Iterative Solution Method for the Linearized Poisson-Boltzmann Equation: Indirect Boundary Integral Equation Approach

An iterative solution scheme is proposed for solving the electrical double-layer interactions governed by the linearized Poisson-Boltzmann equation. The method is based on the indirect integral equation formulation with the double-layer potential kernel of the linearized Poisson-Boltzmann equation. In contrast to the conventional direct integral equation approach that yields Fredholm integral equations of the first kind, the indirect integral equation approach yields well-posed Fredholm integral equations of the second kind. The eigenvalue analysis reveals that the spectral radius of the double-layer integral operator is always less than one. Thus, iterative solution schemes can be successfully implemented for solving the electrical double-layer interactions for very large and complex systems. The utility of the iterative indirect method is demonstrated for several examples which include spherical and spheroidal particles. Copyright 2001 Academic Press.