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Mathematics > Numerical Analysis

arXiv:2204.07958 (math)
[Submitted on 17 Apr 2022]

Title:On an interior-exterior nonoverlapping domain decomposition method for the Poisson--Boltzmann equation

Authors:Xuanyu Liu, Yvon Maday, Chaoyu Quan, Hui Zhang
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Abstract:A nonoverlapping domain decomposition method is studied for the linearized Poisson--Boltzmann equation, which is essentially an interior-exterior transmission problem with bounded interior and unbounded exterior. This problem is different from the classical Schwarz alternating method for bounded nonoverlapping subdomains well studied by Lions in 1990, and is challenging due to the existence of unbounded subdomain. To obtain the convergence, a new concept of interior-exterior Sobolev constant is introduced and a spectral equivalence of related Dirichlet-to-Neumann operators is established afterwards. We prove rigorously that the spectral equivalence results in the convergence of interior-exterior iteration. Some numerical simulations are provided to investigate the optimal stepping parameter of iteration and to verify our convergence analysis.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2204.07958 [math.NA]
  (or arXiv:2204.07958v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2204.07958

Submission history

From: Chaoyu Quan [view email]
[v1] Sun, 17 Apr 2022 08:52:20 UTC (832 KB)
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