Accuracy and von Neumann stability of several highly accurate FDTD approaches for modelling Debye-type dielectric dispersion

A comparative study of the accuracy and stability of several highly accurate finite-difference time-domain (FDTD) approaches, the bilinear transform (BT) approach, the modified Z-transform (MZT) approach and the piecewise linear recursive convolution (PLRC) approach, in modelling the Debye-type dielectric dispersion is conducted with the given numerical models of relative permittivities and compared with their theoretical counterpart. The obtained results from two examples in modelling liquid water and human muscle show that the newly proposed MZT approach has the highest accuracy in modelling the real part of complex permittivity, while the BT approach has the highest accuracy in modelling the imaginary part of permittivity. When combined with the second-order accurate FDTD algorithm, the MZT approach is a little more accurate than the BT and PLRC approaches. It is also demonstrated that all the three approaches are numerically stable with the von Neumann stability limits equal to or a little larger than the Courant stability limit.