By P.L. George
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Additional info for Automatic Mesh Generation and Finite Element Computation
The difficulties when considering such an algorithm are well identified. They consist of: * determining the type of situation which governs the type of construction; * knowing if a point is inside the domain or not; * defining a suitable position when a point is created. Three constraints must be satisfied: the created point must be inside the domain; the element(s) resulting from this point creation must be well-shaped and it (they) must be such that the remaining zone can be dealt with without difficulties at a later stage.
Domain inducing degeneracies. A generation system is associated with such a transformation, which allows us to compute the requested mesh. Variables x, y, (x, y, z) describe the domain (see Fig. 7) while the logical region is described using variables , , (C, 77, 5). The problem now becomes: find the functions x = x(6, n), y = Y(6, *) in two dimensions, and x =x(, , ;), y = y(f, , f), z =z(, 9,;) in three dimensions, assuming that the transformation maps the logical region one-to-one onto the domain and that the boundaries are preserved.
Several choices can be made to construct the control structure (Chapter I). An example is given below depicting such a choice for the case where the only data at our disposal is the contour discretization of the domain. Thus, the control structure is defined as a regular grid enclosing the domain. A cell in this grid has a size Ac depending on the size of the initial data items. For example, in two dimensions, a solution is to set Ac to be twice the length of the smallest edge in the data. This value may induce a too large number of cells so an alternative solution is to set A, to be the average length of the given edges.
Automatic Mesh Generation and Finite Element Computation by P.L. George