Two polynomial methods of calculating functions of symmetric matrices
USSR Computational Mathematics and Mathematical Physics
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
On the stability of the finite-difference time-domain method
Journal of Computational Physics
Stability of FDTD on nonuniform grids for Maxwell's equations in lossless media
Journal of Computational Physics
Hi-index | 31.45 |
In this paper we show that the Finite-Difference Time-Domain method (FDTD method) follows the recurrence relation for Fibonacci polynomials. More precisely, we show that FDTD approximates the electromagnetic field by Fibonacci polynomials in @DtA, where @Dt is the time step and A is the first-order Maxwell system matrix. By exploiting the connection between Fibonacci polynomials and Chebyshev polynomials of the second kind, we easily obtain the Courant-Friedrichs-Lewy (CFL) stability condition and we show that to match the spectral width of the system matrix, the time step should be chosen as large as possible, that is, as close to the CFL upper bound as possible.