High order explicit convolution free time-domain finite element PML implementation

This paper presents a simple, convolution free, uni-axial perfectly matched layer (UPML) implementation applicable to high-order, explicit finite element time-domain (FETD) solvers. While implementing the UPML for the general FETD case is fairly complex, a simple FDTD-inspired implementation can be derived for the special case of diagonalised Cartesian hexahedra (also called Lobatto-cells). The FDTD description is not directly applicable to Lobatto-cells; analysis in a discrete differential-forms framework results in a suitable FEM description. The resulting semi-discrete form is discretised in time using the leapfrog central-difference method, although an approximation (also present in the FDTD implementation) is made to avoid the need for time-convolution.