# Effective “thickness” of finite-difference material elements

I have a 3D finite-difference formulation (for time-harmonic Maxwell using a standard Yee cell grid.) A "perfect electrical conductor" condition can be implemented by enforcing the desired electric field components to 0. (This can also be approximated by making the effective $\epsilon_r$ have a really large imaginary part but for a PEC it's easiest and most stable to just enforce the 0-field magnitude condition.)

If I define a single field component (say Ex of a single Yee cell) to be PEC, I am wondering what the effective dimensions\volume of the defined material would be for a grid-spacing of $dx$. Clearly it's not just a infinitesimally thin line of PEC, but at the same time it does not seem like it would be a full grid cell thick (i.e. be a block of PEC with volume $dx^3$) since the field components around it are not PEC.

Please let me know if the question is unclear at all and I'll try to clarify further. Thanks!

• Are you going to be enforcing the condition on just one, or all four of the Ex edges of the Yee cell? Also, in practice, are you going to do this for a single cell, a line of cells, a plane of cells? – jeffdk Feb 28 '13 at 3:55
• The Yee cell only has a single Ex component. I would be interested in hearing the answer for all of those situations if possible actually! – Costis Feb 28 '13 at 5:29