An Element Decomposition Method for the Helmholtz Equation

An Element Decomposition Method for the Helmholtz Equation

Year:    2016

Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1258–1282

Abstract

It is well-known that the traditional full integral quadrilateral element fails to provide accurate results to the Helmholtz equation with large wave numbers due to the "pollution error" caused by the numerical dispersion. To overcome this deficiency, this paper proposed an element decomposition method (EDM) for analyzing 2D acoustic problems by using quadrilateral element. In the present EDM, the quadrilateral element is first subdivided into four sub-triangles, and the local acoustic gradient in each sub-triangle is obtained using linear interpolation function. The acoustic gradient field of the whole quadrilateral is then formulated through a weighted averaging operation, which means only one integration point is adopted to construct the system matrix. To cure the numerical instability of one-point integration, a variation gradient item is complemented by variance of the local gradients. The discretized system equations are derived using the generalized Galerkin weak form. Numerical examples demonstrate that the EDM can achieves better accuracy and higher computational efficiency. Besides, as no mapping or coordinate transformation is involved, restrictions on the shape elements can be easily removed, which makes the EDM works well even for severely distorted meshes.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.110415.240316a

Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1258–1282

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:   

  1. An Element Decomposition Method for Three-Dimensional Solid Mechanics

    Wang, Gang | Wang, Zhonghu | Zhao, Yue

    International Journal of Computational Methods, Vol. 20 (2023), Iss. 08

    https://doi.org/10.1142/S0219876222500633 [Citations: 3]
  2. An Optimized Generalized Integration Rules for Error Reduction of Acoustic Finite Element Model

    Yao, Lingyun | Tian, Wanyi | Wu, Fei

    International Journal of Computational Methods, Vol. 15 (2018), Iss. 07 P.1850062

    https://doi.org/10.1142/S0219876218500627 [Citations: 3]
  3. Investigation of thermal responses during metallic additive manufacturing using a “Tri-Prism” finite element method

    Liu, Pengwei | Cui, Xiangyang | Deng, Jiashan | Li, She | Li, Zichao | Chen, Lei

    International Journal of Thermal Sciences, Vol. 136 (2019), Iss. P.217

    https://doi.org/10.1016/j.ijthermalsci.2018.10.022 [Citations: 22]
  4. Application of Smoothed Finite Element Method to Two-Dimensional Exterior Problems of Acoustic Radiation

    Chai, Yingbin | Gong, Zhixiong | Li, Wei | Li, Tianyun | Zhang, Qifan | Zou, Zhihong | Sun, Yangbin

    International Journal of Computational Methods, Vol. 15 (2018), Iss. 05 P.1850029

    https://doi.org/10.1142/S0219876218500299 [Citations: 71]
  5. Hybrid gradient smoothing technique with discrete shear gap method for shell structures

    Li, W. | Gong, Z.X. | Chai, Y.B. | Cheng, C. | Li, T.Y. | Zhang, Q.F. | Wang, M.S.

    Computers & Mathematics with Applications, Vol. 74 (2017), Iss. 8 P.1826

    https://doi.org/10.1016/j.camwa.2017.06.047 [Citations: 49]
  6. Diagnosis and analysis of abnormal noise in the pure electric vehicle’s air condition compressor at idle

    Zhiwei, Cheng | Yigang, Lu

    Journal of Low Frequency Noise, Vibration and Active Control, Vol. 37 (2018), Iss. 4 P.711

    https://doi.org/10.1177/1461348418765950 [Citations: 3]