3D FDTD - how do I compute number of variables and required number of iterations?

[giorgi3092]

Hello,

I am trying to solve this problem:

I can't quite get (c) and (d).

Here is my solution:

I computed (a) and (b) I believe correctly. But, not sure how to approach (c) and (d). What do we mean by variables? Is it those 6 E and H variables per Yee cell?
About (d), I simply don't know.

Any ideas will be appreciated.

 

[BradtheRad]

Not saying I know but I suspect part D is asking how many iterations (frames) the simulation must go through, calculating progress of the initial flux field (or wavefront, or voltage) traveling mathematically as one node influences the next to reach the innermost node.

The number of variables could be seen as 480 (by your reckoning, individually)...
or as 6 in the form of 6 arrays as a computer program arranges it.
I guess each array is in three dimensions? Then each variable is a three-dimensional array.

 

[giorgi3092]

For (c), I've come to the understanding that total number of variables must be (480 Yee cells) * (6 variables per cell). These 6 variables are Ex, Ey, Ez, Hx, Hy, Hz.

for (d), I computed as to how long it takes for the wave with slowest phase velocity (er=8 material) to propagate across the diagonal.

Updated computations:

https://imgur.com/a/2MSHzj8