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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

$\displaystyle d(u)=\mathrm{exp}(-[0.015*(nb-i)]^2), u=x,z (i\Delta x \; \mathrm{or} \; i\Delta z)$ (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
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$ .
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next up previous A numerical tour of wave propagation [pdf]

Next: Perfectly Matched Layer (PML) Up: Absorbing boundary condition (ABC) Previous: Clayton-Enquist boundary condition

2021-08-31