File talk:Yee-cube.svg

Hello!

wouldn't it be more meaningful to label field vectors of the Yee-cell as I did in:

www.fuego-lento.com/Bilder/Yee-grid.png www.fuego-lento.com/Bilder/Yee-grid.eps

best regards

129.69.28.75 (talk) 14:36, 16 August 2010 (UTC)[reply]

As far as I can tell, all you did was add some more grid lines and attach the H labels to grid points offset by one pixel. Tastes vary, of course, I don't see how this makes it more "meaningful". — Steven G. Johnson (talk) 00:14, 17 August 2010 (UTC)[reply]

Well I don't care about the auxiliary lines (my Supervise requested it). The paper of Yee (References 1) reads in (13a):

H_z^{n+\frac12}(i+\frac12,j+\frac12)=H_z^{n-\frac12}(i+\frac12,j+\frac12) -\frac1Z\frac{\Delta\tau}{\Delta x}[E_y^n(i+1,j+\frac12)-E_y^n(i,j+\frac12)] +\frac1Z\frac{\Delta\tau}{\Delta x}[E_x^n(i+\frac12,j+1)-E_x^n(i+\frac12,j)] .

Since we get H_z at the point (i+\frac12,j+\frac12) from Ey at the points (i+1,j+\frac12) and (i,j+\frac12) H_z shout have the same "j" (y) value like Ey in a cell. Likewise H_z shout have the same "i" (x) value like E_x.

That's what I mean with more "meaningful".

best regards

129.69.28.75 (talk) 09:04, 17 August 2010 (UTC)[reply]

You're confused. The Yee grid refers to an entire grid in space, not just to the values used in updating a particular point. There are Hz field components at (i+1/2,j+1/2,k) for every value of (i,j,k): they describe a whole grid in space, not just a single point, and it is equally valid to label any of them as H_z. The coordinates are clearly labeled on the diagram; there is no ambiguity. — Steven G. Johnson (talk) 13:43, 17 August 2010 (UTC)[reply]

I don't think, I would be confused, it's just, if you approximate the derivation by x of f(x,y) by the central difference quotient (an this is what Yee does) you get \frac\partial x f(x,y) \approx (f(x+1/2h,y)-f(x-1/2h,y))/h. The value of y is the same. So according to my opinion there is indeed a H_z component where it is labeled now, but it belongs to the upper Yee-cell.

Nevertheless, this does not seem to be a question of "truth" any more. So I leave Wikipedia to you and will use my labeling in my publications.

best regards

129.69.28.75 (talk) 15:21, 20 August 2010 (UTC)[reply]