[1] Fix G J, Marin S P. Variational methods for underwater acoustic problems[J]. Journal of Computational Physics, 1978, 28(2):253-270.[2] Chen I L, Chen J T, Liang M T. Analytical study and numerical experiments for radiation and scattering problems using the CHIEF method[J]. 2001, 248(5):809-828.[3] Ciavaldini J F, Tournemine G. A finite element method to compute stationary steady flows in the hodograph plane[J]. Journal of the Indian Mathematical Society, 1977, 41(1-2):69-82.[4] Plessix, Mulder. Frequency-domain finite-difference amplitude-preserving migration[J]. Geophysical Journal International, 2004, 157(3):975-987.[5] Erlangga Y A. Advances in Iterative Methods and Preconditioners for the Helmholtz Equation[J]. Archives of Computational Methods in Engineering, 2008, 15(1):37-66.[6] J Berkhout A, Pao Y. Seismic Migration Imaging of Acoustic Energy by Wave Field Extrapolation[J]. Journal of Applied Mechanics, 1982, 49(3):682-683.[7] Cai X C, Casarin M A, Elliott F W, et al. Overlapping Schwarz Algorithms For Solving Helmholtz's Equation[J]. Contemporary Mathematics, 1998, 218:391-399.[8] 龙毅, 徐军, 朱汉清. 规则区域上Helmholtz方程的一种快速算法[J]. 电子科技大学学报(微波与激光技术专辑), 1999, 28(4):383-387.[9] 龚东山, 丁方允. 关于大波数k的Helmholtz方程有限元解的误差估计与差量分析[J]. 兰州大学学报, 2003, 38(5):13-23.[10] 丁方允, 吕涛涛. 二维Helmholtz方程非线性边值问题的边界元分析[J]. 兰州大学学报, 1994, 30(2):25-30.[11] 丁方允. 三维Helmholtz方程Dirichlet问题的边界元法及其收敛性分析[J]. 兰州大学学报, 1995, 31(3):30-38.[12] 张雄, 刘岩. 无网格法[M]. 北京:清华大学出版社, 2004.[13] Chu P C, Fan C. A Three-Point Combined Compact Difference Scheme[J]. Journal of Computational Physics, 1998, 140(2):370-399.[14] Liu Jun. Efficient Preconditioners for the Helmholtz Equation Discretized by Combined Compact Difference Method[D]. 华南师范大学硕士学位论文, 2011.[15] 柯日焕, 黎稳. 用CCD法离散求解二维Helmholtz方程的数值方法[J]. 数值计算与计算机应用, 2013, 34(3):221-230.[16] Saad Y. Iterative Methods for Sparse Linear Systems[M]. Society for Industrial & Applied Mathematics. 2003.[17] James W. Cooley, John W. Tukey. An Algorithm for the Machine Calculation of Complex Fourier Series[J]. Mathematics of Computation, 1965, 19(90):297-301.[18] Davis P J. Circulant matrices[M]. American Mathematical Soc., 2012.[19] XQ Jin, YM. Wei, Numerical Linear Algebra and Its Applications[M]. Science Press, Beijing, 2004. |