Sweeping preconditioners for elastic wave propagation with spectral element methods

¹ Sandia National Laboratories, Org. 1442: Numerical Analysis and Applications, Livermore, CA 94550, USA.
² Georgia Institute of Technology, School of Computational Science and Engineering, Atlanta, GA 30332, USA.
³ University of Texas at Austin, Department of Mathematics, Austin, TX 78712, USA.
⁴ Stanford University, Department of Mathematics, Stanford, CA 94305, USA.
lexing@math.stanford.edu

Received: 3 August 2013

Abstract

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 LDL^T factorization. Both sequential and parallel versions of the algorithm are discussed and results for large-scale problems from exploration geophysics are presented.