Fast multipole method for 3-D Poisson-Boltzmann equation in layered electrolyte-dielectric media

•A Funk-Hecke formula for pure imaginary wave numbers enables a compression of the far field of PB potential in layered electrolyte-dielectric media.•Polarization sources defined to represent the reaction field components make the compressions have exponential convergence relied on Euclidean distance.•A recurrence formula provides efficient run-time computations of the Sommerfeld-type integrals in the FMM algorithm.•The FMM algorithm for charge interactions in general layered electrolyte-dielectric media achieves O(N) complexity.