Corrected Trapezoidal Rule-IBIM for linearized Poisson-Boltzmann equation

Abstract: In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with improved accuracy for a boundary integral formulation of the linearized Poisson-Boltzmann equation. More specifically, in contrast to the typical boundary integral formulations, the corrected trapezoidal rule is applied to integrate a system of compacted supported singular integrals using uniform Cartesian grids in $\mathbb{R}^3$, without explicit surface parameterization. A Krylov method, accelerated by a fast multipole method, is used to invert the resulting linear system. We study the efficacy of the proposed method, and compare it to an existing, lower order method. We then apply the method to the computation of electrostatic potential of macromolecules immersed in solvent. The solvent excluded surfaces, defined by a common approach, are merely piecewise smooth, and we study the effectiveness of the method for such surfaces.