An Efficient Higher-Order PML Algorithm Based on the Direct Integration Method

An efficient higher-order (HO) perfectly matched layer (PML) algorithm based on the direct integration (DI) method is proposed for terminating finite-difference time-domain (FDTD) grids. Unlike the vast majority of HO-PML formulas where the spatial differentiation terms have coefficients associated with the PML parameters, the proposed HO-PML is derived by rearranging the PML tensors and converting the update formulas into the sum of the standard FDTD formulas and the PML auxiliary variables. Consequently, the proposed HO-PML is fully independent of the host media in the FDTD computational domain at the code level and is named the DI-HO-iPML, with the letter “i” indicating this characteristic. In addition, by splitting the HO difference equation according to each time step, an algorithm to reduce the memory footprint of the HO difference equation is proposed for the first time and applied to the DI-HO-iPML algorithm. Theoretical analysis shows that the DI-HO-iPML has the advantages of time-saving and universality. An unmagnetized plasma half-space problem is simulated to validate the DI-HO-iPML.