Let’s talk about time for a moment. As in Time Domain. In the previous chapter I stated that one problem with transient\time-domain (TD) methods is the structured mesh, limiting accurate modeling to square-ish structures. What I’m presenting here is not necessarily a problem with TD methods, rather a designation for it. Namely, TD methods are not suitable for some problems, but more suitable than frequency-domain (FD) methods for others.
Consider the case of this patch Antenna:

I know you are thinking to yourself how the meshing is significantly better, right? Well, that’s because I’ve been debugging like crazy and it is a lot more robust and useful now. Back to our subject, however, one would expect such a simple and square structure to run very fast, right?
Well, no. Before I answer why, I’ll drop one more hint. This patch was printed on a thick substrate and designed for
. Do you know now why it’s going to run very slowly?
One more hint: Here is the return loss graph:

That’s it, no more hints. Got it?
Going back to signal processing: A narrower frequency domain impulse response of a filter, results in a longer time domain response. Meaning, such a narrow-band structure would “ring” for a very long time, once excited by a pulse. Let’s see how long:

Or in run-time:

As you can see, the energy in this simulation keeps going up and down, even if the general trend is downward. However, as it approaches the marker, it barely dissipates. This means that either there is a larger resonator (such as the PCB ground) in the simulation that is still ringing, or that there is a numerical problem, e.g. floating point precision trouble that sometime happens with small numbers. This could be resolved by adding more losses to the simulation, or maybe just designing a proper patch with a thicker substrate.
So as my Sensei says: Know your enemy, know yourself. When dealing with narrow-band structures, choose the right solver. Of course, it’s not always available open-source, is it.
Short post this time, but I’m wrapping up this series for now. I would like to thank Thorsten Liebig for publishing this cool piece of software as open-source and also taking the time to answer some of my annoying questions.
Let’s start designing!