2018/07/14 by Chaoyu Quan, Quan, Chaoyu, Benjamin Stamm +3 · 1 citation
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · doi:10.48550/arxiv.1807.05384
openalex publication_date 2018/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a domain decomposition method for the Poisson-Boltzmann (PB) solvation model that is widely used in computational chemistry is proposed. This method, called ddLPB for short, solves the linear Poisson-Boltzmann (LPB) equation defined in \mathbb R3 using the van der Waals cavity as the solute cavity. The Schwarz domain decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in balls. A series of numerical experiments is presented to test the robustness and the efficiency of this method including the comparisons with some existing methods. We observe exponential convergence of the solvation energy with respect to the number of degrees of freedom which allows this method to reach the required level of accuracy when coupling with quantum mechanical descriptions of the solute.