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meshless method; partition of unity; reproducing kernel particle method; reproducing kernel hierarchical partition of unity; enriched reproducing kernel particle method
Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation. This is the reason why they are useful in the case of large deformations, crack propagations and so on. Reproducing kernel particle method (RKPM) is one of meshless methods. In this contribution we deal with some modifications of the RKPM. The construction of the methods considered is given together with simple examples of their applications to solving boundary value problems.
[1] Babuška, I., Banerjee, U., Osborn, J. E.: Survey of meshless and generalized finite element methods: A unified approach. Acta Numer. 12 (2003), 1-125. DOI 10.1017/S0962492902000090 | MR 2249154 | Zbl 1048.65105
[2] Chen, J. S., Pan, C., Wu, C. T.: Large deformation analysis of rubber based on a reproducing kernel particle methods. Comput. Mech. 19 (1997), 211-227. DOI 10.1007/s004660050170 | MR 1443057
[3] Chen, J. S., Pan, C., Wu, C. T., Liu, W. K.: Reproducing kernel particle methods for large deformation analysis of non-linear structures. Comput. Methods Appl. Mech. Engrg. 139 (1996), 195-227. DOI 10.1016/S0045-7825(96)01083-3 | MR 1426009
[4] Joyot, P., Trunzier, J., Chinesta, F.: Enriched reproducing kernel approximation: Reproducing functions with discontinuous derivatives. Meshfree methods for partial differential equation II, Springer, Berlin, 2004, pp. 93-107. MR 2278265
[5] Li, S., Liu, W. K.: Reproducing kernel hierarchical partition of unity. Internat. J. Numer. Methods Engrg. 45 (1999), 251-317. DOI 10.1002/(SICI)1097-0207(19990530)45:3<251::AID-NME583>3.0.CO;2-I | MR 1688030 | Zbl 0945.74079
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