RBF collocation method and stability analysis for phononic crystals

doi:10.1007/s10483-016-2076-8

Abstract

Abstract:

The mesh-free radial basis function (RBF) collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric (MQ), Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs. The choice of the shape parameter and the effects of the knot number are presented.

Key words: radial basis function (RBF), phononic crystal (PC), stability

2010 MSC Number:

65M70

Chunqiu WEI, Zhizhong YAN, Hui ZHENG, Chuanzeng ZHANG. RBF collocation method and stability analysis for phononic crystals. Applied Mathematics and Mechanics (English Edition), 2016, 37(5): 627-638.

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