In this paper, we develop a domain-decomposition method for the generalized Poisson-Boltzmann equation based on a solvent-excluded surface which is widely used in computational chemistry. The solver requires to solve a generalized screened Poisson (GSP) equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for Steric effects. Potential theory arguments transform the GSP equation into two-coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball in which, the spherical harmonics and the Legendre polynomials are used as basis functions in the angular and radial directions. A series of numerical experiments are presented to test the method.

翻译：本文针对计算化学中广泛使用的基于溶剂可及表面的广义泊松-玻尔兹曼方程，提出了一种区域分解方法。该求解器需要求解定义在$\mathbb{R}^3$空间中具有空间依赖介电常数及考虑空间位阻效应的离子排斥函数的广义屏蔽泊松方程。通过势理论论证，将广义屏蔽泊松方程转化为定义在有界域上的两个耦合方程。继而采用施瓦茨分解方法，将溶剂腔分解为重叠球体区域，仅在各球体内求解一组耦合子方程，其中以球谐函数和勒让德多项式分别作为角向和径向基函数。通过系列数值实验验证了该方法的有效性。