Time-Efficient Higher-Order PML Using Bilinear Transform Without Altering Standard FDTD Formulas

Abstract

This letter proposes an efficient higher-order (HO) perfectly matched layer (PML) algorithm based on the bilinear transform (BT) method for truncating finite-difference time-domain (FDTD) lattices. By rearranging the PML tensors, the resulting update formulas become a combination of standard FDTD formulas and PML auxiliary variables, ensuring that the PML implementation does not alter the standard FDTD formulas. This approach makes the proposed HO-PML algorithm completely independent of the update formulas in the host computational domain at the code level, earning it the name BT-HO-iPML. Additionally, a memory-reducing algorithm is developed by splitting the HO difference equations according to each time step and applied to the BT-HO-iPML. Furthermore, to maintain consistency throughout the computational domain, the BT method is also applied to discretize the constitutive relation equation between electric flux density D and the electric field intensity E, which is characterized by simplicity of derivation and can model general media. Theoretical analysis and numerical simulations demonstrate that the BT-HO-iPML has the advantages of being time-saving and universal while having good broadband absorption performance.