Convergence and complexity study of GMRES variants for solving multi-frequency elastic wave propagation problems

In this paper we present a comparison study of three different frameworks of iterative Krylov methods that we have recently developed for the simultaneous numerical solution of frequency-domain wave propagation problems when multiple wave frequencies are present. The three approaches have in common that they require the application of a single shift-and-invert preconditioner at a suitable seed frequency. In particular for three-dimensional problems, we present the efficient application of the elastic shift-and-invert preconditioner by means of an additive coarse grid correction. The focus of the present work lies, however, on the performance of the respective iterative method. We conclude with numerical examples that provide guidance concerning the suitability of the three methods.