Alexander Y. Igumnov Computing the Local Quality Characteristic of Tetrahedral Mesh Elements as a Solution extreme task
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https://doi.org/10.15688/mpcm.jvolsu.2024.4.1
Alexander Y. Igumnov
Candidate of Sciences (Physics and Mathematics) , Associate Professor, Department of Computer Science and Programming Thechnology,
Volzhsky Polytechnic Institute (branch) of the Volgograd State Technical University
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,
https://orcid.org/0000-0002-2120-768X
Engels St, 42 a, 404121 Volzhsky, Russian Federation
Abstract. The paper discusses the problem of calculating the quality cha- racteristic of elements of a triangulation grid (in multidimensional space). We call quality the degree of difference between a mesh element in a sense critical. For example, the difference between a triangle and a degenerate triangle. To calculate this value, the following construction is used. Mesh element vertices are treated as a numbered set of X — points point family. In the space of such sets, the metric proposed in early works is introduced. As a result, the problem boils down to calculating the value of dist(X, Y) — the distance between a set X and a set Y defined by critical elements. In early works, the problem was solved through the empirical classification of families Y ∈ Y and excluding those that are not known to be closest to X. Namely, such that the offset some point in the Y family is given by the Y 0 ∈ Y family, which is closer to X. At the same time, empirical classification led to a large amount of calculations. This work gives a standardized classification of the families of the set Y, allowing you to accurately describe the set of Y− ⊂ Y of such families for which The specified conversion is not possible. That is, Y− is approved
dist(X, Y) = dist(X, Y−) .
In addition, a diagram is given for constructing families of the set Y− — analogues of the points of the assumed extremum in the extremum research problem of the function of numerical variables.
Key words: Triangle non-degeneracy, extremum of a function in the space of point families, families of the expected extremum, coordinate-free extreme research scheme, saving grid properties in mappings.
Computing the Local Quality Characteristic of Tetrahedral Mesh Elements as a Solution extreme task by Alexander Y. Igumnov is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 27 No. 4 2024, pp. 5-16