Volume 27, Issue 2-3
The Ellipsoid Artificial Boundary Method for Three-Dimensional Unbounded Domains

Hongying Huang & Dehao Yu

DOI:

J. Comp. Math., 27 (2009), pp. 196-214.

Published online: 2009-04

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  • Abstract

The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.

  • Keywords

Artificial boundary method Exterior harmonic problem Finite element method Natural boundary reduction Oblate ellipsoid Prolate ellipsoid

  • AMS Subject Headings

65N38 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-196, author = {}, title = {The Ellipsoid Artificial Boundary Method for Three-Dimensional Unbounded Domains}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {196--214}, abstract = {

The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8568.html} }
TY - JOUR T1 - The Ellipsoid Artificial Boundary Method for Three-Dimensional Unbounded Domains JO - Journal of Computational Mathematics VL - 2-3 SP - 196 EP - 214 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8568.html KW - Artificial boundary method KW - Exterior harmonic problem KW - Finite element method KW - Natural boundary reduction KW - Oblate ellipsoid KW - Prolate ellipsoid AB -

The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.

Hongying Huang & Dehao Yu. (2019). The Ellipsoid Artificial Boundary Method for Three-Dimensional Unbounded Domains. Journal of Computational Mathematics. 27 (2-3). 196-214. doi:
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