Resonant frequency of 2D rectangular cavity

Hi
I want to calculate resonant frequency of a 2D rectangular cavity by FDTD & analytic for TE11, TE21, TE22, TE31, TE32, TE33 modes, but i don't know how calculate resonant frequency from analytic solution, can you help me? or suggest a reference that solve this problem by analytic?
I have a another question in FDTD solution of this problem, where should the source place in domain for different modes?
for diiferent modes, should the source be in different places?

I believe the expressions for f0 of a 2D cavity are the same as a 3D cavity, but without the third "depth" term under the square root (so l = 0): https://en.wikipedia.org/wiki/Microw...angular_cavity

This should give you f0 for all modes. For the FDTD case, it may be true that one probe cannot excite all the modes you are interested in (this will be true whenever there is a null at the position of the probe). So you could move around the probe based one knowledge of how you expect the fields to behave.

Eigenmode simulations, however, require no excitation and will simulate f0 and Q for all of your modes. HFSS can do this relatively easily.