I agree with the first reply, the time-domain solutions such as FDTD are not matrix-fill-and-solve methods. They are fundamentally different since they are a very direct numerical solution to Maxwell's equations. Most commercial time-domain tools are very memory efficient (CST-MS, Microstripes, XFDTD, etc.). For example, XFDTD uses only 30 MB RAM for 1 million grid cells. Many of them use automatic graded subgridding for fine geometry modeling, which further improves the memory efficiency.
FEM produces a sparse, banded matrix as opposed to MoM which produces a full matrix. For a code such as HFSS, the matrix contains approximately as many elements as there are tetrahedra nodes. RAM requirements of FEM tools can be pretty hefty. A scheme such as adaptive meshing can help decrease the amount of unknowns in the FEM matrix by only adding tetrahedra where they are required.
Also, running on a 64-bit OS can get around the 2 GB memory addressing limitation of 32-bit systems.