Approximate CN scheme and its open region problems for metamaterial rotational symmetric simulation

In order to simulate metamaterial rotational symmetric open region problems, unconditionally stable perfectly match layer (PML) implementation is proposed in the body of revolution (BOR) finite-difference time-domain (FDTD) lattice. More precisely, the proposed algorithm is implemented by the Crank-Nicolson (CN) Douglas-Gunn (DG) procedure for BOR metamaterial simulation. The constitutive relationship of metamaterial can be expressed by the Drude model and calculated by the piecewise linear recursive convolution (PLRC) approach. The effectiveness including absorption, efficiency, and accuracy is demonstrated through the numerical example. It can be concluded that the proposed implementation is to take the advantages of the CNDG-PML procedure, PLRC approach, and BOR-FDTD algorithm in terms of considerable accuracy, enhanced absorption and remarkable efficiency. Meanwhile, it can be demonstrated that the proposed scheme can maintain its unconditional stability when the time step exceeds the Courant-Friedrichs-Levy (CFL) condition.