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Volume 23, Issue 6
Artificial Boundary Method for the Three-Dimensional Exterior Problem of Elasticity

Hou-De Han & Chun-Xiong Zheng

J. Comp. Math., 23 (2005), pp. 603-618.

Published online: 2005-12

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  • Abstract

The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method.  

  • Keywords

Artificial boundary method, unbounded domains, elasticity.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-603, author = {Hou-De Han and Chun-Xiong Zheng}, title = {Artificial Boundary Method for the Three-Dimensional Exterior Problem of Elasticity}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {6}, pages = {603--618}, abstract = {

The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8841.html} }
TY - JOUR T1 - Artificial Boundary Method for the Three-Dimensional Exterior Problem of Elasticity AU - Hou-De Han & Chun-Xiong Zheng JO - Journal of Computational Mathematics VL - 6 SP - 603 EP - 618 PY - 2005 DA - 2005/12 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8841.html KW - Artificial boundary method, unbounded domains, elasticity. AB -

The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method.  

Hou-De Han and Chun-Xiong Zheng. (2005). Artificial Boundary Method for the Three-Dimensional Exterior Problem of Elasticity. Journal of Computational Mathematics. 23 (6). 603-618. doi:
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