Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Then the evaluation of (3.12a) in uniform subdomains yields
or
E 4-E CE CE - 4Eo = ll2k2E0
1 2 3 4
Within uniform subdomains the same formula qplies to H. Differences
occur if the nodal point 0 is at an interface. Consider as exarrple
a vertical discontinuity:
li
~egio'. I. Region 2
In the absence of region 2 one can write a central difference equa-
tion for E at nodal point O as
where the bracketed superscript indicates the region. In the ab--
sence of region 1 the central difference equation at O is
At the vertical discontinuity we have because of the continuity of
Since also the normal gradient of E is continuous,
The field values E2 (2) and E4 (I) are fictitious and have to be elimi-
nated with the aid of (3.16) and (3.17) fro12 (3.14) and (3.15). The
result is
- where E2 = E2
(1
and E4 Z4
(2)