Topic 7f -- Time-Domain FDM

This lecture introduces the concept of simulating devices in the time-domain using the finite-difference method. While the baseline finite-difference equations are very similar to previous lectures, the implementation is almost completely different. Both the time-domain heat equation and time-domain Maxwell's equations are discussed.

[dereathacross]

I like the explanation at 12:00. Rarely does anyone show that. Oh, and I really like the visual stuff. No one ever does that because it is so much work to do but it helps so much in understanding what is actually going on.

[amithasanarpon]

Dr. Rumpf, I have a question regarding this lecture video. At around 18:50 we discuss the stability condition. I understand the reasoning behind it. The heat front has to be slower than one cell per time step. But I don't understand how this idea comes down to: update coefficient at the i-th cell, c_i < 1/2
Why 1/2? Would this value change based on the approximation scheme used? For example if we use data from 5 grid points instead of 3, would this value change to something other than 1/2?
For a general problem, how can we calculate this value that the update coefficient has to be less than?

[AJ-etvf]

Great video sir. Thank you. Loved this lecture and the visuals with it. The way I understand this, TIme-Domain FDM is simply using the forward euler method to solve the equations in every step and not using Implicit euler or crank-nicholson method. But then, isn't the main disadvantage of this method is the stability condition that severely limits the size of your time step especially when you want to increase your spatial grid resolution?