What do you mean by mode tracking? This is not an electromagnetic problem I have worked on that much, but I did not solve it as an eigen-value problem. I solved it as a scattering problem. The main difference is that my simulations needed a source. I based some of my codes on Pocklinton's integral equation and others on Harrington's integral equations. I played both with gap sources and frill sources. If I were learning this method for the first time, I would go with a gap source and Pocklington's integral equation as that is the easiest approach. I did not see as large of a convergence difference as I was led to believe from the literature.
When solving this as a scattering problem, your final matrix equation is
[Z] = [v]
where [Z] is the impedance matrix, are the unknown currents in your elements, and [v] are the voltages applied to each element. A simple gap source as [v] as all zeros except at the point of the feed where you set it to 1.
You solve the matrix equation as
= [Z]\[v]
If you plot after obtaining the solution you will see the current distribution.