Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics

References

• Claerbout , J. F. 1985 . Imaging the Earth's Interior , Oxford : Blackwell Scientific Publications .
   Google Scholar
• Brandt , A. 1977 . Multi-level adaptive solutions to boundary-value problems . Mathematics of Computation , 31 : 333 – 390 .
   Web of Science ®Google Scholar
• Trottenberg , U. , Oosterlee , C. W. and Schüller , A. 2001 . Multigrid , New York : Academic Press .
   Google Scholar
• Elman , H. R. , Ernst , O. G. and O'Leary , D. P. 2001 . A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations . SIAM Journal on Scientific Computing , 23 : 1291 – 1315 .
   Web of Science ®Google Scholar
• Kim , S. and Kim , S. 2002 . Multigrid simulation for high-frequency solutions of the Helmholtz problem in heterogeneous media . SIAM Journal on Scientific Computing , 24 : 684 – 701 .
   Google Scholar
• Erlangga , Y. A. , Oosterlee , C. and Vuik , C. 2006 . A novel multigrid based preconditioner for heterogeneous Helmholtz problems . SIAM Journal on Scientific Computing , 27 : 1471 – 1492 .
   Web of Science ®Google Scholar
• Riyanti , C. D. , Erlangga , Y. A. , Plessix , R.-E. , Mulder , W. A. , Vuik , C. and Oosterlee , C. 2006 . A new iterative solver for the time-harmonic wave equation . Geophysics , 71–5 : 57 – 63 .
   Google Scholar
• Hustedt , B. , Operto , S. and Virieux , J. 2004 . Mixed-grid and staggered-grid finite difference methods for frequency-domain acoustic wave modelling . Geophysical Journal International , 157 : 1269 – 1296 .
   Web of Science ®Google Scholar
• Cohen , G. 2002 . Higher-Order Numerical Methods for Transient Wave Equations , Berlin : Springer .
   Google Scholar
• Harari , I. and Turkel , E. 1995 . Accurate finite difference methods for timeharmonic wave propagation . Journal of Computational Physics , 119 : 252 – 270 .
   Web of Science ®Google Scholar
• de Zeeuw , P. M. 1990 . Matrix-dependent prolongations and restrictions in a blackbox multigrid solver . Journal of Computational and Applied Mathematics , 33 : 1 – 27 .
   Google Scholar
• Dendy , J. E. Jr. 1983 . Blackbox multigrid for nonsymmetric problems . Applied Mathematics and Computations , 13 : 261 – 283 .
   Web of Science ®Google Scholar
• van der Vorst , H. A. 1992 . Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems . SIAM Journal on Scientific Computing , 13 : 631 – 644 .
   Web of Science ®Google Scholar
• Stüben , K. and Trottenberg , U. 1982 . Multigrid Methods: Fundamental Algorithms, Model Problem Analysis and Applications, in Multigrid Methods , Edited by: Hackbusch , W. and Trottenberg , U. Vol. 960 , 1 – 176 . Berlin : Springer . Lecture Notes in Mathematics
   Google Scholar
• Wienands , R. , Oosterlee , C. and Washio , T. 2000 . Fourier analysis of GMRES(m) preconditioned by multigrid . SIAM Journal on Scientific Computing , 22 : 582 – 603 .
   Google Scholar
• Saad , Y. and Schultz , M. H. 1986 . GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM Journal on Scientific Computing , 7 : 856 – 869 .
   Web of Science ®Google Scholar
• Shapira , Y. , Israeli , M. and Sidi , A. 1996 . Towards automatic multigrid algorithms for spd, nonsymmetric and indefinite problems . SIAM Journal on Scientific Computing , 17 : 439 – 453 .
   Google Scholar
• Shapira , Y. Multigrid techniques for highly indefinite equations . NASA Hampton, VA. Seventh Copper Mountain Conference on Multigrid Methods , Edited by: Melson , N. D. , Manteuffel , T. A. , McCormick , S. F. and Douglas , C. C. pp. 689 – 705 .
   Google Scholar
• Frayssé , V. , Giraud , L. , Gratton , S. and Langou , J. 2005 . Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers . ACM Transactions on Mathematical Software , 31–2 : 228 – 238 .
   Google Scholar
• Bourgeois , A. , Bourget , M. , Lailly , P. , Poulet , M. , Ricarte , P. and Versteeg , R. 1990 . “ Marmousi, model and data ” . 5 – 16 . 52nd Annual International Meeting, EAEG, Extended Abstracts
   Google Scholar
• Amestoy , P. R. , Duff , I. S. and L'Excellent , J.-Y. 2000 . Multifrontal parallel distributed symmetric and unsymmetric solvers . Computational Methods in Applied Mechanics and Engineering , 184 : 501 – 520 .
   Web of Science ®Google Scholar
• Amestoy , P. R. , Duff , I. S. , Koster , J. and L'Excellent , J.-Y. 2001 . A fully asynchronous multifrontal solver using distributed dynamic scheduling . SIAM Journal on Matrix Analysis and Applications , 23 ( 1 ) : 15 – 41 .
   Web of Science ®Google Scholar
• Amestoy , P. R. , Guermouche , A. , L'Excellent , J.-Y. and Pralet , S. 2006 . Hybrid scheduling for the parallel solution of linear systems . Parallel Computing , 32 ( 2 ) : 136 – 156 .
   Web of Science ®Google Scholar
• Karypis , G. and Kumar , V. 1998 . “ METIS – A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices ” . University of Minnesota . Version 4.0
   Google Scholar
• Duff , I. S. and Reid , J. K. 1983 . The multifrontal solution of indefinite sparse symmetric linear systems . ACM Transactions on Mathematical Software , 9 : 302 – 325 .
   Web of Science ®Google Scholar