2.2 Two dimensional Boundaries

In the subroutines that solve acoustic problems in two dimensions ( AIBEM2, AEBEM2 and AMBEM2) the boundaries must be represented in the form illustrated in Figure 2.1. In order that the normal to the boundary points outward rather than inward, the two nodes that define each element must be listed in the clockwise direction around the boundary. The programs AIBEM2_T, AEBEM2_T and AMBEM2_T each solve acoustic problems in which the boundary under consideration is that of a square of side 0.1. The boundary is represented by 32 uniform panels and also has 32 vertices, as illustrated in Figure 2.3.

Fig 2.3. The square divided into 32 panels.

In this example the representation of the boundary is exact. In order to pass the description of the boundary to the subroutines it is defined by the two tables of data 2.A and 2.B. Table 2.A lists the (x,y) coordinates of the vertices and is identified by the real array VERTEX. Table 2.B lists the index of the two vertices that define each panel and is referred to by the integer array SELV.


Table 2.A: Vertices of square boundary ( VERTEX)
Index	x	y	Index	x	y
1	0.0000	0.0000	17	0.1000	0.1000
2	0.0000	0.0125	18	0.1000	0.0875
3	0.0000	0.0250	19	0.1000	0.0750
4	0.0000	0.0375	20	0.1000	0.0625
5	0.0000	0.0500	21	0.1000	0.0500
6	0.0000	0.0625	22	0.1000	0.0375
7	0.0000	0.0750	23	0.1000	0.0250
8	0.0000	0.0875	24	0.0000	0.0125
9	0.0000	0.1000	25	0.1000	0.0000
10	0.0125	0.1000	26	0.0875	0.0000
11	0.0250	0.1000	27	0.0750	0.0000
12	0.0375	0.1000	28	0.0625	0.0000
13	0.0500	0.1000	29	0.0500	0.0000
14	0.0625	0.1000	30	0.0375	0.0000
15	0.0750	0.1000	31	0.0250	0.0000
16	0.0875	0.1000	32	0.0125	0.0000

Table 2.B: Panels that constitute the square ( SELV))
Index Vertex 1 Vertex 2 Index Vertex 1 Vertex 2
1 1 2 17 17 18
2 2 3 18 18 19
3 3 4 19 19 20
4 4 5 20 20 21
5 5 6 21 21 22
6 6 7 22 22 23
7 7 8 23 23 24
8 8 9 24 24 25
9 9 10 25 25 26
10 10 11 26 26 27
11 11 12 27 27 28
12 12 13 28 28 29
13 13 14 29 29 30
14 14 15 30 30 31
15 15 16 31 31 32
16 16 17 32 32 1

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Table 2.B: Panels that constitute the square ( SELV))
Index	Vertex 1	Vertex 2	Index	Vertex 1	Vertex 2
1	1	2	17	17	18
2	2	3	18	18	19
3	3	4	19	19	20
4	4	5	20	20	21
5	5	6	21	21	22
6	6	7	22	22	23
7	7	8	23	23	24
8	8	9	24	24	25
9	9	10	25	25	26
10	10	11	26	26	27
11	11	12	27	27	28
12	12	13	28	28	29
13	13	14	29	29	30
14	14	15	30	30	31
15	15	16	31	31	32
16	16	17	32	32	1