Short answer: no.
BesselSpace may be a bad idea because it has slow convergence. (This is the same situation as using cos/sin for non-periodic functions.) Though perhaps this is worth it in the high-frequency setting. If you wanted to create your own
BesselSpace, I’d be happy to walk you through the process.
Otherwise, there used to be a
DiskSpace based on a hierarchy of Zernike-like polynomials but the code has gone dormant. I’d be keen to get it working again but have limited time at the moment. @MikaelSlevinsky FastTransforms gives a fast and stable way of expanding functions in this basis which should be incorporated.
For cylinders, one would then need to tensor
Chebyshev. This is almost functioning.
Even then, one needs to solve the resulting system efficiently. Helmholtz has the nice property that it’s radially symmetric so this reduces to 2-dimensional solves involving
BandedBlockBandedMatrix, so hopefully that should be efficient. For high frequencies this will break down, but Euan Spence has some nice work on preconditioners for high frequency Helmholtz.