###########Refraction Info##############
Utt=v(x,y)*(Uxx+Uyy)
U(x,y,0)=exp(-10*(x-15)**2)
Ut(x,y,0)=-10(x-15)*exp(-10*(x-15)**2)
U(0,y,t)=U(20,y,t)=0
U(x,0,t)=U(x,10,t)
Domain={(x,y) | 02x-10,
1 otherwise
The basic idea here is simulate the movement of a wave between
materials with different indexes of refraction by changing the a**2
term in the wave equation to a piecwise function of x and y.
a**2 (or v(x,y)) is defined to be 5 for y>2x-10 and 1 otherwise.
You can see this graphically by clicking the link "Refraction Domain" (The x-axis
is vertical and the y horizontal). The top part of the picture that is not covered
with dots has v=1, the bottom part that IS covered with dots has v=5. The wave front
starts at the top of the picture and travels down. Boundary condtions on the top and
bottom of the domain are zero, they are periodic on the left and right hand side. Periodic
boundary conditions allow for a nicer wavefront structure (see Making_Nice_WaveFronts).