I understand your frustration. First, any method can be made to do anything so somebody experienced enough at a method could argue why it may be the best. Second, I see finite-difference and finite element methods as the purest solutions to Maxwell’s equations. It seems like most other methods take advantage of some sort of approximation or simplification. For example, to simulate metallic structures, the method of moments is probably superior. To simulate long periodic structures, semi-analytical methods may be superior. To simulate all-dielectric structures, Fourier methods tend to be superior. Time domain methods tend to be better for transient and nonlinear devices. Frequency-domain tends to be better for single frequency simulations or highly resonant devices. You can get most of these details and more in Lecture 1 here:
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I am not completely sure what your SIW device looks like, but I do not any simplifications to the problem. That is why I pointed you to finite-difference or finite element. I like finite-difference for simulating things in new ways because I can formulate and implement new codes very quickly. Finite-differences also seem to be better right now for simulating very large structures and parallelization, but I don’t think this is a problem for you. Finite element can make more effective use of unstructured grids so will be more efficient for you in the end.