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.

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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: