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.