By P.L. George

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Additional info for Automatic Mesh Generation and Finite Element Computation

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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.

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Automatic Mesh Generation and Finite Element Computation by P.L. George

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