A D-N Alternating Algorithm for Exterior Laplace Problem with Mixed Boundary Value Conditions

DOI

10.2991/ammsa-17.2017.78How to use a DOI?

Keywords

exterior Laplace problem; mixed boundary value conditions; D-N alternating algorithm; natural boundary reduction; Convergence analysis

Abstract

This paper develops a Dirichlet-Neumann (D-N) alternating algorithm to solve the mixed boundary value problem of Laplace equation in an infinite domain, and analyses the convergence of the algorithm. By choosing a circle surrounding the original boundary as an artificial boundary to divide the unbounded domain into two sub-domains, we can make use of the natural boundary reduction (NBR) method in the infinite sub-domain to solve a Dirichlet boundary value problem while use the finite element method in the finite sub-domain to solve a mixed boundary value problem. We prove that the algorithm is convergent geometrically for any relaxation factor between 0 and 1. The numerical experiment results also display that the sequence of iterative solutions is geometrically convergent, the convergence rate is independent of the finite element mesh size h, and the maximum nodal error on 1 is roughly of O(h2) .

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Quan Zheng
AU  - Huihui Jia
PY  - 2017/05
DA  - 2017/05
TI  - A D-N Alternating Algorithm for Exterior Laplace Problem with Mixed Boundary Value Conditions
BT  - Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017)
PB  - Atlantis Press
SP  - 349
EP  - 352
SN  - 1951-6851
UR  - https://doi.org/10.2991/ammsa-17.2017.78
DO  - 10.2991/ammsa-17.2017.78
ID  - Zheng2017/05
ER  -