3.6 Point Placement

The distribution of the mesh points should only depend on the application and the device structure. In practice it is trivial to see that it also depends on the chosen mesh generation method. It is difficult to find and to generate with an algorithm the optimal placement of points without following some trial and error scheme. The mesh points are often sprayed over the simulation domain with a simple method and only afterwards adapted to the application/solution. Many existing and applied methods are not fully flexible with regard to the placement of the mesh points. Two negative and frequently encountered effects can be observed:

• Rotating and translating a model relative to the coordinate system can have a heavy impact on the resulting mesh.
• The location of the mesh points is limited to certain positions within the coordinate system.

Some methods might even fail if the model is slightly tilted relative to the coordinate system. Other methods, e.g. advancing front methods, are fairly independent of such an alignment and produce better boundary-fitted meshes. Unstructured meshes do not possess a regular topology by definition. Some unstructured methods, e.g. cartesian and octree methods, exhibit a certain regularity concerning the distribution of the mesh points. Therefore it is useful to further distinguish unstructured methods with regard to the point placement mechanism. Throughout this text the term fully unstructured will refer to methods which allow an arbitrary placement of the mesh points.