33 and the vertex coordinate data is shown in table

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Unformatted text preview: he rectangles, a traditional data structure would typically add nodes at the centers of all edges and the centers of the rectangular faces. In this example, the midside and face nodes are associated with faces however, they could also have been associated with vertices. Without edge data, the database generally requires additional a priori assumptions. For example, we could agree to list vertices in counterclockwise order. Edge nodes could follow in counterclockwise order beginning with the node that is closest in the counterclockwise direction to the rst vertex. Finally, interior nodes may be listed in any order. The choice of the rst vertex is arbitrary. This strategy is generally a compromise between storing a great deal of data with fast access and having low storage costs but having to recompute information. We could further reduce storage, for example, by not saving the coordinates of the edge nodes. 14 Mesh Generation and Assembly 1 08 1 0 1 0 (4) 17 1 1 018 019 16 0 (3) 0 1100 0011 11 1111 0 0 0 (5) 0 5 15 1 14 40 11111 0 0 0 0 06 1111 0000 11111 00000 (2) 1 (1) 0 120 0 013 1111 11 0 11111 00000 11111 00000 21 22 11111 00000 11111 00000 11111 00000 7 1 1 0 1 0 1 0 9 20 1 0 1 0 1 0 2 10 3 Figure 5.3.4: Sample nite element mesh involving a mixture of quadratic approximations on triangles and biquadratic approximations on rectangles. Face indices are shown in parentheses. Face 1 2 3 4 5 Table 5.3.3: Simpli Vertices Nodes 1 2 5 4 9 12 14 11 21 2 3 6 5 10 13 15 12 22 457 14 17 16 587 18 20 17 568 15 19 18 ed face-vertex data for the mesh of Figure 5.3.4. The type of nite element basis must also be stored. In the present example, we could attach it to the face-vertex table. With the larger database described earlier, we could attach it to the appropriate entity. In the spirit of the shape function decomposition described in Sections 4.4 and 4.5, we could store information about a face shape function with the face and information about an edge shape function with the edge. This would allow us t...
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