On the impact of triangle shapes for boundary layer problems using high-order finite element discretization
The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large angles do not have an adverse impact on solution accuracy. However, a corr...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2016
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| Online Access: | http://hdl.handle.net/1721.1/101266 |
| _version_ | 1826197013714173952 |
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| author | Sun, Huafei Darmofal, David L. Haimes, Robert |
| author2 | Massachusetts Institute of Technology. Aerospace Computational Design Laboratory |
| author_facet | Massachusetts Institute of Technology. Aerospace Computational Design Laboratory Sun, Huafei Darmofal, David L. Haimes, Robert |
| author_sort | Sun, Huafei |
| collection | MIT |
| description | The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large angles do not have an adverse impact on solution accuracy. However, a correct aspect ratio is critical for accuracy for both linear and high-order discretizations. Large angles are also found to be not problematic for the conditioning of the linear systems arising from the discretizations. Further, when choosing preconditioning strategies, coupling strengths among elements rather than element angle sizes should be taken into account. With an appropriate preconditioner, solutions on meshes with and without large angles can be achieved within a comparable time. |
| first_indexed | 2024-09-23T10:41:23Z |
| format | Article |
| id | mit-1721.1/101266 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:41:23Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1012662022-09-27T14:17:26Z On the impact of triangle shapes for boundary layer problems using high-order finite element discretization Sun, Huafei Darmofal, David L. Haimes, Robert Massachusetts Institute of Technology. Aerospace Computational Design Laboratory Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Sun, Huafei Darmofal, David L. Haimes, Robert The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large angles do not have an adverse impact on solution accuracy. However, a correct aspect ratio is critical for accuracy for both linear and high-order discretizations. Large angles are also found to be not problematic for the conditioning of the linear systems arising from the discretizations. Further, when choosing preconditioning strategies, coupling strengths among elements rather than element angle sizes should be taken into account. With an appropriate preconditioner, solutions on meshes with and without large angles can be achieved within a comparable time. Boeing Company 2016-02-25T02:14:27Z 2016-02-25T02:14:27Z 2011-09 2011-09 Article http://purl.org/eprint/type/JournalArticle 00219991 1090-2716 http://hdl.handle.net/1721.1/101266 Sun, Huafei, David L. Darmofal, and Robert Haimes. “On the Impact of Triangle Shapes for Boundary Layer Problems Using High-Order Finite Element Discretization.” Journal of Computational Physics 231, no. 2 (January 2012): 541–557. en_US http://dx.doi.org/10.1016/j.jcp.2011.09.018 Journal of Computational Physics Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier MIT Web Domain |
| spellingShingle | Sun, Huafei Darmofal, David L. Haimes, Robert On the impact of triangle shapes for boundary layer problems using high-order finite element discretization |
| title | On the impact of triangle shapes for boundary layer problems using high-order finite element discretization |
| title_full | On the impact of triangle shapes for boundary layer problems using high-order finite element discretization |
| title_fullStr | On the impact of triangle shapes for boundary layer problems using high-order finite element discretization |
| title_full_unstemmed | On the impact of triangle shapes for boundary layer problems using high-order finite element discretization |
| title_short | On the impact of triangle shapes for boundary layer problems using high-order finite element discretization |
| title_sort | on the impact of triangle shapes for boundary layer problems using high order finite element discretization |
| url | http://hdl.handle.net/1721.1/101266 |
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