An improved interpolating dimension splitting element-free Galerkin method for 3D wave equations

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.

Automated summary

In this paper, an improved interpolating dimension splitting element-free Galerkin method based on nonsingular weight functions is proposed to solve 3D wave equations. The method achieves greater computing speed and precision compared to other similar methods, while also avoiding truncation errors caused by singular weight functions.