References
- Afshar , M. H. , Amani , J. and Naisipour , M. 2012 . A node enrichment adpatative refinement in discrete least squares meshless method for solution of elasticity problems . Eng. Anal. Bound. Elem. , 36 : 385 – 393 . (doi:10.1016/j.enganabound.2011.08.012)
- Alturi , S. N. and Zhu , T. 1998 . A new meshless local Petrov Galerkin (MLPG) approach in computational mechanics . Comput. Mech. , 22 : 223 – 235 .
- Augarde , C. E. and Deeks , A. J. 2008 . The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis . Finite Elem. Anal. Des. , 44 : 595 – 601 . (doi:10.1016/j.finel.2008.01.010)
- Babuska , I. and Melenk , J. M. 1997 . The partition of unity method . Int. J. Numer. Methods Eng. , 40 : 727 – 740 . (doi:10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N)
- Belytschko , T. , Lu , Y. Y. and Gu , L. 1994 . Element-free Galerkin methods . Int. J. Numer. Methods Eng. , 37 : 229 – 256 . (doi:10.1002/nme.1620370205)
- Boztosuna , I. and Charafi , A. 2002 . An analysis of the linear advection–diffusion equation using mesh-free and mesh-dependent methods . Eng. Anal. Bound. Elem. , 26 : 889 – 895 . (doi:10.1016/S0955-7997(02)00053-X)
- Brown , D. 2005 . On approximate cardinal preconditioning methods for solving PDEs with radial basis functions . Eng. Anal. Bound. Elem. , 29 : 343 – 353 . (doi:10.1016/j.enganabound.2004.05.006)
- Chantasiriwan , S. 2004 . Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz, and diffusion convection equations . Eng. Anal. Bound. Elem. , 28 : 1417 – 1425 . (doi:10.1016/j.enganabound.2004.08.004)
- Chen , C. S. , Fan , C. M. and Wen , P. H. 2012 . The method of approximate particular solutions for solving certain partial differential equations . Numer. Meth. Part D, E , 28 ( 2 ) : 506 – 522 . (doi:10.1002/num.20631)
- Florez , W. F. and Power , H. 2002 . Drm multidomain mass conservative interpolation approach for the BEM solution of the two-dimensional Navier–Stokes equations . Comput. Math. Appl. , 43 : 457 – 472 . (doi:10.1016/S0898-1221(01)00298-X)
- Golberg , M. A. and Cheng , C. 1998 . “ The method of fundamental solutions for potential, Helmholtz and diffusion problems ” . In Boundary Integral Methods: Numerical and Mathematical Aspects , Edited by: Golberg , M. 103 – 176 . Southampton : Comput. Mech. Publ., WIT Press .
- Hu , H. Y. , Chen , J. S. and Hu , W. 2007 . Weighted radial basis collocation method for boundary value problems . Int. J. Numer. Meth. Eng. , 69 : 2736 – 2757 . (doi:10.1002/nme.1877)
- Kangzu , S. , Xiong , Z. and Mingwan , L. 2004 . Meshless method based on collocation with consistent compactly supported radial basis functions . ACTA Mechanica Sinica , 20 : 551 – 557 . (doi:10.1007/BF02484278)
- Kansa , E. J. 1990 . Multiquadrics -a scattered data approximation scheme with applications to computational fluid dynamics – II solution to parabolic, hyperbolic and elliptic partial differential equations . Comput. Math. Appl. , 19 : 127 – 145 . (doi:10.1016/0898-1221(90)90270-T)
- Ling , L. , Opfer , R. and Schaback , R. 2006 . Results on meshless collocation techniques . Eng. Anal. Bound. Elem. , 30 : 247 – 253 . (doi:10.1016/j.enganabound.2005.08.008)
- Liszka , T. , Duarte , C. and Tworzydlo , W. 1996 . hp-meshless cloud method . Comput. Methods Appl. Mech. Eng. , 139 : 263 – 288 . (doi:10.1016/S0045-7825(96)01086-9)
- Liu , G. R. and Gu , Y. T. 2001 . A point interpolation method for two-dimensional solids . Int. J. Numer. Methods Eng. , 50 : 937 – 951 . (doi:10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X)
- Liu , W. K. , Jun , S. and Zhang , Y. F. 1995 . Reproducing kernel particle methods . Int. J. Numer. Methods Fluids , 20 : 1081 – 1106 . (doi:10.1002/fld.1650200824)
- Mai-Duy , N. and Tran-Cong , T. 2001 . Numerical solution of differential equations using multiquadric radial basis function networks . Neural Networks , 14 : 185 – 199 . (doi:10.1016/S0893-6080(00)00095-2)
- Mai-Duy , N. and Tran-Cong , T. 2002 . Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations . Eng. Anal. Bound. Elem. , 26 : 133 – 156 . (doi:10.1016/S0955-7997(01)00092-3)
- Mai-Duy , N. and Tran-Cong , T. 2003 . Approximation of function and its derivatives using radial basis function networks . Appl. Math. Model. , 27 : 197 – 220 . (doi:10.1016/S0307-904X(02)00101-4)
- Quak , W. , van den Boogard , A. H. , González , D. and Cueto , E. 2011 . A comparative study on the performance of meshless approximations and their integration . Comput. Mech. , 48 : 121 – 137 . (doi:10.1007/s00466-011-0577-6)
- Sadeghirad , A. , Kani , I. M. , Rahimian , M. and Astaneh , A. V. 2008 . Meshfree local integration on line method (MLILM) for linear elasticity . Arab. J. Sci. Eng. , 33 : 411 – 434 .
- Samaan , M. F. and Rashed , Y. F. 2009 . Free vibration multiquadric boundary elements applied to plane elasticity . Appl. Math. Model. , 33 : 2421 – 2432 . (doi:10.1016/j.apm.2008.07.006)
- Schaback , R. 1995 . “ Multivariate interpolation and approximation by translates of basis functions ” . In Approximation Theory VIII: Wavelets and Multilevel Approximation , Edited by: Schumaker , L. L. and Chui , C. K. 1 – 8 . College Station , TX : World Scientific .
- Timoshenko , S. and Goodier , J. N. 1951 . Theory of Elasticity , Vol. 2 , New York : McGraw-Hill .
- Tolstykh , A. I. and Shirobokov , D. 2003 . On using radial basis functions in a ‘finite difference mode’ with application to elasticity problems . Comput. Mech. , 33 : 68 – 79 . (doi:10.1007/s00466-003-0501-9)
- Zhang , X. , Song , Z. , Lu , M. W. and Liu , X. 2000 . Meshless methods based on collocation with radial basis functions . Comput. Mech. , 26 : 333 – 343 . (doi:10.1007/s004660000181)
- Zhuang , X. , Heaney , C. and Auguarde , C. 2012 . On error control in the element-free Galerkin method . Eng. Anal. Bound. Elem. , 36 : 351 – 360 . (doi:10.1016/j.enganabound.2011.06.011)