Scaled Boundary Perfectly Matched Layer (SBPML): A novel 3D time-domain artificial boundary method for wave problem in general-shaped and heterogeneous infinite domain

Abstract

Artificial boundary method is widely used in the numerical modeling of unbounded wave problem. However, the accurate modeling of truncated infinite domain with general geometry and heterogeneous materials is still a challenging task, especially for direct time-domain analysis in three dimensions (3D). In this paper, a novel 3D time-domain artificial boundary method, called Scaled Boundary Perfectly Matched Layer (SBPML), is proposed. This method is a generalization of the Perfectly Matched Layer (PML) based on a scaled boundary coordinates transformation inspired by the Scaled Boundary Finite Element Method (SBFEM), which is capable of using artificial boundary of general geometry (not necessarily convex) and considering plane physical surfaces and interfaces extending to infinity in the truncated infinite domain. Local scaled boundary coordinates are firstly introduced on the element-level into the truncated infinite domain to describe general geometry properties of the infinite domain. Then, a complex stretching function from PML is applied to radial direction of the local scaled boundary coordinates to map the physical space onto the complex space, resulting in a SBPML domain. The spatial discretization of the SBPML domain produces semi-discrete mixed displacement–stress​ unsplit-field formulations of third orders in time. The order of the obtained formulation can be reduced by one, enabling a seamless coupling with the standard displacement-based finite element formulation of the interior domain. The coupled system can be solved by an explicit time integration algorithm efficiently. The validation of the SBPML is demonstrated through several benchmark tests, including wave problems in unbounded domains with general geometries and heterogeneous material properties. Furthermore, the application of the SBPML in dynamic soil–structure interaction (SSI) is demonstrated using two engineering problems, including an impact analysis of soft rock-nuclear island system and a vibration analysis of soil-lined tunnel system.