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We discuss efficient solutions to systems of shifted linear systems arisingin computations for oscillatory hydraulic tomography (OHT). The reconstructionof hydrogeological parameters such as hydraulic conductivity and specificstorage using limited discrete measurements of pressure (head) obtained fromsequential oscillatory pumping tests, leads to a nonlinear inverse problem. Wetackle this using the quasi-linear geostatistical approach\cite{kitanidis1995quasi}. This method requires repeated solution of theforward (and adjoint) problem for multiple frequencies, for which we useflexible preconditioned Krylov subspace solvers specifically designed forshifted systems based on ideas in \cite{gu2007flexible}. The solvers allow thepreconditioner to change at each iteration. We analyze the convergence of thesolver and perform an error analysis when an iterative solver is used forinverting the preconditioner matrices. Finally, we apply our algorithm to achallenging application taken from oscillatory hydraulic tomography todemonstrate the computational gains by using the resulting method.

A Flexible Krylov Solver for Shifted Systems with Application to Oscillatory Hydraulic Tomography