Multifrontal Hierarchically Semi-separable Solver for 3D Helmholtz Problem Using 27-point Finite-difference Scheme

References

1. Chandrasekaran, S., Dewilde, P., Gu, M. and Somasunderam, N.
   [2010] On the numerical rank of the off-diagonal blocks of Schur complements of discretized elliptic PDEs. SIAM J. Matrix Anal., 2261–2290.
   [Google Scholar]
2. Collino, F. and Tsogka, C.
   [2001] Application of the PML absorbing layer model to the linear elasto-dynamic problem in anisotropic heterogeneous media. Geophysics, 66(1), 294–307.
   [Google Scholar]
3. George, J.A.
   [1973] Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal., 10, 345–363.
   [Google Scholar]
4. Jo, C., Shin, C. and Suh, J.
   [1996] An optimal 9-point finite-difference frequency-space 2-D scalar wave extrapolator. Geophysics, 61, 529–537
   [Google Scholar]
5. Xia, J.
   [2012] Robust and efficient multifrontal solver for large discretized PDEs, High-Perform. In: Berry, M.W. et al. (Eds)Sci. Comput. Springer, 199–217.
   [Google Scholar]
6. Rjasanow, S.
   [2002] Adaptive Cross Approximation of Dense Matrices. Proc. Int. Association for Boundary Element Methods, May28–30, 1–12.
   [Google Scholar]
7. Wang, S., de Hoop, M.V., Xia, J. and Li, X.S.
   [2012] Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3D anisotropic media. Proceedings of the Project Review, Geo-Mathematical Imaging Group (Purdue University, West Lafayette IN), 1, 97–121.
   [Google Scholar]
8. Hackbusch, W.
   [1999] A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices. Computing, 62(2), 89–108.
   [Google Scholar]