Prediction of permeable thin absorbers using the finite-difference time-domain method

Permeable thin materials can play a role similar to porous absorbents, providing high sound absorption at mid- and high-frequencies. In addition, since they can be made from various materials such as cotton, chemical fibers, and metal fibers, they can be hygienic, durable, and easy to recycle. Their absorption characteristics are often discussed with analytical approaches, and a few studies have even applied the boundary element method and the finite element method to predict the practical effects of permeable thin absorbers. However, to the best of the authors' knowledge, the finite-difference time-domain (FDTD) method has yet to be used. Herein a formulation to deal with a permeable thin absorber as a permeable boundary in the FDTD method is proposed and the stability conditions for a permeable boundary are derived considering the state transition equations. The proposed formulation is validated by comparing the numerical and analytical results, which agree well.