FDTD Stability: Critical Time Increment

A new approach suitable for determination of the maximal stable time increment for the Finite-Difference Time-Domain (FDTD) algorithm in common curvilinear coordinates, for general mesh shapes and certain types of boundaries is presented. The maximal time increment corresponds to a characteristic value of a Helmholz equation that is solved by a finite-difference (FD) method. If this method uses exactly the same discretization as the given FDTD method (same mesh, boundary conditions, order of precision etc.), the maximal stable time increment is obtained from the highest characteristic value. The FD system is solved by an iterative method, which uses only slightly altered original FDTD formulae. The Courant condition yields a stable time increment, but in certain cases the maximum increment is slightly greater [2]