An edge-based smoothed finite element method combined with Newmark method for time domain acoustic wave scattering problem

Abstract

Time domain obstacle scattering widely exists in the scientific fields of geophysics, remote sensing, seismology, and medicine. However, it is difficult to solve the time domain scattering problems with arbitrarily shaped obstacles only within the fixed domain of interest. In this paper, an edge-based smoothed finite element method using linear triangular elements (ES-FEM-T3) combined with the Newmark method is proposed for the two-dimensional time domain acoustic scattering by an arbitrarily shaped obstacle. In the algorithm, a time domain transparent boundary condition (TBC) and the Newmark method are introduced to transform the time domain problem in an unbounded domain into a series of steady-state PDEs on a bounded domain, which is suitable for an arbitrary shaped obstacle scattering problem. In the numerical discretization, ES-FEM-T3 is used to construct a close-to-exact stiffness matrix by the smoothed gradient technique, making it space stable and obtaining more accurate results compared to FEM-T3. Especially, through in advance calculating the function σ(t), the convolution term in the time-domain TBC can be quickly calculated. Finally, through the numerical experiments, the effectiveness of the proposed method is demonstrated. Especially, ES-FEM-T3 can better improve the time convergence stability of the Newmark method and have better accuracy at γ = 0.5 compared to FEM-T3.