×

zbMATH — the first resource for mathematics

New concepts in meshless methods. (English) Zbl 0988.74075
Summary: Two kinds of truly meshless methods, the meshless local boundary integral equation (MLBIE) method and the meshless local Petrov-Galerkin (MLPG) approach, are presented and discussed. Both methods use the moving least-squares approximation to interpolate the solution variables, while the MLBIE method uses a local boundary integral equation formulation, and the MLPG employs a local symmetric weak form. The two methods are truly meshless methods as both of them do not need a finite element or boundary element mesh, either for purposes of interpolation of the solution variables or for the integration of the ‘energy’. All integrals can be easily evaluated over regularly shaped domains (in general, spheres in three-dimensional problems) and their boundaries. Numerical examples show that high rates of convergence with mesh refinement are achievable.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lucy, The Astronomical Journal 8 pp 1013– (1997)
[2] Nayroles, Computational Mechanics 10 pp 307– (1992) · Zbl 0764.65068 · doi:10.1007/BF00364252
[3] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 229– (1994) · Zbl 0796.73077 · doi:10.1002/nme.1620370205
[4] Belytschko, Computational Mechanics 17 pp 186– (1995) · Zbl 0840.73058 · doi:10.1007/BF00364080
[5] Krysl, Computational Mechanics 17 pp 26– (1995) · Zbl 0841.73064 · doi:10.1007/BF00356476
[6] Organ, Computational Mechanics 18 pp 225– (1996) · Zbl 0864.73076 · doi:10.1007/BF00369940
[7] Zhu, Computational Mechanics 21 pp 211– (1998) · Zbl 0947.74080 · doi:10.1007/s004660050296
[8] Mukherjee, Computational Mechanics 19 pp 264– (1997) · Zbl 0884.65105 · doi:10.1007/s004660050175
[9] Liu, Computational Mechanics 18 pp 73– (1996) · doi:10.1007/BF00350529
[10] Zhu, Computational Mechanics 21 pp 223– (1998) · Zbl 0920.76054 · doi:10.1007/s004660050297
[11] Zhu, Computational Mechanics 22 pp 174– (1998) · Zbl 0924.65105 · doi:10.1007/s004660050351
[12] Atluri, Computational Mechanics 22 pp 117– (1998) · Zbl 0932.76067 · doi:10.1007/s004660050346
[13] Atluri, Computational Modelling Simulation Engineering
[14] Atluri, Computational Mechanics (1999)
[15] Atluri, Computational Mechanics (1999)
[16] Lancaster, Mathematics of Computation 37 pp 141– (1981) · doi:10.1090/S0025-5718-1981-0616367-1
[17] Theory of Elasticity, 3rd edn. McGraw-Hill: New York, 1970.
[18] The finite Element Method. Prentice-Hall; Englewood Cliffs, NJ, 1987.
[19] An Analysis of the Finite Element Method. Prentice-Hall; Englewood Cliffs, NJ, 1973.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.