Conforming simplicial partitions of product-decomposed polytopes

Sergey Korotov; Jon Eivind Vatne

Applications of Mathematics (2025)

  • Issue: 1, page 1-10
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Korotov, Sergey, and Vatne, Jon Eivind. "Conforming simplicial partitions of product-decomposed polytopes." Applications of Mathematics (2025): 1-10. <http://eudml.org/doc/299911>.

@article{Korotov2025,
abstract = {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.},
author = {Korotov, Sergey, Vatne, Jon Eivind},
journal = {Applications of Mathematics},
keywords = {conforming simplicial partition; product polytope; red refinement; finite element method},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Conforming simplicial partitions of product-decomposed polytopes},
url = {http://eudml.org/doc/299911},
year = {2025},
}

TY - JOUR
AU - Korotov, Sergey
AU - Vatne, Jon Eivind
TI - Conforming simplicial partitions of product-decomposed polytopes
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 1
EP - 10
AB - 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.
LA - eng
KW - conforming simplicial partition; product polytope; red refinement; finite element method
UR - http://eudml.org/doc/299911
ER -

References

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  2. Bey, J., 10.1007/s002110050475, Numer. Math. 85 (2000), 1-29. (2000) Zbl0949.65128MR1751367DOI10.1007/s002110050475
  3. Ciarlet, P. G., The Finite Element Method for Elliptic Problems, Studies in Mathematics and Its Applications 4. North-Holland, Amsterdam (1978). (1978) Zbl0383.65058MR0520174
  4. Freudenthal, H., 10.2307/1968813, Ann. Math. (2) 43 (1942), 580-582 German. (1942) Zbl0060.40701MR0007105DOI10.2307/1968813
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  6. Khademi, A., Korotov, S., Vatne, J. E., 10.1016/j.cam.2019.03.003, J. Comput. Appl. Math. 358 (2019), 29-33. (2019) Zbl1426.65177MR3926696DOI10.1016/j.cam.2019.03.003
  7. Khademi, A., Korotov, S., Vatne, J. E., 10.1007/978-3-030-55874-1_62, Numerical Mathematics and Advanced Applications. ENUMATH 2019 Lecture Notes in Computational Science and Engineering 139. Springer, Cham (2021), 633-640. (2021) Zbl1475.65192MR4266542DOI10.1007/978-3-030-55874-1_62
  8. Korotov, S., Křížek, M., 10.1007/978-1-4614-7333-6_5, Differential and Difference Equations with Applications Springer Proceedings in Mathematics & Statistics 47. Springer, New York (2013), 63-68. (2013) Zbl1317.65063MR3110255DOI10.1007/978-1-4614-7333-6_5
  9. Korotov, S., Vatne, J. E., 10.1007/978-3-030-76798-3_15, Numerical Geometry, Grid Generation and Scientific Computing Lecture Notes in Computational Science Engineering 143. Springer, Cham (2021), 241-248. (2021) Zbl1496.74120MR4391448DOI10.1007/978-3-030-76798-3_15
  10. Křížek, M., 10.21136/AM.1991.104461, Appl. Math., Praha 36 (1991), 223-232. (1991) Zbl0728.41003MR1109126DOI10.21136/AM.1991.104461
  11. Kuhn, H. W., 10.1147/rd.45.0518, IBM J. Res. Dev. 4 (1960), 518-524. (1960) Zbl0109.15603MR0124038DOI10.1147/rd.45.0518

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