Convergence Analysis of a Solver for the Linear Poisson–Boltzmann Model

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-06-10 DOI:10.1137/24m1717087

Xuanyu Liu, Yvon Maday, Chaoyu Quan, Hui Zhang

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Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1232-1253, June 2025.
Abstract. This work investigates the convergence of a domain decomposition method for the Poisson–Boltzmann model that can be formulated as an interior-exterior transmission problem. To study its convergence, we introduce an interior-exterior constant providing an upper bound of the [math] norm of any harmonic function in the interior, and establish a spectral equivalence for related Dirichlet-to-Neumann operators to estimate the spectrum of interior-exterior iteration operator. This analysis is nontrivial due to the unboundedness of the exterior subdomain, which distinguishes it from the classical analysis of the Schwarz alternating method with nonoverlapping bounded subdomains. It is proved that for the linear Poisson–Boltzmann solvent model in reality, the convergence of interior-exterior iteration is ensured when the relaxation parameter lies between 0 and 2. This convergence result interprets the good performance of ddLPB method developed in [C. Quan, B. Stamm, and Y. Maday, SIAM J. Sci. Comput., 41 (2019), pp. B320–B350] where the relaxation parameter is set to 1. Numerical simulations are conducted to verify our convergence analysis and to investigate the optimal relaxation parameter for the interior-exterior iteration.

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线性泊松-玻尔兹曼模型求解器的收敛性分析

SIAM数值分析杂志，第63卷，第3期，1232-1253页，2025年6月。摘要。这项工作研究了泊松-玻尔兹曼模型的区域分解方法的收敛性，该模型可以表述为内部-外部传输问题。为了研究其收敛性，我们引入了一个内外常数，给出了内调和函数的[数学]范数的上界，并建立了相关Dirichlet-to-Neumann算子的谱等价来估计内外迭代算子的谱。由于外子域的无界性，这种分析是不平凡的，这与经典的具有非重叠有界子域的Schwarz交替方法分析不同。在现实中证明了线性泊松-玻尔兹曼溶剂模型，当松弛参数在0 ~ 2之间时，保证了内外迭代的收敛性。这一收敛结果解释了[C]中开发的ddLPB方法的良好性能。Quan， B. Stamm和Y. Maday, SIAM J. Sci。第一版。[j], 41 (2019), pp. B320-B350]，其中松弛参数设置为1。数值模拟验证了我们的收敛性分析，并研究了内外迭代的最优松弛参数。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.