The shape function of the finite element-least square point interpolation method (FE-LSPIM) combines the quadrilateral element for partition of unity and the least square point interpolation method (LSPIM) for local approximation, and inherits the completeness properties of meshfree shape functions and the compatibility properties of FE shape functions, and greatly reduces the numerical dispersion error. This paper derives the formulas and performs the dispersion analysis for the FE-LSPIM. Numerical results for benchmark problems show that, the FE-LSPIM yields considerably better results than the finite element method (FEM) and element-free Galerkin method (EFGM).
Dispersion Error Reduction for Acoustic Problems Using the Finite Element-Least Square Point Interpolation Method
Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 14, 2013; final manuscript received November 11, 2014; published online January 20, 2015. Assoc. Editor: Lonny Thompson.
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Yao, L. Y., Zhou, J. W., Zhou, Z., and Li, L. (April 1, 2015). "Dispersion Error Reduction for Acoustic Problems Using the Finite Element-Least Square Point Interpolation Method." ASME. J. Vib. Acoust. April 2015; 137(2): 021013. https://doi.org/10.1115/1.4029160
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