I-tutorial 1.7.1 merging problems

I'm interested in calculating resonance values using PML for scattering equations. In a basic case I consider the unit circle and assume a constant valued scatterer n. My goal is to verify a resonance value that I calculated by hand before modifying the code for more interesting shapes and scatterers. The equation of interest is given by:
[tex]\Delta u + (1+n)\omega^2 u =0[/tex]
with Sommerfeld radiation condition
[tex]\lim_{r \to \infty} r^{1/2}
\bigg(
\frac{\partial u }{ \partial r} - i \omega u
\bigg) = 0[/tex]

to calculate the resonance values I can modify the code in the tutorial to add the unit circle along with defining a PML region. The problem I'm having is that with the radiation condition I have a boundary term in the weak formulation. This is seen in the line of code from 1.7.1 tutorial by

The issue is that the example to calculate resonances does not have this boundary term. Ideally I'm trying to solve the following integral equation for [tex]\lambda = \omega^2[/tex] but I do not believe the Arnoldi solver will suffice:

[tex]\int_\Omega\big[ \nabla u \cdot \nabla \bar v \big]
\, dx -
i \,\omega\, \int_{\partial \Omega} u \bar v \, ds = \int_{\Omega} \omega^2 u \bar v[/tex]

Could anyone provide some insight as to how I would solve this problem?