COMPUTING THE LOCAL QUALITY CHARACTERISTIC OF TETRAHEDRAL MESH ELEMENTS AS A SOLUTION EXTREME TASK
Alexander Igumnov ยท Mathematical Physics and Computer Simulation ยท 2024
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 ๐ โ 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(๐,๐ด) โ the distance between a set ๐ and a set ๐ด defined by critical elements. In early works, the problem was solved through the empirical classification of families ๐ โ ๐ด and excluding those that are not known to be closest to ๐. Namely, such that the offset some point in the ๐ family is given by the ๐ โฒ โ ๐ด family, which is closer to ๐. 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 ๐ด, allowing you to accurately describe the set of ๐ดโ โ ๐ด of such families for which The specified conversion is not possible. That is, ๐ดโ is approved dist(๐,๐ด) = dist(๐,๐ดโ) . In addition, a diagram is given for constructing families of the set ๐ดโ โ analogues of the points of the assumed extremum in the extremum research problem of the function of numerical variables.