That makes sense, but I still think you might have better luck using parametric CAD geometry concepts to join simple shapes together. Acoustically, a stepped series of conical or cylindrical shapes represent most horn geometry, so it might just be a case of sensibly dividing the final horn geometry into fine enough segments?
You can also 'draw' and join surface shapes using Gmsh itself, either in the GUI or via the CLI. I've not tried anything complex, but I did find it a little easier than defining the geometry directly in AKABAK3 for anything that isn't a simple set of flat, planar rectangles.
That might also be where you're getting confused about how the mesh is defined. You do only end up with triangles, since the BEM only solves the integral across the defined surfaces, and not for the volume between or around those. That's also true for videogames and the like, the stuff you see is 'just triangles' - but the tricky maths is defining where those patched triangular surfaces go to sufficiently portray a complex three-dimensional shape.
Think of it like this; unless your horn is using purely flat planes or conic sections, then the mesh generation algorithm has to consider curvature and deformation in 3D. That also may be a reason why models exported from SketchUp are often a memory-heavy mess of thin, oddly oriented slices - exactly the sort of thing the BEM solver hates.
Considering the wealth of tools for creating parametric surfaces in 3D, many of them free, at least you have options!
As for the solver stalling, this might be a memory issue. Try breaking the model into more subdomains, which appears to help with the distribution of the matrix calculations across your CPU's threads - each of which need to have 4 GB of RAM available (quoting from memory (sorry)
) alongside enough memory to store the general model without writing to your disk's swap file, or generating errors which require a recalculation of that matrix index...
That means you might find faster, more stable results setting the AKABAK3 preferences to use fewer threads if you're 'short' on RAM. I've got 12 threads available on my desktop, and I had to upgrade to 48 GB of RAM mid-way through my dissertation to prevent the BEM solver step stalling on complicated models with ~9000 elements or more.
Eventually, I got fed up and re-drew the entire cabinet geometry from scratch in CAD, sliced it up in a different way, and ensured 'best practice' for mesh element length based on the distances involved. These models were of 8 LABhorn, and there's no copy/paste for subdomains or groups in AKABAK3, so you can imagine this was a
chore.
The new single horn model solved in 11 minutes, compared to the previous one's 2 hours. For the clustered array models, results were in VACS in hours rather than days 😆 I opened the original model in the new version of AKABAK3 last week, and sure enough, there were some pink bits identified by this new mesh checking process. Only a tiny few, but they count!