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Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics
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A penteract partition by means of the optimal subdivision of cells
(naslov ne postoji na srpskom)
Technical University, Gabrovo, Bulgaria
Ključne reči: Measure of degeneracy; congruence classes; refinement strategies
Sažetak
(ne postoji na srpskom)
Freudental's algorithm obtained way back in early forties have been traditionally used for simplicial triangulating of the hypercube. The main advantage of this algorithm is that it only generates one congruence class. Unfortunately, Freudental's algorithm is not optimal with respect to the measure of degeneracy. The multigrid methods require the degeneracy measure to be as small as possible. The minimal subdivision in the 3-dimensional case and the uniform tesseract corner subdivision in the 4-dimensional case are optimal in regards the measure of degeneracy and multigrid applications. The question about the optimal refinement strategy in more dimensional cases is still an open problem. This paper deals with a penteract subdivision with degeneracy measure much better than one obtained by the Freudental algorithm.
Reference
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Ardila, F., Ceballos, C. (2013) Acyclic Systems of Permutations and Fine Mixed Subdivisions of Simplices. Discrete Comput Geom, 49: 485-510
Bey, J. (1998) Simplicial grid refinement: On Freudenthal's algorithm and the optimal number of congruence classes. Numerische Mathematik, 85(1): 1-29
Forsyth, A.R. (1930) Geometry of Four Dimensions. UK: Cambridge University Press, First Edition edition
Inselberg, A. (2009) Parallel Coordinates: Visual Multidimensional Geometry and Its Applications. New York: Springer-Verlag, pp. 554
Kendall, M.G. (2004) A Course in the Geometry of N Dimensions. Dover Courier, 80 pages
Ma, T., Wang, S. (2016) Spectral Theory of Differential Operators and Energy Levels of Subatomic Particles. J. Math. Study, 49(3): 259-292
Petrov, M.S., Todorov, T.D. (2018) Stable subdivision of 4D polytopes. Numerical Algorithms, 79(2): 633-656
Todorov, T.D. (2013) The optimal refinement strategy for 3-D simplicial meshes. Computers & Mathematics with Applications, 66(7): 1272-1283
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/SPSUNP1901041P
objavljen u SCIndeksu: 16.07.2019.

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