ESAIM: Mathematical Modelling and Numerical Analysis

Multiscale problems and techniques

Sweeping preconditioners for elastic wave propagation with spectral element methods

Paul Tsujia1, Jack Poulsona2, Björn Engquista3 and Lexing Yinga4

a1 Sandia National Laboratories, Org. 1442: Numerical Analysis and Applications, Livermore, CA 94550, USA.

a2 Georgia Institute of Technology, School of Computational Science and Engineering, Atlanta, GA 30332, USA.

a3 University of Texas at Austin, Department of Mathematics, Austin, TX 78712, USA.

a4 Stanford University, Department of Mathematics, Stanford, CA 94305, USA..


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.

(Online publication February 20 2014)

Key Words:

  • Elastic wave;
  • seismic wave;
  • time-harmonic;
  • frequency domain;
  • spectral elements;
  • parallel preconditioner;
  • iterative solver;
  • sparse-direct;
  • perfectly matched layers;
  • full waveform inversion

Mathematics Subject Classification:

  • 65F08 ;
  • 65N22 ;
  • 65N80