On the Link between Mesh Size Adaptation and Irregular Vertices

Author(s): D. Zint, R. Grosso

Abstract: In numerical simulations and computer graphics meshes are often required to have varying element sizes. High resolution, ie small elements, should be only used where necessary. The transition between element sizes requires introducing irregular vertices. In this work, we examine the occurance of irregular vertices in transition regions by setting up an advancing front triangulation that generates optimal transitions. We establish a relation between the appearance of irregular vertices and the properties of the size function and show that a linear transition between different element sizes can be achieved without any singularities on the interior of the transition. Therefore, we can optimize triangulations by setting transition fronts accordingly. These results are used to estimate properties of block-structured grids, eg how many blocks are required to represent a given domain correctly.

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