2023/09/13 by Abhinav Jha, Jha, Abhinav, Benjamin Stamm +1
Computer Science · Engineering · Mathematics · #65N35 #65N55 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Number Theory (math.NT) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2309.06862
openalex publication_date 2023/09/13 · openalex created_date 2023/09/15 · openalex updated_date 2026/07/28
In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in ℝ3 with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for steric effects. Potential theory arguments transform the nonlinear equation into two coupled equations defined in a bounded domain. Then, the Schwarz 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 each ball. The main novelty of the proposed method is the introduction of a hybrid linear-nonlinear solver used to solve the equation. A series of numerical experiments are presented to test the method and show the importance of the nonlinear model.