# Those mesh entities elements faces edges and vertices

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Unformatted text preview: boundaries have pointers to relevant geometric structures de ning the problem domain. This structure, called the SCOREC mesh database, is shown in Figure 5.3.1. Nodes may be introduced as xed points in space to be associated with shape functions. When done, these may be located by pointers from any mesh entity. Element Face Geometric Model Entities Edge Vertex Figure 5.3.1: SCOREC hierarchical mesh database. Let us illustrate the data structure for the two-dimensional domain shown in Figure 5.2.5. As shown in Figure 5.3.2, this mesh has 20 faces (two-dimensional elements), 36 edges, and 17 vertices. The face and edge-pointer information is shown in Table 5.3.1. Each edge has two pointers back to the faces that contain it. These are shown within brackets in the table. The use of tables and integer indices for pointers is done for convenience and does not imply an array implementation of pointer data. The edge and 5.3. Data Structures 11 vertex-pointer information and the vertex-point coordinate data are shown in Table 5.3.2. Backward pointers from vertices to edges and pointers from vertices and edges on the boundary to the geometric database have not been shown to simplify the presentation. We have shown a small portion of the pointer structure near Edge 18 in Figure 5.3.3. Links between common entities allow the mesh to be traversed by faces, edges, or vertices in two dimensions. Problem and solution data is stored with the appropriate entities. 5 4 7 3 2 1 6 11 10 9 8 13 4 3 20 9 12 19 2 8 14 15 14 13 10 15 36 16 11 20 19 24 7 12 1 18 5 6 17 22 17 18 25 21 35 34 33 23 27 26 32 28 30 16 31 29 4 3 2 7 17 9 8 1 6 5 12 11 13 16 10 14 15 Figure 5.3.2: Example illustrating the SCOREC mesh database. Faces are indexed as shown at the upper left, edge numbering is shown at the upper right, and vertex numbering is shown at the bottom. 12 Mesh Generation and Assembly Face Edge Edge Edge 111 7 1 2] 6 1 9] 222 8 2 3] 7 2 1] 3 8 3 2] 9 3 4] 12 3 6] 434 10 4 5] 9 4 3] 5 10 5 4] 14 5 7] 13 5 6] 6 12 6 3] 13 6 5] 11 6 11] 747 15 7 8] 14 7 5] 8 15 8 7] 5 8 16 8 13] 9 6 9 1] 17 9 10] 22 9 10 17 10 9] 19 10 11] 18 10 14] 11 11 11 6] 20 11 12] 19 11 10] 12 20 12 11] 21 12 13] 24 12 14] 13 16 13 8 ] 25 13 20] 21 13 12] 14 18 14 10] 24 14 12] 23 14 15] 15 23 15 14] 27 15 18] 26 15 ] 16 29 16 ] 30 16 17] 31 16 ] 17 28 17 ] 32 17 18] 30 17 16] 18 27 18 15] 33 18 19] 32 18 17] 19 33 19 18] 35 19 20] 34 19 ] 20 25 20 13] 36 20 ] 35 20 19] Table 5.3.1: Face and edge-pointer data...
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