P. R. AMESTOY, I. S. DUFF, J. KOSTER, AND J.-Y. L'EXCELLENT,
A fully asynchronous multifrontal solver using distributed dynamic
scheduling,
SIAM J. Matrix Anal., 23 (2001), no. 1, pp. 15-41.
F. AMINZADEH, J. BRAC, AND T. KUNZ,
3-D Salt and Overthrust Models,
SEG/EAGE 3-D Modeling Series 1, Society of Exploration Geophysicists,
Tulsa, OK, 1997.
C. ASHCRAFT, R. GRIMES, J. LEWIS, B. PEYTON, AND H. SIMON,
Progress in sparse matrix methods for large sparse linear systems on
vector supercomputers,
Internat. J. Supercomputer Applications, 1 (1987), pp. 10-30.
I. M. BABUŠSKA AND S. A. SAUTER,
Is the pollution effect of the FEM avoidable for the Helmholtz equation
considering high wave numbers?,
SIAM Review, 42 (2000), no. 3, pp. 451-484.
M. BOLLHOEFER, M. GROTE, AND O. SCHENK,
Algebraic multilevel preconditioner for the Helmholtz equation in
heterogeneous media,
SIAM J. Sci. Comp., 31 (2009), pp. 3781-3805.
H. CALANDRA, S. GRATTON, X. PINEL, AND X. VASSEUR,
An improved two-grid preconditioner for the solution of three-dimensional
Helmholtz problems in heterogeneous media,
CERFACS, Toulouse, France, Technical Report, 2012, TR/PA/12/2.
Available at: http://www.cerfacs.fr/algor/reports/2012/TR_PA_12_2.pdf.
E. CHAN, M. HEIMLICH, A. PURKAYASTHA, AND R. A. VAN DE GEIJN,
Collective communication: theory, practice, and experience,
Concurrency and Computation: Practice and Experience, 19 (2007), no. 13,
pp. 1749-1783.
I. S. DUFF AND J. K. REID,
The multifrontal solution of indefinite sparse symmetric linear equations,
ACM Trans. Math. Software, 9 (1983), pp. 302-325.
B. ENGQUIST AND L. YING,
Sweeping preconditioner for the Helmholtz equation: hierarchical matrix
representation,
Commun. on Pure and App. Math., 64 (2011), pp. 697-735.
B. ENGQUIST AND L. YING,
Sweeping preconditioner for the Helmholtz equation: moving perfectly
matched layers,
SIAM J. Multiscale Modeling and Simulation, 9 (2011), pp. 686-710.
Y. ERLANGGA, C. VUIK, AND C. OOSTERLEE,
On a class of preconditioners for solving the Helmholtz equation,
Applied Numer. Math., 50 (2004), pp. 409-425.
O. G. ERNST AND M. J. GANDER,
Why it is difficult to solve Helmholtz problems with classical iterative
methods,
in Numerical Analysis of Multiscale Problems, I. Graham, T. Hou, O. Lakkis,
and R. Scheichl, eds., Springer-Verlag, New York, NY, 2011, pp. 325-363.
M. J. GANDER AND F. NATAF,
AILU for Helmholtz problems: a new preconditioner based on the analytic
parabolic factorization,
in J. Comput. Acoustics, 9 (2001), pp. 1499-1506.
A. GEORGE, J. W. H. LIU, AND E. NG,
Communication reduction in parallel sparse cholesky factorization on a
hypercube,
in Hypercube Multiprocessors, M. T. Heath, ed., SIAM, Philadelphia, PA, 1987,
pp. 576-586.
A. GUPTA, S. KORIC, AND T. GEORGE,
Sparse matrix factorization on massively parallel computers,
Proc. of Conf. on High Perf. Comp. Networking, Storage, and Anal. (SC '09),
ACM, New York, NY, 2009. Article 1, 12 pages. Available at:
http://doi.acm.org/10.1145/1654059.1654061.
A. GUPTA, G. KARYPIS, AND V. KUMAR,
A highly scalable parallel algorithm for sparse matrix factorization,
IEEE Trans. Parallel and Dist. Systems, 8 (1997), no. 5, pp. 502-520.
M. JOSHI, A. GUPTA, G. KARYPIS, AND V. KUMAR,
A high-performance two dimensional scalable parallel algorithm for solving
sparse triangular systems,
Proc. of Internat. Conf. on High Perf. Comp. (HiPC), (1997), pp. 137-143.
P.-G. MARTINSSON AND V. ROKHLIN,
A fast direct solver for scattering problems involving elongated
structures,
J. Comput. Phys., 221 (2007), no. 1, pp. 288-302.
S. G. JOHNSON,
Notes on perfectly matched layers (PMLs),
Massachusetts Institute of Technology, Technical Report, 2007; updated 2010.
Available at: http://www-math.mit.edu/~stevenj/18.369/pml.pdf.
J. POULSON, B. MARKER, R. A. VAN DE GEIJN, J. R. HAMMOND, AND
N. A. ROMERO,
Elemental: a new framework for distributed memory dense matrix
computations,
ACM Trans. Math. Software, Note: to appear.
P. RAGHAVAN,
Domain-Separator Codes for the parallel solution of sparse linear systems,
The Pennsylvania State University, University Park, PA,
Technical Report, 2002, CSE-02-004.
Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual method for solving nonsymmetric linear systems,
SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
R. SCHREIBER,
Scalability of sparse direct solvers,
in Graph Theory and Sparse Matrix Computation, A. George, J. R. Gilbert, and
J. W. H. Liu, eds., Springer-Verlag, New York, NY, 1993, pp. 191-209.
V. SIMONCINI AND E. GALLOPOULOS,
Convergence properties of block GMRES and matrix polynomials,
Linear Algebra and its Applications, 247 (1996), pp. 97-119.
C. STOLK,
A rapidly converging domain decomposition method for the Helmholtz
equation,
CoRR, abs/1208.3956 (2012), 14 pages. Available at:
http://arxiv.org/abs/1208.3956.
P. TSUJI, B. ENGQUIST, AND L. YING,
A sweeping preconditioner for time-harmonic Maxwell's equations with
finite elements,
J. Comp. Phys, Note: to appear.
P. TSUJI AND L. YING,
A sweeping preconditioner for Yee's finite difference approximation of
time-harmonic Maxwell's Equations,
J. Frontiers of Math. China, Note: to appear.
S. WANG, M. V. DE HOOP, AND J. XIA,
On 3D modeling of seismic wave propagation via a structured parallel
multifrontal direct Helmholtz solver,
Geophysical Prospecting, 59 (2011), pp. 857-873.
S. WANG, X. S. LI, J. XIA, Y. SITU, AND M. V. DE HOOP,
Efficient scalable algorithms for hierarchically semiseparable matrices,
Submitted to SIAM J. Sci. Comput., 2011.
Available at: http://www.math.purdue.edu/~xiaj/work/parhss.pdf.
J. XIA, S. CHANDRASEKARAN, M. GU, AND X. LI,
Superfast multifrontal method for large structured linear systems of
equations,
SIAM J. Matrix Anal. Appl., 31 (2009), no. 3, pp. 1382-1411.