Abstract

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, the most expensive point of the MPB solver is the evaluation of Green's function. The evaluation of Green's function requires solving high-dimensional partial differential equations, which is the computational bottleneck for solving MPB equations. Numerically, the MPB solver only requires the evaluation of Green's function as the diagonal part of the inverse of the discrete elliptic differential operator of the Debye-Hückel equation. Therefore, we develop a fast algorithm by a coupling of the selected inversion and hierarchical interpolative factorization. By the interpolative factorization, our new selected inverse algorithm achieves linear scaling to compute the diagonal of the inverse of this discrete operator. The accuracy and efficiency of the proposed algorithm will be demonstrated by extensive numerical results for solving MPB equations.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.