Assuring conformity in three dimensional self adaptive mesh generation for the finite element method (EM problems)

Desirable properties in an automatic mesh generation scheme are set out and the influence of use within a self-adaptive environment is explained. A mesh generation technique based upon the concept of the Delaunay partition is then seen to offer many advantages when used under these conditions. The theoretical basis for the Delaunay approach is given and its practical implementation is undertaken. This process brings to light three separate difficulties associated with the method, solutions to which are evolved. The first drawback encountered is the existence within the Delaunay approach of degenerate node locations. The second is the technique's tendency toward creation of elements of poor quality, often known as slivers. Finally, there is the problem of ensuring the mesh is consistent with all physical boundaries present, that is, ensuring that the mesh is compatible. In each of these cases the development of a strategy to tackle the particular difficulty is described. Emphasis in this paper though, is given to the steps taken to overcome the problem of enforcing mesh compatibility. The theoretical basis for the compatibility problem in relation to the Delaunay partition is outlined first. Examples characterising its rate of occurrence in practice are then given. There then follows a detailed examination of the steps taken, first to identify the occurrence of an incompatibility, then to correct it. The success of these measures is illustrated by further practical tests. In conclusion an example of successful integration of the mesh generation algorithm into a self adaptive analysis system is provided.<
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