On Jul 31, 2008, at 3:28 AM, Jefferson Thomas wrote:
> Thanks. One more thing about adding the sources in case of
> symmetries :
> If I have a box of sizes 4, 4, 4 with odd symmetry on X and I want
> to add
> a source with Ex with
> f.add_point_source(Ex, src, vec(1, 1, 1), 10); where 10 means
> the amplitude
> then as far as I understand I have to add a symmetric source with
> f.add_point_source(Ex, src, vec(3, 1, 1), 10);
Right. Technically, that is an odd-symmetry source even though the two
sources have the same sign, because of the way you mirror-flip a
vector field.
> But if my symmetry was not on X but on Y axis then I think I should
> add a source with a negative amplitude :
> f.add_point_source(Ex, src, vec(1, 3, 1), -10);
Right, that's the how you do an odd mirror flip of a vector field when
the mirror plane is parallel to the field.
Basically, to mirror a vector field you just imagine an arrow being
reflected in a mirror. Then if it is odd, you flip the direction of
the arrow after mirroring it. If it is a pseudovector (e.g. magnetic
field or magnetic current) then you have to multiply by an additional
factor of -1.
> Furthermore, if I have both X and Y symmetries then
> beside adding previous two sources I should also add an additional
> source in :
> f.add_point_source(Ex, src, vec(3, 3, 1), -10);
> Is it correct ?
Just to be clear, if you have both X and Y symmetries then you need to
have four point sources, because your original source is doubled
twice. i.e. (for odd X and odd Y):
f.add_point_source(Ex, src, vec(1, 1, 1), 10);
f.add_point_source(Ex, src, vec(4-1, 1, 1), 10);
f.add_point_source(Ex, src, vec(1, 4-1, 1), -10);
f.add_point_source(Ex, src, vec(4-1, 4-1, 1), -10);
Alternatively, you could create a source that is odd in both X and Y
by putting a single Hz source at the center:
f.add_point_source(Hz, src, vec(2, 2, 1), 10);
(This is odd in X and Y because of the extra factor of -1 for
pseudivectors mentioned above. Equivalently, you can imagine an Hz
source, a magnetic dipole, as corresponding to an infinitesimal
electric current loop in the plane perpendicular to Hz -- if you think
about the directions of the electric fields in a current loop, you
will see that the fields are odd in both X and Y.)
Note also that when you define your volume v, you can call
v.center_origin() to put the (0,0,0) origin at the center of the
volume. This may make it a bit easier to think about the symmetry.
Steven
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