Article
| Title: | Conforming simplicial partitions of product-decomposed polytopes (English) |
| Author: | Korotov, Sergey |
| Author: | Vatne, Jon Eivind |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 1-10 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We propose some approaches for the generation of conforming simplicial partitions with various regularity properties for polytopic domains that are products or a union of products, thus generalizing our earlier results. The techniques presented can be used for finite element simulations of higher-dimensional problems. (English) |
| Keyword: | conforming simplicial partition |
| Keyword: | product polytope |
| Keyword: | red refinement |
| Keyword: | finite element method |
| MSC: | 65N30 |
| MSC: | 65N50 |
| DOI: | 10.21136/AM.2024.0163-24 |
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| Date available: | 2025-03-07T09:23:48Z |
| Last updated: | 2025-03-10 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152881 |
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| Reference: | [3] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems.Studies in Mathematics and Its Applications 4. North-Holland, Amsterdam (1978). Zbl 0383.65058, MR 0520174 |
| Reference: | [4] Freudenthal, H.: Simplizialzerlegungen von beschränkter Flachheit.Ann. Math. (2) 43 (1942), 580-582 German. Zbl 0060.40701, MR 0007105, 10.2307/1968813 |
| Reference: | [5] Hacon, D., Tomei, C.: Tetrahedral decompositions of hexahedral meshes.Eur. J. Comb. 10 (1989), 435-443. Zbl 0723.05040, MR 1014551, 10.1016/S0195-6698(89)80017-4 |
| Reference: | [6] Khademi, A., Korotov, S., Vatne, J. E.: On the generalization of the Synge-Křížek maximum angle condition for $d$-simplices.J. Comput. Appl. Math. 358 (2019), 29-33. Zbl 1426.65177, MR 3926696, 10.1016/j.cam.2019.03.003 |
| Reference: | [7] Khademi, A., Korotov, S., Vatne, J. E.: On mesh regularity conditions for simplicial finite elements.Numerical Mathematics and Advanced Applications. ENUMATH 2019 Lecture Notes in Computational Science and Engineering 139. Springer, Cham (2021), 633-640. Zbl 1475.65192, MR 4266542, 10.1007/978-3-030-55874-1_62 |
| Reference: | [8] Korotov, S., Křížek, M.: On conforming tetrahedralizations of prismatic partitions.Differential and Difference Equations with Applications Springer Proceedings in Mathematics & Statistics 47. Springer, New York (2013), 63-68. Zbl 1317.65063, MR 3110255, 10.1007/978-1-4614-7333-6_5 |
| Reference: | [9] Korotov, S., Vatne, J. E.: Preserved structure constants for red refinements of product elements.Numerical Geometry, Grid Generation and Scientific Computing Lecture Notes in Computational Science Engineering 143. Springer, Cham (2021), 241-248. Zbl 1496.74120, MR 4391448, 10.1007/978-3-030-76798-3_15 |
| Reference: | [10] Křížek, M.: On semiregular families of triangulations and linear interpolation.Appl. Math., Praha 36 (1991), 223-232. Zbl 0728.41003, MR 1109126, 10.21136/AM.1991.104461 |
| Reference: | [11] Kuhn, H. W.: Some combinatorial lemmas in topology.IBM J. Res. Dev. 4 (1960), 518-524. Zbl 0109.15603, MR 0124038, 10.1147/rd.45.0518 |
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