# Finite difference time domain and dynamic permittivity

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.?

• Yes, you can use the method with a coefficient that changes with time. – nicoguaro Mar 11 '18 at 15:54

## 1 Answer

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.

• 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... – OD IUM May 25 '18 at 13:20