The Perfectly Matched Layer (PML)

Up to now, we have only briefly mentioned the issue of absorbing boundary conditions (ABCs). Actually, one of the most flexible and efficient ABCs is the perfectly matched layer (PML) developed by Berenger. The basic idea is this: if a wave is propagating in medium A and it impinges upon medium B, the amount of reflection is dictated by the intrinsic impedances of the two media

If these two media have the equal impedances, the reflection coefficient would be zero and no reflection would occur. This still doesn’t solve our problem, because the pulse will continue propagating in the new medium. What we really want is a medium that is also lossy so the pulse will die out before it hits the boundary. This is accomplished by making both permittivity and permeability of Eq. (2) complex, because the imaginary part represents the part that causes decay.
The PML is implemented in the program fd2d_002. Figure 1 illustrates the effectiveness of an 5-layer PML with the source in the center of problem space.

If you want to get this FDTD program fd2d_002, please contact with me by Email: aifors@126.com.