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Research Article | Open Access

A D-N alternating algorithm for exterior 3-D problem with ellipsoidal artificial boundary

School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan, Changsha 410114, China
College of Liberal Arts and Sciences, National University of Defense Technology, Hunan, Changsha 410073, China
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Abstract

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.

Keywords

D-N alternating algorithmexterior 3-D poisson problemellipsoidal artificial boundarynatural boundary reduction
CLC number: 65N38, 65N55

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 455-466
DOI: 10.3934/math.2022029

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Cite this article:
Luo X. A D-N alternating algorithm for exterior 3-D problem with ellipsoidal artificial boundary. AIMS Mathematics, 2022, 7(1): 455-466. https://doi.org/10.3934/math.2022029

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Received: 26 July 2021
Accepted: 02 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)