References
- Atluri, S.N ., Kim. H.G ., Cho , J.Y.(1999) A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG) and Local Boundary Integral Equation(LBIE) methods, Computational Mechanics. 24, pp.348-372 https://doi.org/10.1007/s004660050457
- Becker. E.B ., Carey. G.F., Oden , J.T.(1981) Finite Elements: An Introduction, Prentice-Hall, Englewood Cliffs, N.J
- Belikov , V.V ., Yu Semenov. A.(2000) Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive isolines generation, Applied Numerical Mathematics, 37, 2000, pp.371-387 https://doi.org/10.1007/978-0-387-22750-4_9
- Belytschko , T ., Lu . Y.Y ., Gu , L.(1994) Element-free Galerkin methods, Internetionel Journal for Numerical Methods in Engineering, 37, pp.229-256 https://doi.org/10.1002/nme.1620370205
- Bower. A,(1981) Computing Dirichlet tessellations, The Computer Journal, 24, pp.162-166 https://doi.org/10.1093/comjnl/24.2.162
- Dolbow. J. , Belytschko , T. (1999 ) Numerical integration of the Galerkin weak form in meshfree methods, Computational mechanics. 23, pp.219-230 https://doi.org/10.1007/s004660050403
- Duarte. C.A ., Oden , J.T.(1996) An h-p adaptive method using clouds, Computer Methods in Applied Mechanics and Engineering, 139, pp. 237-262 https://doi.org/10.1016/S0045-7825(96)01085-7
- Green. P.J ., Sibson , R.(1978) Computing Dirichlet tessellations in the plane, The Computer Journal, 21, pp.168-173 https://doi.org/10.1093/comjnl/21.2.168
- Hivoshi , H ., Sugihara. K.(1999) Two generalizations of an interpolant based on Voronoi diagrams, International Journal of Shape Modeling, 5, pp,219-231 https://doi.org/10.1142/S0218654399000186
- Krongauz , Y ., Belytschko , T. (1996) Enforcement of essential boundary conditions in meshless approximations using finite elements, Computer Methods in Applied Mechanics and Engineering, 131, pp.133-145 https://doi.org/10.1016/0045-7825(95)00954-X
- Liu , W.K ., Jun. J ., Zhang. Y.F.(1995) Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids, 20, pp,1081-1106 https://doi.org/10.1002/fld.1650200824
- Melenk. J.M ., Babuska , I.(1996) The partition of unity finite element method: Basic theory and applications, Computer Methods in Applied Mechanics and Engineering, 139, pp,289-314 https://doi.org/10.1016/S0045-7825(96)01087-0
- Nayroles. B ., Touzot G ., Villon , P. (1992) Generalizing the finite element method: diffuse approximation and diffuse elements, Computational Mechanics, 10, pp.307-318 https://doi.org/10.1007/BF00364252
- Okabe , A ., Boots. B ., Sugihara. K.(1992) Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, John Wiley & Sons, Chichester, England
- Sambridge , M ., Braun. J ., McQueen. H.(1995) Geophysical parameterization and interpolant of irregular data using natural neighbors, Geophysical Journal International, 122, pp,837-857 https://doi.org/10.1111/j.1365-246X.1995.tb06841.x
- Sibson , R.(1980) A vector identity for Dirichlet tessellation, Mathematical Proceedings of the Cambridge Philosophical Society, 87, pp .151-155
- Sukumar , N .(1998) The natural element method in solid mechanics, Ph. D. Thesis, Theoretical and Applied Mechanics, Northwestern University, Evanston. IL, U.S.A
- Sukumar , N ., Moran. B ., Yu Semenov. A., Belikov , V.V.(2001) Natural neighbor Galerkin methods, International Journal for Numerical Methods in Engineering, 50, pp, 1-27 https://doi.org/10.1002/1097-0207(20010110)50:1<1::AID-NME14>3.0.CO;2-P
- Watson. D.F .(1994) nngridr: An implementation of natural neighbor interpolation, David Watson
- Watson. D.F.(1981) Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes, The Computer Journal, 24, pp. 167-172 https://doi.org/10.1093/comjnl/24.2.167
- Zhu , T ., Atluri , S.N.(1998) A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method, Computational Mechanics, 21, pp.211-222 https://doi.org/10.1007/s004660050296