A Symmetry Treatment in Cylindrical Explicit and Unconditionally Stable FDTD Method

A symmetry treatment in cylindrical explicit and unconditionally stable FDTD (CEUS-FDTD) method is given. The system matrix of CEUS-FDTD method is unsymmetric, which will render instability since the explicit central–difference scheme is used for temporal discretization. By splitting the grid matrix reasonably and modifying the corresponding coefficients, the system matrix is transformed into a new symmetric matrix compulsively. Then an additional diagonal matrix will be obtained naturally on the other side of the equation to ensure that the time marching equation still holds. At last, unstable modes could be obtained by solving generalized eigenvalue problem of the new symmetric system matrix with respect to the diagonal matrix. Numerical results illustrates that the stability of CEUS-FDTD could be ensured and the accuracy would not be affected.