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"LOGOS" SOFTWARE PACKAGE: QUALITATIVE IMPROVEMENT OF VOLUMETRIC CELLS BY ELIMINATING SMALL EDGES WITH THE CUTOFF METHOD DURING THE GENERATION OF MESHES

D. N. Smolkina
VANT. Ser.: Mat. Mod. Fiz. Proc 2022. Вып.2. С. 61-71.

The paper describes an approach used in the "Logos" software package to eliminate small edges in polyhedral cells with the cutoff method during the generation of unstructured meshes. Small edges are eliminated by cutting off cells of the stencil mesh using triangles of the surface mesh. A small edge is a polyhedral mesh’s edge which length is 30% less than the edge length in cells of the stencil mesh. The cut off cells are of the two types: those containing characteristic features of the model and simples cells.Approaches used to eliminate small edges for each type of cells are significantly different. For simple cells, an algorithm based on the method of marching cubes is used. To eliminate small edges in cells containing characteristic features of the model, the analysis of the set of tetrahedral volumes built by partitioning a convex cut off cell and its vicinity is performed. The way of building tetrahedrons and the convexity condition for a cell and its vicinity ensure positive volumes of all generated tetrahedrons and this is the necessary condition for elimination of small edges. The performed testing of these algorithms demonstrates that this approach allows eliminating from the mesh up to 70% of small edges and is an automatic and general-purpose approach, because it does not depend on the class of problems in consideration. This allows using the approach to build polyhedral meshes for geometric models of an arbitrary level of complexity.

Keywords: "Logos" software package, an unstructured mesh, mesh quality improvement, small edges, the cutoff method.








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