Adaptive Control Space Structure for Anisotropic Mesh Generation
T. Jurczyk
B. Glut
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Abstract
The article concerns problem of automated generation of anisotropic finite element meshes on 3D surfaces. The meshes are created using a modification of Delaunay incremental insertion algorithm working in Riemannian space (using metric transformation approach). During the meshing process the generator relies on a special structure (called control space) to provide the required size and shape of elements at any point within the domain being discretized. Organization of this control space structure directly influences both the quality of the obtained mesh and the efficiency of the meshing process. It should allow to combine sizing information gathered automatically from different sources (in both discrete and continuous form). The quadtree grid and background mesh structure are typically used for control space representation. This article describes an implementation of a adaptive control space structure with emphasis on efficiency and versatility necessary in automated adaptation process. The metric required during mesh generation is stored in the discrete nodes of the structure and is interpolated between the nodes. Metric values at the nodes are set during initialization procedure and are calculated from the available sizing data. We inspect cases with either too sparse or too dense sets of these initial data. The structure is adapted with respect to the diversity of metric data. The smoothness of the obtained metric field is also inspected and appropriately adjusted. In case of sizing data gathered from several different sources (e.g. model geometry, adaptation process, user input) we start with creation of separate control space structures for each type of source. Then the resultant control space is calculated using the intersection procedure, which takes into account both structure and metric data from the nodes of all control spaces. Finally, the utilization of this control space during mesh generation process is briefly described and examples of created meshes are presented.