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.