In this paper, the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on nonsingular weight functions is proposed to solve 3D wave equations. By utilizing the dimension splitting method (DSM), a 3D wave equation is divided into a series of 2D problems. For 2D wave equations, the improved interpolating moving least-squares (IIMLS) method based on nonsingular weight functions is applied to construct the shape function. The finite difference method (FDM) is used both in time domain and splitting direction for obtaining the solutions. By adopting the IIDSEFG method, the essential boundary conditions can be imposed directly, and the truncation error caused by singular weight functions can be avoided. In this paper, the method of changing the diagonal element to 1 is selected as the boundary condition treatment method. Three numerical examples are chosen to verify the superiority of the IIDSEFG method. Compared with the improved element-free Galerkin (IEFG) method and the dimension splitting element-free Galerkin (DSEFG) method, the IIDSEFG method has greater computing speed and precision.

本文提出了一种基于非奇异权函数的改进插值维分裂无元伽辽金(IIDSEFG)方法来求解3D波动方程。通过使用维数分裂方法 (DSM)，将 3D 波动方程划分为一系列 2D 问题。对于二维波动方程，应用基于非奇异权函数的改进插值移动最小二乘法(IIMLS)构造形状函数。有限差分法（FDM）用于时域和分裂方向以获得解。采用IIDSEFG方法，可以直接施加本质边界条件，避免奇异权函数引起的截断误差。在本文中，选择对角线元素为1的方法作为边界条件处理方法。选取三个数值例子来验证IIDSEFG方法的优越性。与改进的无元伽辽金（IEFG）方法和维数分裂无元伽辽金（DSEFG）方法相比，IIDSEFG方法具有更高的计算速度和精度。