Geodesic
Sweeping preconditioners for elastic wave propagation with spectral element methods
ESAIM: Mathematical Modelling and Numerical Analysis , Multiscale problems and techniques. Special Issue, Tome 48 (2014) no. 2, pp. 433-447

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We present a parallel preconditioning method for the iterative solution of the time-harmonic elastic wave equation which makes use of higher-order spectral elements to reduce pollution error. In particular, the method leverages perfectly matched layer boundary conditions to efficiently approximate the Schur complement matrices of a block LDLT factorization. Both sequential and parallel versions of the algorithm are discussed and results for large-scale problems from exploration geophysics are presented.

DOI : 10.1051/m2an/2013114
Classification : 65F08, 65N22, 65N80
Keywords: elastic wave, seismic wave, time-harmonic, frequency domain, spectral elements, parallel preconditioner, iterative solver, sparse-direct, perfectly matched layers, full waveform inversion 
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     title = {Sweeping preconditioners for elastic wave propagation with spectral element methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {433--447},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {2},
     year = {2014},
     doi = {10.1051/m2an/2013114},
     mrnumber = {3177852},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013114/}
}
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Tsuji, Paul; Poulson, Jack; Engquist, Björn; Ying, Lexing. Sweeping preconditioners for elastic wave propagation with spectral element methods. ESAIM: Mathematical Modelling and Numerical Analysis , Multiscale problems and techniques. Special Issue, Tome 48 (2014) no. 2, pp. 433-447. doi: 10.1051/m2an/2013114

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