A hybrid smoothed moving least-squares interpolation method for acoustic scattering problems

Wu, Shunchuan; Xiang, Yang; Li, Wanyou

doi:10.1007/s00366-022-01780-w

Cited by 1 publication

(1 citation statement)

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“…Moreover, the numerical waves generated by these two schemes travel faster than the exact waves. This is because the numerical model of the two schemes has an over-stiff behavior [61,62], leading to a smaller numerical wavenumber than the exact wavenumber. By contrast, the OFEM-N6 model, with the close-to-exact stiffness of the exterior acoustic scattering systems, can provide the most precise solutions among all numerical methods.…”

Section: The Computational Accuracymentioning

confidence: 99%

A Coupled Overlapping Finite Element Method for Analyzing Underwater Acoustic Scattering Problems

Jiang,

Yu,

et al. 2023

JMSE

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It is found that the classic finite element method (FEM) requires much time for adequate meshes to acquire satisfactory numerical solutions, and is restricted to acoustic problems with low and middle frequencies. In this work, a coupled overlapping finite element method (OFEM) is employed by combining the overlapping finite element and the modified Dirichlet-to-Neumann (mDtN) boundary condition to solve underwater acoustic scattering problems. The main difference between the OFEM and the FEM lies in the construction of the local field approximation. In the OFEM, virtual nodes are utilized to form the partition of unity functions while no degree of freedom is assigned to these virtual nodes, which suppresses the linear dependence issue in other generalized finite element methods. Moreover, the user-defined enrichment functions can be flexibly utilized in the local field, and thus the numerical dispersions can be significantly mitigated. To truncate the infinite problem domain and satisfy the Sommerfeld radiation condition, an artificial boundary is constructed by incorporating the mDtN technique. Several numerical examples are studied and it is shown that the proposed method can greatly diminish the numerical error and is insensitive to distorted meshes, indicating that the proposed method is promising in predicting underwater acoustic scattering.

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Section: The Computational Accuracymentioning

confidence: 99%