RBF collocation method and stability analysis for phononic crystals

Chunqiu Wei; Zhizhong Yan; Hui Zheng; Chuanzeng Zhang

doi:10.1007/s10483-016-2076-8

RBF collocation method and stability analysis for phononic crystals

Chunqiu Wei, Zhizhong Yan^*, Hui Zheng, Chuanzeng Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	627-638
Number of pages	12
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	37
Issue number	5
DOIs	https://doi.org/10.1007/s10483-016-2076-8
Publication status	Published - 1 May 2016

Keywords

phononic crystal (PC)
radial basis function (RBF)
stability

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10.1007/s10483-016-2076-8

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title = "RBF collocation method and stability analysis for phononic crystals",

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.",

keywords = "phononic crystal (PC), radial basis function (RBF), stability",

author = "Chunqiu Wei and Zhizhong Yan and Hui Zheng and Chuanzeng Zhang",

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T1 - RBF collocation method and stability analysis for phononic crystals

AU - Wei, Chunqiu

AU - Yan, Zhizhong

AU - Zheng, Hui

AU - Zhang, Chuanzeng

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - phononic crystal (PC)

KW - radial basis function (RBF)

KW - stability

UR - https://www.scopus.com/pages/publications/84964388715

U2 - 10.1007/s10483-016-2076-8

DO - 10.1007/s10483-016-2076-8

M3 - Article

AN - SCOPUS:84964388715

SN - 0253-4827

VL - 37

SP - 627

EP - 638

JO - Applied Mathematics and Mechanics (English Edition)

JF - Applied Mathematics and Mechanics (English Edition)

IS - 5

ER -

RBF collocation method and stability analysis for phononic crystals

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Keywords

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