In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear 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 nonlinear 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. The main novelty of the proposed method is the introduction of a hybrid linear-nonlinear solver used to solve the equation. A series of numerical experiments are presented to test the method and show the importance of the nonlinear model.

翻译：本文针对计算化学中广泛使用的溶剂可及表面，提出了一种非线性泊松-玻尔兹曼方程的区域分解方法。该模型采用定义在$\mathbb{R}^3$上的非线性方程，其中包含空间依赖的介电常数和用于描述空间位阻效应的离子排斥函数。通过位势理论论证，将非线性方程转化为定义在有界区域内的两个耦合方程。随后应用Schwarz分解方法，将空腔分解为重叠球体，仅在每个球体内求解一组耦合子方程，从而构建局部问题。该方法的主要创新在于引入了用于求解方程的混合线性-非线性求解器。通过一系列数值实验对方法进行测试，并验证了非线性模型的重要性。