2.3  Two dimensional Boundaries

In the subroutines that solve Helmholtz problems in two dimensions ( HIBEM2, HEBEM2 and HMBEM2) 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 HIBEM2_T, HEBEM2_T and HMBEM2_T each solve Helmholtz 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.

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.