  In this paper, a domain decomposition method for the Poisson-Boltzmann (PB)
solvation model that is widely used in computational chemistry is proposed.
This method, called ddLPB for short, solves the linear Poisson-Boltzmann (LPB)
equation defined in $\mathbb R^3$ using the van der Waals cavity as the solute
cavity. The Schwarz domain 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 balls. A series of numerical experiments is
presented to test the robustness and the efficiency of this method including
the comparisons with some existing methods. We observe exponential convergence
of the solvation energy with respect to the number of degrees of freedom which
allows this method to reach the required level of accuracy when coupling with
quantum mechanical descriptions of the solute.
