This paper proposes an efficient localized meshless technique for approximating the viscoelastic wave model. This model is a significant methodology to explain wave propagation in solids modeled with a wide collection of viscoelastic laws. In the first method, a difference scheme with the second-order accuracy is implemented to obtain a semi-discrete scheme. Then, a localized radial basis function partition of unity scheme is adopted to get a full-discrete scheme. This localization technique consists of decomposing the initial domain into several sub-domains and constructing a local radial basis function approximation over every sub-domain. A well-conditioned resulting linear system and a low computational burden are the main merits of this technique compared to global collocation methods. Further, the stability and convergence analysis of the temporal discretization scheme are deduced using discrete energy method. Numerical results are shown to validate the accuracy and effectiveness of the proposed method.

本文提出了一种有效的局部无网格技术来逼近粘弹性波模型。该模型是解释固体中波传播的一种重要方法，该方法使用大量粘弹性定律建模。在第一种方法中，实施具有二阶精度的差分方案以获得半离散方案。然后，采用统一方案的局部径向基函数划分得到全离散方案。这种定位技术包括将初始域分解为几个子域并在每个子域上构建局部径向基函数近似。与全局搭配方法相比，条件良好的结果线性系统和低计算负担是该技术的主要优点。更多，利用离散能量法推导出时间离散化方案的稳定性和收敛性分析。数值结果证明了所提出方法的准确性和有效性。