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

摘要

An iterative solution scheme is proposed for solving the electri- cal 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 conven- tional direct integral equation approach that yields Fredholrn inte- gral equations of the first kind, the indirect integral equation ap- proach yields well-posed Fredholrn 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, itera- tive 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.