Since the permittivity of any material is usually complex function of temperature, frequency, density, etc. I was wondering if it is possible to use a dynamic permittivity which changes as a function of time using the fdtd method. This would also enable to simulate moving objects. Any hints, keywords, etc.?

  • $\begingroup$ Yes, you can use the method with a coefficient that changes with time. $\endgroup$
    – nicoguaro
    Commented Mar 11, 2018 at 15:54

1 Answer 1


FDTD can be applied for modeling of objects with time-varying coefficients. Depending on the type of variation, different techniques can be applied. Commonly, in computational EM the following situations are usually considered:

  • linear dispersion: dielectric permittivity ($\epsilon$) and magnetic permeability ($\mu$) of the material vary with frequency $\omega$: $\epsilon(\omega)$, $\mu(\omega)$
  • nonlinearity dispersion: $\epsilon(\omega,E,H)$, $\mu(\omega,E,H)$, dependence on the field intensity

In addition, your question implies some multiphysics component (temperature), which, depending on the model can be considered as a simple contribution to material properties nonlinearity, as well as a whole additional physics to solve.

My go-to reference for FTDT in computational EM is

Chapter 9 "Dispersive and Nonlinear Materials" is talking about the relevant techniques that should be of interest to you.

  • $\begingroup$ Thanks for the hint. It looks like the proposed methods (piecewise linear recursive convolution and auxiliary differential equation) automatically take care of the time-dependence of permittivity. I'm just wondering if the methods need to be modified if the electron-density is not constant during each step, but changes as well. Maybe there should be an additional term? Need to take a closer look at inverse Fourier-transform... $\endgroup$
    – OD IUM
    Commented May 25, 2018 at 13:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.