Application of the complex frequency shifted perfectly matched layer absorbing boundary conditions in transient electromagnetic method modeling

Instead of the conventional Dirichlet boundary condition (DBC),the complex frequency shifted perfectly matched layer (CFS-PML) absorbing boundary condition was applied in transient electromagnetic (TEM) method modeling. A finite difference time domain (FDTD) method was used for space discretization and time stepping. We obtained the plane wave solutions inside the CFS-PML and pointed out the reason why the regular PML fails for TEM modeling. We also provided a criterion for the selection of the parameters of CFS-PML. These ideas were validated for both the whole space and the half space models. The results of a whole space model using CFS-PML showed excellent consistency with the analytical solutions, while those using DBC deviated more than one order of magnitude at the latest delay time. The results of a half space model also showed great superiority of CFS-PML compared to DBC. However, the lack of absorbing ability of CFS-PML in the air caused some errors which could increase with time slowly. Proper models should be designed according to the permitted error.