  In this paper, we develop a domain decomposition method for the nonlinear
Poisson-Boltzmann equation based on a solvent-excluded surface widely used in
computational chemistry. The model relies on a nonlinear equation defined in
$\mathbb{R}^3$ with a space-dependent dielectric permittivity and an
ion-exclusion function that accounts for steric effects. Potential theory
arguments transform the nonlinear equation into two coupled equations defined
in a bounded domain. Then, the Schwarz decomposition method is used to
formulate local problems by decomposing the cavity into overlapping balls and
only solving a set of coupled sub-equations in each ball. The main novelty of
the proposed method is the introduction of a hybrid linear-nonlinear solver
used to solve the equation. A series of numerical experiments are presented to
test the method and show the importance of the nonlinear model.
