A hybrid artificial boundary combining perfectly matched layer and infinite elements for analysing semi-infinite problems

Abstract

Artificial boundaries are crucial for simulating the dynamic response of semi-infinite problems. In this paper, a novel hybrid artificial boundary for the simulation of the far field is proposed by combining the perfectly matched layer (PML) and infinite element method (IEM), while the near field is simulated by the finite element method (FEM). The new hybrid artificial boundary (PML-IEM) is devised such that it can enjoy the relative advantage of each method. To start, a brief description is given on the fundamentals of the PML, IEM and the proposed PML-IEM. Then, the procedure for implementing the FEM-PML (using finite elements) and the IEM (using infinite elements) in the stretched coordinates is derived. In the parametric analysis, the factors affecting the accuracy of the PML, IEM, and the proposed PML-IEM are assessed in details. Based on this, optimal parameters are selected for implementing the proposed PML-IEM. Through the examples, the accuracy and reliability of the hybrid method proposed for analysing the semi-infinite problems under the surface line loads are demonstrated to be superior to those by the pure PML or IEM.