61
Direction of
Wave Propagation
x
Figure 4.3: Waves passing through a lateral boundary unaffected by the boundary.
according to Snells law. Equation 4.46 or 4.47 are used to eliminate the amplitude outside
of the domain from the tridiagonal matrix equation. To illustrate equation 4.47 is finite
differenced at the lower lateral boundary as
A(I,1) A(I,0) A(I,1) + A(I,0)
AY im 2
Solving for A(I,0)
i imAY
A(I,0) = tVa(I,1) (4.50)
1 + im^-
Thus A(I,0) is eliminated in terms of A(I,1). similarly at the upper boundary A(I,N+1) is
eliminated in terms of A(I,N). The same procedure is used with equation 4.46 which yields
the simple relationships
A(I,0) = A(I,1) (4.51)
and
A(I,N+1) = A(I,N)
(4.52)