Dispersion error reduction for acoustic problems using the smoothed finite element method (SFEM) |
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| Authors: | Lingyun Yao Yunwu Li Li Li |
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| Affiliation: | College of Engineering and Technology, Southwest University, Chongqing, China |
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| Abstract: | The smoothed finite element method (SFEM), which was recently introduced for solving the mechanics and acoustic problems, uses the gradient smoothing technique to operate over the cell‐based smoothing domains. On the basis of the previous work, this paper reports a detailed analysis on the numerical dispersion error in solving two‐dimensional acoustic problems governed by the Helmholtz equation using the SFEM, in comparison with the standard finite element method. Owing to the proper softening effects provided naturally by the cell‐based gradient smoothing operations, the SFEM model behaves much softer than the standard finite element method model. Therefore, the SFEM can significantly reduce the dispersion error in the numerical solution. Results of both theoretical and numerical experiments will support these important findings. It is shown clearly that the SFEM suits ideally well for solving acoustic problems, because of the crucial effectiveness in reducing the dispersion error. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | acoustic numerical method smoothed finite element method (SFEM) finite element method (FEM) dispersion error |
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