I am trying to numerically find roots of an infinite metallic nanowire to plot dispersion diagram. I write a "for" loop in MATLAB, and set frequency value at each time, and then proceed to find the value of propagation constant which makes the dispersion function zero. I used muller method as the root-finding scheme. The problem is that the result is so much dependent on initial values I choose.
First, I considered Drude model with zero damping (no losses) for modeling the metal from which the nanowire is made of. In this case, I was able to make 2D plot of absolute value of dispersion function versus freq and propagation constant, for all the values are real. Therefore, it was easy to check which initial values give the correct results.
But when I included damping in Drude model of the metal, I could not make such a 2D plot because value of propagation constant complex in this case. Hence, I was not able to get reasonable results. Can anyone help me with this? Is there any other root-finding method which migth give better results?
Thanks
A suggestion is to change the problem of finding zeros to an optimization problem. A new function can be defined as the absolute value of dispersion and the goal is to find its minima values, i.e, the zeros of the original dispersion function.
As far as you find roots of analytical (holomorphic) complex valued function of the complex valued variable, you can use Newton method or secant method or Newton-like method with an approximative calculation of the derivative by means of finite differences - the last is preferable. For any of such methods you need good enough initial guess. Another possibility - to find all roots of the function in a given domain. These last methods are more complicated and rather slow, but give the trustful result.
Who forbids you to plot real and imaginary parts in one plane and see when both of them are zero? A similar plot of the function modules can be helpful too. It is slow, but maybe just what you want. At least, it can be used as initial guess for Newtonian methods above mentioned.
As far as you find roots of analytical (holomorphic) complex valued function of the complex valued variable, you can use Newton method or secant method or Newton-like method with an approximative calculation of the derivative by means of finite differences - the last is preferable. For any of such methods you need good enough initial guess. Another possibility - to find all roots of the function in a given domain. These last methods are more complicated and rather slow, but give the trustful result.
Who forbids you to plot real and imaginary parts in one plane and see when both of them are zero? A similar plot of the function modules can be helpful too. It is slow, but maybe just what you want. At least, it can be used as initial guess for Newtonian methods above mentioned.
- Badges
- Science topic
- Similar topics
- Computer Science and Engineering
- Algorithms