On Dec 26, 2010, at 5:36 PM, adrian wrote:
I'd like to produce different resolutions in different
directions in cylindrical coordination with the certain azimuthal
number through coordination stretching.
I read through "Coordinate Transformation & Invariance in
Electromagnetism" but the result from stretching coordination is not
consistent with that without stretching coordination.
For example, original resolution is 0.1 \epsilon=12.5.
Now I'd like to have the resolution along r as 0.05 and along z as
0.1, respectively, then new \epsilon I used is
epsilon-diag ( (\ 12.5 2) (\ 12.5 2) 12.5) (the resolution is
still 0.1)
But the output field is black.
If I tried epsilon-diag ( (* 12.5 2) (* 12.5 2) 12.5)
The output field is not consistent with the original one.
Maybe I misunderstood that paper but I wonder if anyone has this
experience to share with.
If I understand what you are doing correctly, your desired Jacobian
matrix is (in Matlab notation):
J = diag(0.5, 0.5, 1)
with det(J) = 0.25, corresponding to keeping z fixed and dividing x
and y by 2.
In this case, your original (scalar) epsilon and mu should get
multiplied by
J * J' / det(J)
= diag(1,1,4)
So, your new epsilon should be diag(12.5, 12.5, 12.5 * 4) and your new
mu should be diag(1,1,4).
Steven
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