A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS

This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.

Iterative physical optics method based on efficient occlusion judgment with bounding volume hierarchy technology

This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the original O(N^(3))to O(N^(2)logN).Numerical results show that the proposed method is more efficient than the traditional method.It is verified in multiple examples that the proposed method can complete the convergence of the current.Moreover,the proposed method avoids the error of judging the lit-shadow relationship based on the normal vector,which is beneficial to current iteration and convergence.Compared with the brute force method,the current method can improve the simulation efficiency by 2 orders of magnitude.The proposed method is more suitable for scattering problems in electrically large cavities and complex scenarios.

On acoustic performance for viscoelastic coating containing axisymmetric cavities using the multiple scattering method

A semi-analytical/numerical model based on the multiple scattering （MS） method has been established for analyzing the effect of acoustic performance on main energy attenua- tion mechanism in viscoelastic coating containing axisymmetric cavities. The basic functions of stress and displacement of the axisymmetric cavity surface are derived in the system of spheri- cal coordinates. The transition matrix between the incident wave and the scattering wave are obtained by the numerical integral of the basic functions of the cavity surface. The reflection, transmission and absorption performance of viscoelastic materials containing periodic cavities are calculated using the MS method and the wave propagating theory of the multi-layered medium. The results indicate that low frequency energy is mainly attenuated through cavity resonance. The resonant properties are found to be very sensitive to the boundary conditions. The coupling of the double-cavity is capable of extending the absorption to even lower fre- quencies. The absorption performance of the viscoelastic coating in the high frequency range is independent of the backing material. Its energy attenuation depends mainly on acoustic properties of cavity scattering and mode conversion.