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

•Linear scaling selected inverse of elliptic operators.•Fast solver for modified Poisson-Boltzmann equation.•Hierarchical interpolative factorization. This paper studies an efficient numerical method for solving modified Poisson-Boltzmann (MPB) equations with the self Green's function as a stat...

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Bibliographic Details
Published in:Journal of computational physics Vol. 461; p. 110893
Main Authors: Tu, Yihui, Pang, Qiyuan, Yang, Haizhao, Xu, Zhenli
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 15.07.2022
Elsevier Science Ltd
Subjects:
Algorithms
Boltzmann transport equation
Computational physics
Elliptic operator
Equations of state
Factorization
Green's functions
Hierarchical interpolative factorization
Linear scaling
Mathematical analysis
Modified Poisson-Boltzmann equations
Numerical methods
Operators (mathematics)
Partial differential equations
Selected inverse
Self Green's function
Solvers
Modified Poisson-Boltzmann equations
Linear scaling
Elliptic operator
Hierarchical interpolative factorization
Self Green's function
Selected inverse
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:•Linear scaling selected inverse of elliptic operators.•Fast solver for modified Poisson-Boltzmann equation.•Hierarchical interpolative factorization. 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.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110893