Frequency-domain Elastic wave Simulation Based on the Nonoverlapping Domain Decomposition Method

Show more

References

[1] A. Bayliss, C. I. Goldstein and E. Turkel, “The Numerical Solution of the Helmholtz Equation for Wave Propagation Problmes in Underwater Acoustics,” Computers and Mathematics with Applications, Vol. 11, No. 7-8, 1985, pp. 655-665. doi:10.1016/0898-1221(85)90162-2

[2] R. E. Plexxis, “A Helmholtz Iterative Solver for 3D Seismic-imaging Problems,” Geophysics, Vol. 72, No. 5 2007, pp. SM185-SM197. doi:10.1190/1.2738849

[3] F. Ihlenburg and I. Babuska, “Finite Element Solution of the Helmholtz Equation with High Wave Number. Part I: The H-version of the FEM,” Computers and Mathematics with Applications, Vol. 30, No. 9, 1995, pp. 9-37. doi:10.1016/0898-1221(95)00144-N

[4] F. Ihlenburg and I. Babuska, “Finite Element Solution of the Helmholtz Equation with High Wave Number. Part II: The Hp-version of the FEM,” SIAM Journal on Numerical Analysis, Vol. 34, No. 1, 1997, pp. 315-358. doi:10.1137/S0036142994272337

[5] A. Bayliss, C. I. Goldstein and E. Turkel, “An Iterative Method for the Helmholtz Equation,” Journal of Computational Physics, Vol. 49, No. 3, 1983, pp. 443-457. doi:10.1016/0021-9991(83)90139-0

[6] Y. A. Erlangga, “Advances in Iterative Methods and PreConditioners for the Helmholtz Equation,” Archives of Computational Methods in Engineering, Vol. 15, No. 1 2008, pp. 37-66. doi:10.1007/s11831-007-9013-7

[7] T. F. Chan and T. P. Mathew, “Domain Decomposition Algorithms,” Acta Numerica, Vol. 3, 1994, pp. 61-143. doi:10.1017/S0962492900002427

[8] A. Tosseli and O. Widlund, “Domain Decomposition Methods-Algorithms and Theory,” Springer, Berlin, 2005.

[9] J. Xu, “Iterative Methods by Space Decomposition and Subspace Correction,” SIAM Review, Vol. 34, No. 4, 1992, pp. 581-613. doi:10.1137/1034116

[10] J. Xu and J. Zou, “Some Nonoverlapping Domain Decomposition Methods,” SIAM Review, Vol. 40, No. 4, 1998, pp. 857-914. doi:10.1137/S0036144596306800

[11] C. Cerjan, D. Kosloff, R. Kosloff and M. Reshef, “A Non-reflecting Boundary Condition for Discrete Acoustic and Elastic Wave Equations,” Geophysics, Vol. 50, No. 4, 1985, pp. 705-708. doi:10.1190/1.1441945

[12] R. Clayton and B. Engquist, “Absorbing Boundary Conditions for Acoustic and Elastic Wave Equations,” Bulletin of the Seismological Society of America, Vol. 67, No. 6, 1977, pp. 1529-1540.

[13] J. P. Berenger, “A Perfectly Matched Layer for Absorbing of Electromagnetic Waves,” Journal of Computational Physics, Vol. 114, No. 2, 1994, pp. 185-200. doi:10.1006/jcph.1994.1159

[14] S. Kim, “Domain Decomposition Iterative Procedures for Solving Scalar Waves in the Frequency Domain”, Numerische Mathematik, Vol. 79, No. 2, 1998, pp. 231-259. doi:10.1007/s002110050339

[15] S. Larsson, “A Domain Decomposition Method for the Helmholtz Equation in a Multilayer Domain,” SIAM Journal on Scientific Computing, Vol. 20, No. 5, 1999, pp. 1713-1731. doi:10.1137/S1064827597325323

[16] F. Magoulès, F. X. Roux and S. Salmon, “Optimal Discrete Transmission Conditions for a Nonoverlapping Domain Decomposition Method for the Helmholtz Equation,” SIAM Journal on Scientific Compting, Vol. 25, No. 5, 2004, pp. 1497-1515. doi:10.1137/S1064827502415351

[17] Y. A. Erlangga, C. Vuik and C. W. Oosterlee, “On a Class of Preconditioners for Solving the Helmholtz Equation,” Applied Numerical Mathematics, Vol. 50, No. 3-4, 2003, pp. 409-425. doi:10.1016/j.apnum.2004.01.009

[18] T. Airaksinen, E. Heikkola, A. Pennanen and J. Toivanen, “An Algebraic Multigrid based Shifted-Laplacian P[econditioner for the Helmholtz Equation,” Journal of Computational Physics, Vol. 226, No. 1, 2007, pp. 1196-1210.doi:10.1016/j.jcp.2007.05.013