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Acoustic simulation using α-FEM with a general approach for reducing dispersion error

机译：使用α-FEM的声学模拟以及减少色散误差的通用方法

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摘要

The alpha finite element method (α-FEM) developed recently has showed outstanding features in solving solid mechanics and acoustic problems. In the a-FEM, a parameter alpha has been introduced to make the best use of "over-stiffness" of the FEM model and "over-softness" of the NS-FEM model to achieve the ultimate performance. Because the parameter alpha varies with the problems and the mesh size, it is difficult to find a general approach to determine, which holds back the application of the oc-FEM method. In this paper, acoustic simulation using α-FEM with a general approach for reducing dispersion error is proposed. We first carry out a theoretical analysis of dispersion error, leading to a very important relation between the dispersion error and the parameter alpha. Next, the parameter of alpha is then determined by minimizing the dispersion error. The determined parameter alpha enables a proper gradient smoothing operation in the a-FEM, and provides a perfect balance between the stiffness and mass in the discrete system matrix, which dramatically reduces the dispersion error. The properties of the present a-FEM have been confirmed numerically via examples of ID, 2D and 3D acoustic problems with various boundary conditions.
机译：最近开发的α有限元方法（α-FEM）在解决固体力学和声学问题方面显示出杰出的功能。在a-FEM中，引入了参数alpha，以充分利用FEM模型的“过度刚度”和NS-FEM模型的“过度软度”以实现最终性能。由于参数alpha随问题和网格大小而变化，因此很难找到一种通用的方法来确定，这阻碍了oc-FEM方法的应用。在本文中，提出了一种使用α-FEM进行声学模拟的通用方法，以减少色散误差。首先，我们对色散误差进行了理论分析，得出了色散误差与参数alpha之间的非常重要的关系。接下来，然后通过使色散误差最小化来确定α的参数。确定的参数alpha可以在a-FEM中进行适当的梯度平滑操作，并在离散系统矩阵中的刚度和质量之间实现完美的平衡，从而大大降低了色散误差。通过具有各种边界条件的ID，2D和3D声学问题的示例，已在数值上证实了本a-FEM的特性。

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  • 来源
    《Engineering analysis with boundary elements》 |2015年第12期|241-253|共13页
  • 作者

    Z.C. He; Eric Li; G.Y. Li; F. Wu; G.R. Liu; X. Nie;

  • 作者单位

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China,State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;

    School of Aerospace Systems, University of Cincinnati, Cincinnati, OH 45221-0070, USA;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Numerical method; Alpha finite element method (a-FEM); Smoothed finite element methods; Gradient smoothing operation; Acoustics; Dispersion error;

    机译：数值方法;Alpha有限元方法（a-FEM）;平滑有限元方法;渐变平滑操作;声学;色散误差;

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