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We currently have two other pages on EM analysis:
Using Sonnet for EM analysis (Sonnet Software)
Computational electromagnetics
Note to EM software suppliers... we could use your help, and you could use ours! Special thanks to Jim from Sonnet, who fixed up our definitions of 2.5D and 3D during October 2009!
The original "inventor" of electromagnetic simulation was James Clerk Maxwell. Over one hundred years ago, Maxwell's equations provided the solution to every EM problem that man has encountered. Too bad he didn't have a computer to help him with all the calculus that is required to solve even the simplest EM problems. By the way, it was Oliver Heaviside that reduced Maxwell's many equations to the four we all know and love.
When you purchase or use EM software, there is a convention that tells you how many of the three primary dimensions (X, Y and Z) are considered in the analysis.
2D implies transverse EM waves are analyzed (X and Y directions only), most typically for microstrip transmission lines. No RF currents are permitted in the Z-axis (into or out of the substrate.)
2.5D implies that RF currents are allowed in two directions only (X and Y), and fields are calculated in all three dimensions (X Y and Z). No vertical currents are allowed. Examples would include microstrip or stripline filters which do not contain vias to ground. Note: This term has also been used to refer to 3D planar solvers such as Sonnet (Sonnet Software product) and Momentum (Keysight product) even though they all allow vertical currents.
3D Planar implies that currents and fields are allowed in all 3 directions, but circuits are restricted to stratified dielectric media. Examples would include most MMIC, RFIC, and PCB circuits. Examples include Sonnet (Sonnet Software product) and Momentum (Keysight product).
3D Arbitrary or 3D Full implies electromagnetic interactions in all directions are incorporated in the simulation. If you are an antenna designer, you can skip all the cheap stuff and go right to 3D analysis. Here's an entire Microwaves101 page devoted to this topic!
Another differentiator between 3D Planar and 3D Arbitrary is how ports are handled. For 3D planar, port values are read directly from conductor currents. For 3D Arbitrary, port values are usually inferred from the fields at port locations. This can make a difference in the accuracy, and even the definition of the resulting S-parameters.