3-d convolutional perfectly matched layer models for dynamic soil-structure interaction analysis in the finite element time-domain

The perfectly matched layer (PML) has been employed as a very efficient absorbing boundary condition for solving elastodynamic problems in bounded domains by using the finite difference method. However, in the finite element time domain (FETD), the application of PML formulations usually involves a mixed scheme with velocity/displacement and stresses as unknowns to avoid temporal convolution operations, which could lead to an increase in computational costs especially when three-dimensional (3-D) simulations are used. This paper presents the preliminary research on 3-D convolutional PML models for dynamic soil-structure interaction (SSI) analysis in FETD with displacements as the only unknowns. The variational formulation is derived for the use of finite element method (FEM) to discretize the problem domain, which avoids tricky coordinate transformation and requires minor modification of existing displacement-based finite element software. The stability and efficiency of the proposed formulation are first demonstrated by relevant 3-D benchmark examples even with small bounded domains. Numerical results are also presented for the classical SSI problem of a building with rigid footing on layers on a half-space