论文标题
线性泊松 - 波尔兹曼模型的求解器的收敛分析
Convergence analysis of a solver for the linear Poisson--Boltzmann model
论文作者
论文摘要
这项工作调查了可以作为外部传动问题配方的泊松玻璃体模型的域分解方法的收敛性。为了研究其收敛性，我们引入了一个内部常数，该常数提供了内部任何谐波功能的$ l^2 $ norm的上限，并为相关的dirichlet to dirichlet to-neumann操作员建立光谱等效性，以估计内部迭代操作员的频谱。由于外部子域的无限性，该分析是不平凡的，这将其与对施瓦茨交替方法的经典分析区分开来，该方法具有非重叠的有界子域。事实证明，对于现实中的线性Poisson-Boltzmann溶剂模型，当放松参数位于0到2之间时，可以确保内部迭代的收敛性。这种收敛性结果解释了DDLPB方法的良好性能在[Siam Journal on Scientific Computing on Scientific Computing，41（2019），pp。B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320-B320]。为了验证我们的收敛分析并研究内部迭代的最佳松弛参数。
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 $L^2$ 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 [SIAM Journal on Scientific Computing, 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.
