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    A parallel sweeping preconditioner for frequency-domain seismic wave propagation

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    Type
    Conference Paper
    Authors
    Poulson, Jack
    Engquist, Björn
    Li, Siwei
    Ying, Lexing
    Date
    2012-10-25
    Online Publication Date
    2012-10-25
    Print Publication Date
    2012-09
    Permanent link to this record
    http://hdl.handle.net/10754/597371
    
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    Abstract
    We present a parallel implementation of Engquist and Ying's sweeping preconditioner, which exploits radiation boundary conditions in order to form an approximate block LDLT factorization of the Helmholtz operator with only O(N4/3) work and an application (and memory) cost of only O(N logN). The approximate factorization is then used as a preconditioner for GMRES, and we show that essentially O(1) iterations are required for convergence, even for the full SEG/EAGE over-thrust model at 30 Hz. In particular, we demonstrate the solution of said problem in a mere 15 minutes on 8192 cores of TACC's Lonestar, which may be the largest-scale 3D heterogeneous Helmholtz calculation to date. Generalizations of our parallel strategy are also briefly discussed for time-harmonic linear elasticity and Maxwell's equations.
    Citation
    Poulson J, Engquist B, Li S, Ying L (2012) A parallel sweeping preconditioner for frequency-domain seismic wave propagation. SEG Technical Program Expanded Abstracts 2012. Available: http://dx.doi.org/10.1190/segam2012-0765.1.
    Sponsors
    The authors thank TACC for access to Lonestar, and particularly Bill Barth for suggesting that we enforce local memory allocations and Tommy Minyard for organizing the large runs. We also thank Sergey Fomel, Anshul Gupta, Edgar Solomonik, and Laura Grigori for helpful discussions. The work is financially supported by KAUST and the TCCS sponsors.
    Publisher
    Society of Exploration Geophysicists
    Journal
    SEG Technical Program Expanded Abstracts 2012
    DOI
    10.1190/segam2012-0765.1
    ae974a485f413a2113503eed53cd6c53
    10.1190/segam2012-0765.1
    Scopus Count
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