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

By P.L. George

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L 134 CHAPIER ill PL. George 134 EL . r I i I I I I i I Ii I I i R I j FIG. 6. Optimal point in three dimensions. the domain (see above discussion), if element ABCPk is positive and empty and, in addition, if the region delimited by this element and the neighboring faces of the front remains well shaped. As soon as a point verifies all these properties, it is retained. When no point is selected, we return to (a) while the size of the visited neighborhood is increased, * tetrahedron AB CPk is formed (see below discussion) and the front is updated.

In this case, r, the size defining the examined region, is increased until a point P is found which can become a member of the list and can then be retained. As soon as a point verifies all these properties, it is retained. In the case where no point is selected, we return to (a) while the size of the visited neighborhood (r in Fig. 4) is increased, * triangle ABPk is formed (see below discussion) and the front is updated. B A FIG. 4. Candidates. Advancing-front type mesh generation SECTION 16 133 Angles /1 and 2 are used to ensure that the element in creation will not cause trouble latter (Fig.

The process is iterative: a front, initialized by the collection of boundary items, is analyzed to determine a departure zone, from which one or several internal elements are created; the front is then updated and the element creation process is pursued as long as the front is not empty. The process can be summarized as follows: * Initialization of the front; fPL. George 118 CHAPIER 11 FIG. 4. Quadtree method. * (a) Analysis of the front: - Determination of the departure zone; - Analysis of this zone: * Creation of internal point(s) and internal element(s); * Update of the front.