Numerical solution of differential and integral equations
The report is devoted to problem of irregular tetrahedral meshes construction in domains with complicated non-uniformly scaled geometry. Non-uniformly scaled geometry means that domain contains constructive macroelements which sizes are several orders greater than microelements sizes. Moreover, in those tasks the effects that produced by microelements are explored. Thus we need to condense mesh near the microelements. At the same time, for macroelements discretization sufficiently rough mesh can be used. Applying of existing mesh construction methods to domains with non-uniformly scaled geometry is related to many difficulties of domain description or mesh cells size control.
In the report the approach based on sections replication method is considered. When the sections replication method is used the three-dimensional mesh is constructed by filling of the space between neighbor sections by tetrahedrons. On those sections two-dimensional triangulation is set. Most implementations of this method require the constant number of nodes on all sections.
We consider the generalized sections replication method, which allows to set different triangulations on the neighbor sections. Thus the constant nodes number constraint is eliminated.
The main feature of generalized sections replication method is the ability to construct the tetrahedral mesh between pair of sections with different triangulations. In addition, one triangulation must be detail and another one must be rough. Also particular coincidence of triangulations is allowed. The offered method consists of two stages. At the first stage, for each triangle belong to the rough triangulation its image in detail triangulation is sought. The second stage consists of two steps. The first step is the decomposition of image onto three subareas. Each subarea this is a peculiar surroundings of the vertex of triangle belong to the rough triangulation. Those subareas are necessary to build tetrahedrons. The second step is the tetrahedrons building in the space between triangle from rough triangulation and its image in detail triangulation.
In the report the image seeking algorithm, image decomposition algorithm and manner of tetrahedrons building are considered. The example of mesh construction for research problem is presented. The comparison of results obtained on the mesh constructed by standard sections replication method and the mesh constructed by generalized sections replication method is given.
Note. Abstracts are published in author's edition
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