Mesh Generation and Adaptation

In the recent years we have been tackling problems of automated two- and three-dimensional mesh generation and adaptation. Mesh generation can be described as approximate covering of a domain with a finite number of simple adjacent elements, forming the mesh. Such meshes are commonly used in simulation of physical processes (e.g. FEM), but also in other areas, such as computer graphics, geodesy or computational geometry.

The developed generator is capable of creating unstructured triangular and quadrilateral meshes on planes or 3D surfaces, and tetra- or hexahedral volumetric meshes. For hexahedral meshes we investigate two types of methods: indirect (based on tetrahedral mesh, which has to be created earlier) and direct, using Medial Axis Transform.

We investigate also the problem of mesh adaptation for the considered model – i.e. their optimization while keeping the number of elements low, with respect to both domain geometry and simulated process. In the latter case the goal of adaptation is to obtain the best possible precision of results while reducing the computation cost (anisotropic meshes are also used). The developed methods allow for multi-criteria adaptation of meshes in order to conform to requirements obtained from different sources.

Recently, we have been investigating the problem of parallelization of the mesh generation process. It is mainly caused by the still growing sizes of used meshes. In such cases the sequential generation poses problems regarding both the computational and memory cost. This subject is developed in cooperation with Universite de Technologie de Compiegnein France.

In all problems mentioned above the particular stress is put on the efficiency and reliability of algorithms and proper selection of data structures. The important factors are also portability to different platforms and extendability of algorithms and data structures to constantly growing possibilities of the generator.

Researchers: B.Głut, T.Jurczyk, K. Boryczko, J.Kitowski

Triangular mesh

Quadrilateral mesh