Open AccessA D-N alternating algorithm for exterior 3-D problem with ellipsoidal artificial boundary
Author(s) -
Xiaopeng Luo
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022029
Subject(s) - mathematics , ellipsoid , convergence (economics) , boundary (topology) , algorithm , dirichlet boundary condition , boundary value problem , neumann boundary condition , dirichlet distribution , series (stratigraphy) , mathematical analysis , geometry , physics , paleontology , astronomy , economics , biology , economic growth
In this study, based on a general ellipsoidal artificial boundary, we present a Dirichlet-Neumann (D-N) alternating algorithm for exterior three dimensional (3-D) Poisson problem. By using the series concerning the ellipsoidal harmonic functions, the exact artificial boundary condition is derived. The convergence analysis and the error estimation are carried out for the proposed algorithm. Finally, some numerical examples are given to show the effectiveness of this method.