Two-Level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics

Pleiades Publishing Ltd - Tập 5 Số 2 - Trang 175-181 - 2012
Henri Calandra1, Serge Gratton1, Rafael Lago1, Xavier Pinel1, Xavier Vasseur1
1Centre Scientifique et Technique Jean Féger, ave. de Larribau, F-64000, Pau, France

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Aminzadeh, F., Brac, J., and Kunz, T., 3-D Salt and Overthrust Models: Society of Exploration Geophysicists 3-D Modeling Series, no. 1, 1997.

Berenger. J.-P., A Perfectly Matched Layer for Absorption of Electromagnetic Waves, J. Comp. Phys., 1994, vol. 114, pp. 185–200.

Berenger, J.-P., Three-Dimensional Perfectly Matched Layer for Absorption of Electromagnetic Waves, J. Comp. Phys., 1996, vol. 127, pp. 363–379.

Bollhöfer, M., Grote, M. J., and Schenk, O., Algebraic Multilevel Preconditioner for the Solution of the Helmholtz Equation in Heterogeneous Media, SIAM J. Sci. Comp., 2009, vol. 31, pp. 3781–3805.

Calandra, H., Gratton, S., Langou, J., Pinel, X., and Vasseur, X., Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics, Toulouse: CERFACS, 2011 (Tech. Rep. TR/PA/11/14).

Cohen, G., Higher-Order Numerical Methods for Transient Wave Equations, Springer, 2002.

Elman, H., Ernst, O., O’Leary, D., and Stewart, M., Efficient Iterative Algorithms for the Stochastic Finite Element Method with Application to Acoustic Scattering, Comp. Methods Appl. Mech. Engrg., 2005, vol. 194, no. 1, pp. 1037–1055.

Elman, H.C., Ernst, G., and O’Leary, D.P., A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations, SIAM J. Sci. Comp., 2001, vol. 23, pp. 1291–1315.

Engquist, B. and Ying, L., Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers, to appear in Multiscale Model. Simulation.

Harari, I. and Turkel, E., Accurate Finite Difference Methods for Time-Harmonic Wave Propagation, J. Comp. Phys., 1995, vol. 119, pp. 252–270.

Notay, Y., Convergence Analysis of Perturbed Two-Grid and Multigrid Methods, SIAM J. Num. Anal., 2007, vol. 45, pp. 1035–1044.

Pinel, X, A Perturbed Two-Level Preconditioner for the Solution of Three-Dimensional Heterogeneous Helmholtz Problems with Applications to Geophysics, PhD thesis, Toulouse: CERFACS and INP, 2010.

Riyanti, C.D., Kononov, A., Erlangga, Y.A., Plessix, R.-E., Mulder, W.A., Vuik, C., and Oosterlee, C., A Parallel Multigrid-Based Preconditioner for the 3D Heterogeneous High-Frequency Helmholtz Equation, J. Comp. Phys., 2007, vol. 224, pp. 431–448.

Saad, Y., A Flexible Inner-Outer Preconditioned GMRES Algorithm, SIAM J. Sci. Stat. Comp., 1993, vol. 14, pp. 461–469.

Saad, Y. and Schultz, M.H., GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comp., 1986, vol. 7, pp. 856–869.

Simoncini, V. and Szyld, D.B., Recent Computational Developments in Krylov Subspace Methods for Linear Systems, Num. Linear Alg. Appl., 2007, vol. 14, pp. 1–59.

Stüben, K. and Trottenberg, U.,Multigrid Methods: Fundamental Algorithms, Model Problem Analysis and Applications, in MultigridMethods,Hackbusch, W. and Trottenberg, U., Eds., Lect. Notes Math., vol. 960, 1982.

Trottenberg, U., Oosterlee, C.W., and Schüller, A., Multigrid, London: Academic Press, 2001.

Umetani, N., MacLachlan, S.P., and Oosterlee, C.W., A Multigrid-Based Shifted Laplacian Preconditioner for Fourth-Order Helmholtz Discretization, Num. Linear Alg. Appl., 2009, vol. 16, pp. 603–626.

Virieux, J. and Operto, S., An Overview of Full Waveform Inversion in Exploration Geophysics, Geophys., 2009, vol. 74, no. 6, pp.WCC127–WCC152.

Virieux, J., Operto, S., Ben Hadj Ali, H., Brossier, R., Etienne, V., Sourbier, F., Giraud, L., and Haidar, A., Seismic Wave Modeling for Seismic Imaging, The Leading Edge, 2009, vol. 25, no. 8, pp. 538–544.