ABSTRACT
Figure 9.17 Rectangular and nonrectangular physical spaces. (a) Rectangular physical space. (b) Quarter-round physical space.
Figure 9.17a illustrates this situation. When the physical space is not rectangular, however, problems arise. Consider the quarter-round physical space illustrated in Figure 9.17b, which is discretized by a rectangular finite difference grid. Except for rare points, grid points do not fall on the curved boundary of the physical space, thus making it impossible to specify boundary conditions. The finite difference grid is not uniform at interior points adjacent to the curved boundary. Obviously, some new finite difference approach is required.
