Some trade-offs in the application of unconditionally-stable schemes to the finite-element time-domain method

It is often surmised that adopting an unconditionally stable scheme for the finite-element time-domain (FETD) method is desirable. This is because a larger timestep Δt can decrease the overall number of time steps and hence potentially yield a shorter computing time. However, FETD involves a linear solve at every time step (in contrast to FDTD), so the characteristics of the associated linear system play a significant role in assessing its performance. In this regard, two fundamental questions arise. The first one asks how the condition numbers of the system matrices of unconditionally- and conditionally-stable schemes behave and whether there are any significant differences between the two. The second question asks how these differences, if any, behave as a function of mesh refinement level and/or size.