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Heavyside-Function and Divison by Zero
Posted Feb 11, 2013, 2:13 p.m. EST RF & Microwave Engineering, Parameters, Variables, & Functions Version 4.3a 2 Replies
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I stumble realising a Gaussian-beam like in the tutorial model "Nanorods" (using RF-module).
Problem:
Part of the wave function has a singularity: constant/z
Solution in tutorial:
Define a piecewise-function covering the singularity like:
z<-z0 : constant/z
-z0<z<z0 : constant/z0
z0<z : constant/z
But in contrary to the example I need frequency-dependent borders respectively frequency-dependent z0 [Z0(freq)].
As this is not possible with piecewise-function (i guess) i tried a sum of Haevyside-functions (like recommended in several forum-posts):
(constant/z)*flc2hs(-z-Z0(freq),range)
+(constant/z0)*flc2hs(z+Z0(freq),range)*flc2hs(-z+Z0(freq),range)
+(constant/z)*flc2hs(z-Z0(freq),range)
Does the same when being plotted from the Global_Definition/Anayltics-Node. Produces also no error when the model is being computed. But trying to plot from Solution1-Node producing the error:
Evaluation of result expression failed
Error in user-defined function
Failed to evaluate expression
This error does not occur if the (constant/z)-function is replaced by a non-singularity-function. So plotting after computing messes somehow with the Heavyside-function.
Any idea or experience how to get that work? This starts to erode my self-confidence.
Thanks for any help
edit: Problem was, i think, not the above expression but the fact that inside of the wave-function something gets divided by that expression. And i think the smoothening of the heavyside-function leads to a zero at the singularity. And then again divided by zero ^.^ -> error
Though i am not sure.
But in this case using the inverse function just works fine : )
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if you plot your function as "something/z" with a "z=0" ituation you wil lend up with a NaN, isnt it that what happens, so you need to ensure you are never close to z=0, even when the solver is searching for new values
--
Good luck
Ivar
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It was the case that i did not fully understand my own problem : )
It is like:
Something/R(z) and R(z)=Anything/z
I was just looking at R(z) and taking care of it by adding heavyside-functions.
Now i think the smoothening of this functions lead to R(0)=0 somewhere between R(-0.01)=-infinity and R(0.01)=infinity. And then Something/R(z) causes problems.
I am just guessing because:
Something*R(z) made no problems.
When realizing that the trouble came from Something/R(z) I just used Something*R(z)^(-1).
That works fine ; )
Maybe I will run some trial&errors to ensure my thoughts.
Sry for circumstances, i did not delete my topic because maybe it helps someone. As far as is see I can not tag it as solved.
Have a nice evening!