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By P.L. George

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Additional resources for Automatic Mesh Generation and Finite Element Computation

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5. Surface definition. FIG. 6. Surface mesh. z FIG. 7. Surface mesh. 125 126 PL. George CHAPIER I Z FIG. 8. Surface mesh. 5 shows an example of a surface definition including patches with different sizes while Fig. 6 illustrates the corresponding surface mesh (from StrimlO, the CAD-CAM system by Cisigraph). 7 (courtesy of Cisigraph) and Fig. 8 (courtesy of SDRC) illustrate two other examples of surface meshes created by the two mentioned CAD-CAM systems. CHAPTER III Automatic Method (1): Advancingfront Type Mesh Generation Introduction This class of mesh generators, adapted to arbitrary geometries, has been studied by GEORGE [1971], L6HNER and PARIKH [1988a,b], PERAIRE, PEIRO, FORMAGGIA, MORGAN and ZIENKIEWICZ [1988], and, more recently, by GOLGOLAB [1989].

This kind of mesh generator constructs the mesh of the domain from its boundary. The elements created are triangles in two dimensions and tetrahedra in three dimensions. Variations exist, in two dimensions, which enable us to create quadrilaterals almost everywhere in the domain, depending on the number of sides forming the given boundary (see Lo [1991] and ZHU, ZIENKIEWICZ, HINTON and Wu [1991]). The data required consists of the boundary, or more precisely, a polygonal discretization of it (dimension 2), input as a set of segments, or a polyhedral discretization (dimension 3), input as a set of triangular faces.

Nevertheless, surface mesh generation algorithms exist, such as: * local algorithms designed to deal with a given patch, * more global algorithms able to deal with a collection of patches enjoying some particular properties. I--- -~ I i ~ 0 FIG. 2. Different types of restricted patches. 124 P1L. George CHAPTIER II FIG. 3. Real patch, u, v patch and "metric" patch. For a quadrilateral patch, a local algorithm generally consists of using an algebraic method (or an equivalent method) with respect to the variables u, v serving at the description of the patch under consideration.

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