A Novel "Finite Element-Meshfree" Triangular Element Based on Partition of Unity for Acoustic Propagation Problems

The accuracy of the conventional finite element (FE) approximation for the analysis of acoustic propagation is always characterized by an intractable numerical dispersion error. With the aim of enhancing the performance of the FE approximation for acoustics, a coupled FE-Meshfree numerical method based on triangular elements is proposed in this work. In the proposed new triangular element, the required local numerical approximation is built using point interpolation mesh-free techniques with polynomial-radial basis functions, and the original linear shape functions from the classical FE approximation are employed to satisfy the condition of partition of unity. Consequently, this coupled FE-Meshfree numerical method possesses simultaneously the strengths of the conventional FE approximation and the meshfree numerical techniques. From a number of representative numerical experiments of acoustic propagation, it is shown that in acoustic analysis, better numerical performance can be achieved by suppressing the numerical dispersion error by the proposed FE-Meshfree approximation in comparison with the FE approximation. More importantly, it also shows better numerical features in terms of convergence rate and computational efficiency than the original FE approach; hence, it is a very good alternative numerical approach to the existing methods in computational acoustics fields.