Numerical treatment of acoustic problems with the smoothed finite element method

• Published in: Applied acoustics 2010-08, Vol.71 (8), p.743-753
• Main Authors: Yao, L.Y., Yu, D.J., Cui, X.Y., Zang, X.G.
• Format: Article
• Language: English
• Subjects: Acoustic analysis; Acoustics; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Nodal irregularity; Noise: its effects and control; Physics; Smoothed finite element method
• ISSN: 0003-682X; 1872-910X
• DOI: 10.1016/j.apacoust.2010.03.006

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.