Frequency-domain seismic and electromagnetic modeling requires solving the linear systems resulting from the discretization of the corresponding time-harmonic equations. Geophysical inversion is typically performed using several discrete frequencies and multiple (up to tens of thousands) source/receiver combinations. Limitations of classical direct and iterative sparse linear solvers have caused the development of the so-called hybrid methods that can be viewed as an intermediate approach between the direct and iterative methods. We present an efficient parallel solver based on the SPIKE algorithm. Several examples in frequency domain electromagnetic modeling illustrate the computational efficiency of the developed method in terms of memory demand and floating-point operations. Multiple sources can be efficiently handled by employing sparse direct solvers in the factorization of diagonal blocks of the system matrix. Based on the divide and conquer idea, this kind of algorithms exposes different parallelism levels, being suitable to take advantage of multiple accelerator devices. The SPIKE solver partially overcomes the fill-in problem of direct solvers, allowing to solve much larger domains on the same system.


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  1. Castillo, O., de la Puente, J., Puzyrev, V. and Cela, J.M.
    [2015] Edge-based electric field formulation in 3D CSEM simulations: a parallel approach. In: Proceedings of the 6th International Conference and Workshop on Computing and Communication. IEEE. Vancouver, Canada.
    [Google Scholar]
  2. Li, X.S.
    [2005] An Overview of SuperLU: Algorithms, Implementation, and User Interface. ACM Transactions on Mathematical Software, 31(3), 302–325.
    [Google Scholar]
  3. Polizzi, E. and Sameh, A.
    [2007] SPIKE: A parallel environment for solving banded linear systems. Computers & Fluids, 36(1), 113–120.
    [Google Scholar]
  4. Puzyrev, V. and Cela, J.M.
    [2015] A review of block Krylov subspace methods for multisource electromagnetic modelling. Geophysical Journal International, 202(2), 1241–1252.
    [Google Scholar]
  5. Sameh, A.H. and Kuck, D.J.
    [1977] Parallel direct linear system solvers-a survey. Mathematics and Computers in Simulation, 19(4), 272–277.
    [Google Scholar]
  6. [1978] On stable parallel linear system solvers. Journal of the ACM (JACM), 25(1), 81–91.
    [Google Scholar]
  7. Schenk, O. and Gärtner, K.
    [2004] Solving unsymmetric sparse systems of linear equations with PAR-DISO. Future Generation Computer Systems, 20(3), 475–487.
    [Google Scholar]
  8. Sourbier, F., Haidar, A., Giraud, L., Ben-Hadj-Ali, H., Operto, S. and Virieux, J.
    [2011] Three-dimensional parallel frequency-domain visco-acoustic wave modelling based on a hybrid direct/iterative solver. Geophysical Prospecting, 59(5), 834–856.
    [Google Scholar]

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