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Analysis of underwater acoustic scattering problems using stable node-based smoothed finite element method. (English) Zbl 1403.76042

Summary: A stable node-based smoothed finite element method (SNS-FEM) is presented that cures the “overly-soft” property of the original node-based smoothed finite element method for the analysis of underwater acoustic scattering problems. In the SNS-FEM model, the node-based smoothed gradient field is enhanced by additional stabilization term related to the gradient variance items. It is demonstrated that SNS-FEM provides an ideal stiffness of the continuous system and improves the performance of the NS-FEM and FEM. In order to handle the acoustic scattering problems in unbounded domain, the well known Dirichlet-to-Neumann (DtN) boundary condition is combined with the present SNS-FEM to give a SNS-FEM-DtN model for exterior acoustic problems. Several numerical examples are investigated and the results show that the SNS-FEM-DtN model can achieve more accurate solutions compared to the NS-FEM and FEM.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics
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