COMPUTING THE LOCAL QUALITY CHARACTERISTIC OF TETRAHEDRAL MESH ELEMENTS AS A SOLUTION EXTREME TASK

The paper discusses the problem of calculating the quality characteristic 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 ′ ∈ 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.