Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared ...Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.展开更多
An optimized Neumann series（NS） approximation is described based on Frobenius matrix decomposition, this method aims to reduce the high complexity, which caused by the large matrix inversion of detection algorithm i...An optimized Neumann series（NS） approximation is described based on Frobenius matrix decomposition, this method aims to reduce the high complexity, which caused by the large matrix inversion of detection algorithm in the massive multiple input multiple output（MIMO） system. The large matrix in the inversion is decomposed into the sum of the hollow matrix and a Frobenius matrix, and the Frobenius matrix has the diagonal elements and the first column of the large matrix. In order to ensure the detection performance approach to minimum mean square error（MMSE） algorithm, the first three terms of the series approximation are needed, which results in high complexity as O（K;）, where K is the number of users. This paper further optimize the third term of the series approximation to reduce the computational complexity from O（K;） to O（K;）. The computational complexity analysis and simulation results show that the performance of proposed algorithm can approach to MMSE algorithm with low complexity O（K;）.展开更多
基金supported by NSFC (11071039,11161130002)Natural Science Foundation of Jiangsu Province (BK2011584)
文摘Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.
文摘An optimized Neumann series（NS） approximation is described based on Frobenius matrix decomposition, this method aims to reduce the high complexity, which caused by the large matrix inversion of detection algorithm in the massive multiple input multiple output（MIMO） system. The large matrix in the inversion is decomposed into the sum of the hollow matrix and a Frobenius matrix, and the Frobenius matrix has the diagonal elements and the first column of the large matrix. In order to ensure the detection performance approach to minimum mean square error（MMSE） algorithm, the first three terms of the series approximation are needed, which results in high complexity as O（K;）, where K is the number of users. This paper further optimize the third term of the series approximation to reduce the computational complexity from O（K;） to O（K;）. The computational complexity analysis and simulation results show that the performance of proposed algorithm can approach to MMSE algorithm with low complexity O（K;）.
