A numerical tour of wave propagation

Sponge ABC

The sponge ABC was proposed by Cerjan et al. (1985). The principle is very simple: attenuating the refections exponentially in the extended artificial boundary (Figure 8) area by multiplying a factor less $d(u)$ than 1. Commonly, we use the factor

$$d(u)=\mathrm{exp}(-[0.015*(nb-i)]^2), u=x,z (i\Delta x \; \mathrm{or} \; i\Delta z)$$ (21)

where $nb$ is the thickness of the artificial boundary on each side of the model. Usually, we choose it to be $nb=20 \sim30$ . The sponge ABC can be easily applied to a wide range of wave propagation problems, including some governing wave equations for complicated medium.

extbndr
Figure 8. A schematic diagram of extended artificial boundary area. $A_1A_2A_3A_4$ is the original model zone, which is extended to be $B_1B_2B_3B_4$ with artificial boundary. In the extended bounary area, the attenuation coeffcient $d(u)\neq 0$ ; In the model zone $A_1A_2A_3A_4$ , $d(u)= 0$ , $u=x,z$ .

A numerical tour of wave propagation