Linear-scaling selected inversion based on hierarchical interpolative factorization for self Green's function for modified Poisson-Boltzmann equation in two dimensions

This paper studies an efficient numerical method for solving modified Poisson-Boltzmann (MPB) equations with the self Green's function as a state equation to describe electrostatic correlations in ionic systems. Previously, most expensive point of MPB solver is evaluation function. The requires high-dimensional partial differential equations, which computational bottleneck equations. Numerically, only diagonal part inverse discrete elliptic operator Debye-Hückel equation. Therefore, we develop fast algorithm by coupling selected inversion and hierarchical interpolative factorization. By factorization, our new achieves linear scaling compute this operator. accuracy efficiency proposed will be demonstrated extensive results