Three-dimensional hybrid implicit–explicit finite-difference time-domain method in the cylindrical coordinate system

A novel hybrid implicit-explicit (HIE) finite-difference time-domain (FDTD) method, which is extremely useful for problems with very fine structures along the ϕ-direction in cylindrical coordinate system, is presented. This method has higher computation efficiency than conventional cylindrical FDTD methods, because the time step in this method is only determined by the space discretisations in the radial and vertical directions. The numerical stability of the proposed HIE-FDTD method is presented analytically. Compared with the cylindrical alternating-direction implicit (ADI)-FDTD method, this HIE-FDTD method has higher accuracy, especially for larger time step size. At each time step, the HIE-FDTD method requires the solution of two tridiagonal matrices and four explicit updates. While maintaining the same size of time step, the central processing unit (CPU) time for this weakly conditionally stable FDTD method can be reduced to about 3/5 of that for the ADI-FDTD scheme. The numerical performance of the proposed HIE-FDTD over the conventional cylindrical FDTD method and cylindrical ADI-FDTD method is demonstrated through numerical examples.