In this talk, I will introduce hybrid methods that we developed recently using solution and domain decompositions, finite element, and finite difference techniques to fast calculate the electrostatics of protein in ionic solvent. In particular, they have been applied to the numerical solutions of three dielectric continuum models – the Poisson-Boltzmann equation, a size modified Poisson-Boltzmann equation, and a nonlocal modified Poisson-Boltzmann equation. Their performance will be discussed and compared with the corresponding finite element solvers. These hybrid techniques can also be extended to solve a class of nonlinear interface boundary value problems. This project is a joined work with my student, Jinyong Ying, under the support by NSF award DMS-1226259.