Reformulation of the Fourier–Bessel mode solver using Ampere's and Faraday's law..

Simpler and fewer expressions required for system matrix building.

Converged results generally achieved using fewer terms in expansion basis series.

Mode family symmetry facilitates system matrix order reduction.

Two forms of the system matrix are provided with advantages and disadvantages to each indicated.

Two application examples are presented, one for a dielectric SNAP resonator with material variations in the permittivity only, the other for a quasi-crystal containing variations in both permittivity and permeability.

The simplified nature of the reformulated Fourier–Bessel numerical solver makes it attractive to all researchers with a moderately performant desktop PC.