  A numerical method using implicit surface representations is proposed to
solve the linearized Poisson-Boltzmann equations that arise in mathematical
models for the electrostatics of molecules in solvent. The proposed method used
an implicit boundary integral formulation to derived a linear system defined on
Cartesian nodes in a narrowband surrounding the closed surface that separate
the molecule and the solvent. The needed implicit surfaces is constructed from
the given atomic description of the molecules, by a sequence of standard level
set algorithms. A fast multipole method is applied to accelerate the solution
of the linear system. A few numerical studies involving some standard test
cases are presented and compared to other existing results.
