Solving Mid-Frequency Acoustic Problem by the Meshless Method

Abstract:

It is well known that traditional finite element (FEM) is an efficient method in solving engineering problems. However, when solving the acoustic problems in medium frequency, FEM suffers from the so-called pollution effect, which is directly related to the dispersion. In this paper, meshless method based on radial basis function (RBF) is introduced to solve the acoustic problem, which shows that the dispersion can be greatly reduced, thus it is very suitable for the solution of mid-frequency acoustic problem. In addition, an algorithm is presented to treat the boundary condition, which improves the performance of the meshless method.

• Periodical: Applied Mechanics and Materials (Volumes 444-445)
• Pages: 1471-1476
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.444-445.1471
• Online since: October 2013
• Authors: Shuang Wang, Qi Bai Huang, Shan De Li
• Keywords: Acoustic Problem, Medium Frequency, Meshless Method, Radial Basis Function (RBF)

References

[1] Shande Li and Qibai Huang, A new fast multipole boundary element method for two dimensional acoustic problems, Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 9, pp.1333-1340, (2010).

DOI: 10.1016/j.cma.2010.11.005

[2] F. Chevillotte and R. Panneton, Coupling transfer matrix method to finite element method for analyzing the acoustics of complex hollow body networks, Applied Acoustics, vol. 72, no. 12, pp.962-968, (2011).

DOI: 10.1016/j.apacoust.2011.06.005

[3] F. Ihlenburg and I Babuska, Finite element solution of the Helmholtz equation with High Wave number. Part 1: The h-Version of the FEM, Computers & Mathematics with Applications, vol. 38, no. 9, pp.9-37, (1995).

DOI: 10.21236/ada277396

[4] K. li, Q.B. Huang, J.L. Wang and L.G. Lin, An improved localized radial basis function meshless method for computational aeroacoustics, Engineering Analysis with Boundary Elements, vol. 35, no. 1, p.35: 47-55, (2011).

DOI: 10.1016/j.enganabound.2010.05.015

[5] Y. Miao and Y. Wang, Meshless analysis for three-dimensional elasticity with singular hybrid boundary node method, Applied Mathematics and mechanics, vol. 35, no. 5, pp.673-681, (2006).

DOI: 10.1007/s10483-006-0514-z

[6] Liu. GR, Meshfree methods-moving beyond the finite element method, CRC Press, Washington, (2009).

[7] Kansa EJ. Multiquadrics-A scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates. Comput Math Appl 1990; 19: 127-145.

DOI: 10.1016/0898-1221(90)90270-t

[8] X. Liu, G.R. Liu, K. Tai, K.Y. Lam. Radial point interpolation collocation method (RPICM) for partial differential equations. Coumput math appl 2005; 50: 1425-1442.

DOI: 10.1016/j.camwa.2005.02.019

[9] X.Y. Cui, G.R. Liu, G.Y. Li. A smoothed Hermite radial point interpolation method for thin plate analysis. ARCH APPL MECH 2011; 81: 1-18.

DOI: 10.1007/s00419-009-0392-0