Why have radiation boundary box in FEM but no radiation box in MoM

I thought in order to solve Maxwell's equations you have to have boundary conditions, so in HFSS (FEM) it uses a radiation (or air) box to simulate that, but in MoM solvers it does not have that. Could someone explain?

Also, I know the underlying method to solve MoM is Green's functions. What is the underlying method to solve FEM?

Thanks.

In FEM, you need to discretize the analysis volume, including the air around your device, and have to define the boundary conditions at the sides of that analysis volume.

In MoM, you solve for the currents on the conductors (surface meshing) and there is no need to discretize the volume around the device. The boundary conditions are already implicit in the coupling functions (Green's functions) used by the solver: open space for some MoM solvers, closed metal box for some other MoM solvers.

Thanks, volker. Could you elaborate on this statement"
"The boundary conditions are already implicit in the coupling functions (Green's functions) "

How are they implicit?

Refer to Balanis's book chapter 14.

This question is really asking how we solve partial differential equations (PDEs). PDE is governing the quantity relations, however, only the PDEs are not sufficient to completely represent the problem. PDEs + boundary conditions (BCs) will. Therefore, for differential-based solver, such as FEM and FDTD, the problem domain is finite and and BCs are always required. Otherwise the problem is incomplete, and # of solutions can be infinite.

Another way to describe the problem is the unit response (impulse response), which means when the system is driven by a Dirac delta source, and the solution to such source is known (Green's function). Then the system to an arbitrary source can be obtained by superpositioning system responses with many Dirac delta sources applied (similar to convolution, when take the limit, the solution becomes an integral). This is the base of MoM. Please NOTE, that the system response (Green's function) is not easy to find, for free-space or layered medium (both assume boundless problems), the closed form of Green's functions can be found. You can also try to get a Green's function with PEC bounding your problem domain, however I do not know how to analytically find it. Since you have to solve the point source radiation within such structure.