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 inversion based on hierarchical interpolative factorization for self Green's function for modified Poisson-Boltzmann equation in two dimensions
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DOI：
10.1016/j.jcp.2021.110893
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Y. Tu;Qiyuan Pang;Haizhao Yang;Zhenli Xu
中科院分区：
文献类型：
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作者：
Y. Tu;Qiyuan Pang;Haizhao Yang;Zhenli Xu
本文研究了一种有效的数值方法来求解修正的Poisson-Boltzmann（MPB）方程，该方程以自绿色函数为状态方程来描述离子体系中的静电关联。以前，MPB求解器的最昂贵的点是绿色函数的评估。计算绿色函数需要求解高维偏微分方程，这是求解MPB方程的计算瓶颈。在数值上，MPB求解器只需要将绿色函数作为德拜-休克尔方程的离散椭圆微分算子的逆的对角部分来计算。因此，我们发展了一种快速算法的选择反演和分层插值因式分解的耦合。通过插值因式分解，我们的新的选择逆算法实现了线性缩放来计算该离散算子的逆的对角线。通过求解MPB方程的大量数值结果，证明了该算法的准确性和有效性。
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.