Stabilizing Liao´s absorbing boundary conditions using single-precision arithmetic

The boundary conditions given by Z.P. Liao et al. (Scientia Sinica, vol.XXVII, no.10, p.1065, 1984) for finite difference time-domain analysis have been shown to yield excellent results in scalar as well as vector electromagnetics problems using double-precision arithmetic. However, it is more desirable to use single-precision arithmetic if possible, since the time required to perform a real, double-precision multiplication is two to three times that of a single-precision operation. But with a single-precision implementation, it is observed that the solution becomes unstable as the number of time steps grows. The authors present a procedure for remedying this problem.<>