| Title:
|
Face-to-face partition of 3D space with identical well-centered tetrahedra (English) |
| Author:
|
Hošek, Radim |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
6 |
| Year:
|
2015 |
| Pages:
|
637-651 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The motivation for this paper comes from physical problems defined on bounded smooth domains $\Omega $ in 3D. Numerical schemes for these problems are usually defined on some polyhedral domains $\Omega _h$ and if there is some additional compactness result available, then the method may converge even if $\Omega _h \to \Omega $ only in the sense of compacts. Hence, we use the idea of meshing the whole space and defining the approximative domains as a subset of this partition. \endgraf Numerical schemes for which quantities are defined on dual partitions usually require some additional quality. One of the used approaches is the concept of \emph {well-centeredness}, in which the center of the circumsphere of any element lies inside that element. We show that the one-parameter family of Sommerville tetrahedral elements, whose copies and mirror images tile 3D, build a well-centered face-to-face mesh. Then, a shape-optimal value of the parameter is computed. For this value of the parameter, Sommerville tetrahedron is invariant with respect to reflection, i.e., 3D space is tiled by copies of a single tetrahedron. (English) |
| Keyword:
|
rigid mesh |
| Keyword:
|
well-centered mesh |
| Keyword:
|
approximative domain |
| Keyword:
|
single element mesh |
| Keyword:
|
Sommerville tetrahedron |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 06537666 |
| idMR:
|
MR3436566 |
| DOI:
|
10.1007/s10492-015-0115-5 |
| . |
| Date available:
|
2015-11-17T20:31:17Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144451 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
