Keywords: size prediction, mesh generation, tetrahedral mesh, anisotropic metric, control space.

The information about the final number of volume blocks in the mesh being created could be utilised in a number of ways. It may influence the decision whether to continue the discretization procedure or rather to modify the input data in order to obtain either smaller or more refined mesh, depending on the situation. The dynamic data structures used during the meshing procedure (e.g. for storing the mesh entities) could be more efficiently managed. In the case of parallel mesh generation, the ability to assess the final number of elements created in a given subdomain leads to better load balancing and in consequence increases the speedup of the whole process.

For three-dimensional domains, described by a triangular surface mesh, the tetrahedral meshes are constructed via an iterative triangulation method using a concept of local non-Euclidean metric, which allows the generation of meshes with varying density and anisotropic shape of elements[1]. During the meshing process the generator uses a special adaptive control space (ACS) structure to provide the requested metric (governing the size, shape and directionality of elements) at any point within the domain being discretized [2]. The mesh generation using the Delaunay technique consists of the following steps: preparation of the ACS, triangulation of boundary nodes, boundary constraining, insertion of inner nodes and smoothing.

The prediction based on the boundary elements may be calculated using the mesh faces (and inertial centre of the surface mesh vertices) or using the boundary constrained volume elements. Prediction based on the incremental Delaunay refinement utilises a quality criterion of a selected tetrahedron in a heap structure of elements set for refinement. The technique based on the octree ACS structure calculates the prediction using the metric information from ACS directly (with additional introduction of inside/outside information).

The methods described of volume mesh size prediction were implemented as a part of the mesh generator developed by authors and they were tested on a variety of tetrahedral meshes of different characteristics. The results obtained were discussed with respect to the observed accuracy of the predictions, the prerequisite meshing steps and an additional running cost of the prediction procedure. The technique of mesh size prediction developed using octree control space structure clearly outperforms other presented methods in terms of accuracy.

1

T. Jurczyk, "Efficient Algorithms of Automatic Discretization of Non-Trivial Three-Dimensional Geometries and its Object-Oriented Implementation", PhD thesis, AGH University of Science and Technology, Kraków, Poland, November 2007.

2

T. Jurczyk, B. Glut, P. Breitkopf, "Parallel 3D Mesh Generation using Geometry Decomposition", in Proc. of Int. Conf. NUMIFORM'07, Porto, Portugal, 1579-1584, 2007.

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