Free 3D Maxwell's equations solver for cylinder cavity resonator?

Hi,

I'm trying to build an air filled cylinder cavity resonator excited by coaxial probe like this:(view using fix font)

port1 50 ohm coax feedline port 2 | | | ___________________ | | | | | | | | | V | | V -------- -------- ---------- ----------- -------- -------- | | | || | |-------||---------- ^ tuning screw

The coax probe is expected to excite the E field inside the cavity. The resonator is expected to work in TM011 mode. I want to solve the E and M fields inside the cavity and get the S parameters giving the size of the cavity, the probes and the characteristics of the metal. My EM theory tells me this configuration should work. I'm not a paid RF/MW engineer or an academic so I couldn't afford the commercial EM solver. This is a hobby project. Does anyone know if there is any free solver can handle this problem? Is this problem best solved by FDTD? How about MoM and FEM?

thanks, Calvin