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The Artificial Boundary Method for a Nonlinear Interface Problem on Unbounded Domain

De-hao Yu1 ,Hong-ying Huang2
LSEC, ICMSEC, Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing, 100190, China.
School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, China.

Computer Modeling in Engineering & Sciences 2008, 35(3), 227-252. https://doi.org/10.3970/cmes.2008.035.227

Abstract

In this paper, we apply the artificial boundary method to solve a three-dimensional nonlinear interface problem on an unbounded domain. A spherical or ellipsoidal surface as the artificial boundary is introduced. The exact artificial boundary conditions are derived explicitly in terms of an infinite series and then the well-posedness of the coupled weak formulation in a bounded domain, which is equivalent to the original problem in the unbounded domain, is obtained. The error estimate depends on the mesh size, the term after truncating the infinite series and the location of the artificial boundary. Some numerical examples are presented to demonstrate the effectiveness and accuracy of this method.

Keywords

Artificial boundary method, Dirichlet to Neumann mapping, Finite element method, Natural integral operator, Nonlinear interface problem.

Cite This Article

Yu, D. (2008). The Artificial Boundary Method for a Nonlinear Interface Problem on Unbounded Domain. CMES-Computer Modeling in Engineering & Sciences, 35(3), 227–252.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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