  In this paper, we propose a fast multipole method (FMM) for 3-D linearized
Poisson-Boltzmann (PB) equation in layered media. The main framework of the
algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered
media [1,2], using an extension of the Funk-Hecke formula for pure imaginary
wave number. Moreover, a recurrence formula is provided for the run-time
computation of the Sommerfeld-type integrals used in the FMM algorithm. Due to
the similarity between Helmholtz and linearized PB equation, the recurrence
formula can also be used for the FMM of Helmholtz equation in layered media
with minor changes as mentioned in [1] . Numerical results validate that the
FMM for interactions of charges under screen's potentials in layered media has
the same accuracy and CPU complexity as the classic FMM for charge interactions
in free space.
