Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

4. Model calculations. for tl1.r,ee--d~nei~sioi~a1. structures
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4.1. Introduction -
In the three-dimensional case the TE- and TM-mode become mixed and
cannot longer be treated separately. Now the differential equation
for a vector field instead of a scalar field is to be solved. In
numerical solutions questions of storage and computer time become
important. Assume as example that in approach A a basic domain with
20 cells in each direction is chosen. In this case, only the storage
of the electric field vector would require 48000 locations. For an
iterative improvement of one field component at least 0.0005 sec
are needed for each cell. This yields 12 sec for a complete itera-
tion, and 20 min for 100 iterations. This appears to be the ].east
time required for this model. Hence methods for a reduction of com-
puter time and.storage are particularly appreciated in this case.
The equation to be solved is
cur1213 - (r) - -t k2 (r) E (r) = - i ~ l(g) i ~ ~ ~
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where k2.(r) = i~p~c(g).
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1 (r) is the source current density.
-e -
After the splitting
where E is that solution of
-11
curlZE (r) + k2(r)F, (r) = -impo&
-11 - n--n-
(4.3)
which vanishes at infinity, we obtain for the anomalous field the
two alternative equations
c ~ r l . + ~ k2E ~ = - k2E
-a n-a a
Eq. (4.4a) is the starting point for the volume integral or integral
equation approach, Eq. (4.4b) is the point or-' starting for the sur-
face integral approach.