A hybrid Finite element-Meshfree method based on partition of unity for transient wave propagation problems in homogeneous and inhomogeneous media

摘要

The quality of the classical finite element solutions for wave propagation problems are always plagued by the numerical dispersion error and this issue is even more severe in the relatively large wave number range. The present paper focused on employing a hybrid Finite element-Meshfree method based on partition of unity concept to solve transient wave propagation problems in homogeneous and inhomogeneous media. In this novel method, the classical parametric shape functions of the linear triangular element are used to construct the partition of unity and the radial-polynomial basis functions from the radial point interpolation meshfree method are used for the local approximation. As a consequence, both the individual properties of the finite element and meshfree method are strengthened in this triangular element. Through the obtained numerical results, it is confirmed that the ability of the present triangular element to suppress the numerical dispersion error surpasses the original linear triangular element and this new triangular element has great potential for solving practical wave propagation problems in engineering application.