郑权, 高玥, 秦凤
郑权, 高玥, 秦凤. Helmholtz方程外边值问题的基于修正的DtN边界条件的有限元方法[J]. 计算数学, 2016, 38(2): 200-211.
Zheng Quan, Gao Yue, Qin Feng. THE FINITE ELEMENT METHOD WITH A MODIFIED DtN BOUNDARY CONDITION FOR EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATION[J]. Mathematica Numerica Sinica, 2016, 38(2): 200-211.
Zheng Quan, Gao Yue, Qin Feng
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[1] Yu D H. Natural Boundary Integral Method and Its Applications[M], Beijing/Dordrecht/New York/London:Kluwer Academic Publisher/Science Press, 2002.[2] Han H D, Wu X N. Artificial Boundary Method[M], Beijing:Tsinghua University Press, 2012.[3] Enquist B, Majda A. Absorbing boundary conditions for numerical simulation of waves[J]. Math. Comput., 1977, 31(139):629-651.[4] Bayliss A, Gunzburger M, Turkel E. Boundary conditions for the numerical solution of elliptic equations in exterior regions[J]. SIAM J. Appl. Math., 1982, 42(2):430-451.[5] Feng K. Finite element method and natural boundary reduction[C]. In:Proc. Inter. Cong. Math., Warszawa, 1983, 1439-1453.[6] Feng K. Asymptotic radiation conditions for reduced wave equation[J]. J. Comput. Math., 1984, 2(2):130-138.[7] Feng K, Yu D. Canonical integral equations of elliptic boundary value problems and their numerical solutions[C]. In:(K. Feng, J.L. Lions, eds.) Proc. China-France Symp. on the Finite Element Method (April 1982), pp. 211-252. Beijing:Science Press, 1983.[8] Keller J B, Givoli D. Exact nonreflecting boundary condition[J]. J. Comput. Phys., 1989, 82(1):172-192.[9] Harari I and Hughes T J R. Galerkin/least squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains[J]. Comput. Methods Appl. Mech. Engrg., 1992, 98(3):411-454.[10] Bao G. Finite element approximation of time harmonic waves in periodic structures[J]. SIAM J. Numer. Anal., 1995, 32(4):1155-1169.[11] Li R. On The coupling of BEM and FEM for exterior problems for the Helmholtz equation[J]. Math. Comput., 1999, 68(227):945-953.[12] Harari I. A survey of finite element methods for time-harmonic acoustics[J]. Comput. Methods Appl. Mech. Engrg., 2006, 195(13):1594-1607.[13] Grote M G, Keller J B. On nonreflecting boundary conditions[J]. J. Comput. Phys., 1995, 122(2):231-243.[14] Koyama D. Error estimates of the DtN finite element method for the exterior Helmholtz problem[J]. J. Comput. Appl. Math., 2007, 200(1):21-31.[15] Goldstein C l. A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains[J], Math. Comput., 1982, 39(160):309-324.[16] Hsiao G C, Nigamb N, Pasciak J E, Xu L. Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis[J]. J. Comput. Appl. Math., 2011, 235(17):4949-4965.[17] Koyama D. Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition[J]. J. Comput. Appl. Math., 2009, 232(1):109-121.[18] Masmoudi M. Numerical solution for exterior problems[J]. Numer. Math., 1987, 51(1):87-101.[19] Jiang X, Li P J, Wei Y. Numerical solution of acoustic scattering by an adaptive DtN finite element method[J], Commun. Comput. Phys., 201313(5):1227-1244.[20] Koyama D. A controllability method with an artificial boundary condition for the exterior Helmholtz problem[J]. Japan J. Indust. Appl. Math., 2003, 20(1):117-145. |
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