C1 natural neighbor interpolant for partial
differential equations,
Numerical Methods for Partial Differential Equations,
15, Number 4: 417-447.
- 11.
- Sukumar, N., B. Moran, A. Yu
Semenov and V. V. Belikov (2001).
Natural neighbour Galerkin methods,
International Journal for Numerical Methods in Engineering,
50, Number 1; 1-27.
- 12.
- Sukumar, N. (2003).
Voronoi cell finite difference method for the diffusion operator on
arbitrary unstructured grids,
International Journal for Numerical Methods in Engineering,
57, Number 1; 1-34.
- 13.
- Traversoni, L. (1994).
Natural neighbor finite elements, In
International Conference on Hydraulic Enginnering
Software, Hydrosoft Proceedings 2: 291-297,
Computational Mechanics Publications.
- 14.
- Voronoi, G. M. (1908).
Nouvelles applications des paramètres continus à la
théorie des formes quadratiques. deuxième Mémoire: Recherches
sur les parallélloèdres primitifs, J. Reine Angew. Math.
134: 198-287.
- 15.
- Watson, D. F. (1994).
nngridr: An implementation of natural neighbor interpolation,
David Watson.
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