Absorbing boundary conditions for the multidimensional Klein-Gordon equation

Communications in Mathematical Sciences

Volumn 5, Issue 3, 2007, Pages 743-764

  Han, Houde ^a   Yin, Dongsheng ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Absorbing boundary condition; Artificial boundary; Klein Gordon equation

Indexed keywords

EID: 35348961944     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2007.v5.n3.a12     Document Type: Article

References (22)

1. B. Alpert, L. Greengard and T. Hagstrom, Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation, SIAM J. Numer. Anal., 37, 1138-1164, 2000.
2. L.C. Andrews, Special Functions of Mathematics for Engineers, McGraw-Hill, New York, NY (United States), 1992.
3. A. Bayliss and E. Turkel, Radiation boundary conditions for wave like equations, Comm. Pure. Appl. Math., 23, 707-725, 1980.
4. J.P. Berenger, A perfectly matching layer for the absorbing of electromagnetic waves, J. Comput. Phys., 114, 185-200, 1994.
5. B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., 31, 629-651, 1977.
6. A. Erdélyi, Tables of Integral Transforms, Vol II, McGraw-Hill, 1954.
7. D. Givoli, Non-reflecting boundary conditions: a review, J. Comput. Phys., 94, 1-29, 1991.
8. D. Givoli, High-order local non-reflecting boundary conditions: a review, Wave Motion, 39, 319-326, 2004.
9. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, sixth edition, Academic Press.
10. W. Greiner, Relativistic Quantum Mechanics-wave Equations, third edtion, Springer, 2000.
11. M.J. Grote and J.B. Keller, Exact nonreflecting boundary conditions for the time dependent wave equation, SIAM J. Appl. Math., 55, 280-297, 1995.
12. T. Hagstrom, Radiation boundary conditions for the numerical simulation of waves, Acta. Numerica, 8, 47-106, 1999.
13. 2, Commun. Math. Sci., 2(1), 79-94, 2004.
14. H. Han and C.X. Zheng, Exact nonreflecting boundary conditions for exterior problems of the hyperbolic equation, Chinese J. Comput. Phys., 22(2), 95-107, 2005.
15. H. Han and C.X. Zheng, Exact nonreflecting boundary conditions for acoustic problem in three dimensions, J. Comput. Math., 21, 15-24, 2003.
16. 3, Numerical Methods for Partial Differential Equations, 23(3), 511-533, 2007.
17. R.L. Higdon, Absorbing boundary conditions for difference approximation to the multidimensional wave equation, Math. Comput., 47, 437-459, 1986.
18. R. Kosloff and D. Kosloff, Absorbing boundaries for wave propagation problems, J. Comput. Phys., 63, 363-376, 1986.
19. C. Lubich and A. Schädle, Fast convolution for nonreflecting boundary conditions, SIAM J. Sci. Comput., 24, 161-182, 2002.
20. I.L. Sofronov, Conditions for complete transparency on the sphere for the three-dimensional wave equation, Russian. Acad. Sci. Dokl, 46, 397-401, 1993.
21. Z.H. Teng, Exact boundary condition for time-dependent wave equation based on boundary integral, J. Comput. Phys., 190, 398-418, 2003.
22. L. Ting and M.J. Miksis, Exact boundary conditions for scattering problems, J. Acoust. Soc. Amer., 80, 1825-1827, 1986.