  Rational Krylov subspace (RKS) techniques are well-established and powerful
tools for projection-based model reduction of time-invariant dynamic systems.
For hyperbolic wavefield problems, such techniques perform well in
configurations where only a few modes contribute to the field. RKS methods,
however, are fundamentally limited by the Nyquist-Shannon sampling rate, making
them unsuitable for the approximation of wavefields in configuration
characterized by large travel times and propagation distances, since wavefield
responses in such configurations are highly oscillatory in the
frequency-domain. To overcome this limitation, we propose to precondition the
RKSs by factoring out the rapidly varying frequency-domain field oscillations.
The remaining amplitude functions are generally slowly varying functions of
source position and spatial coordinate and allow for a significant compression
of the approximation subspace. Our one-dimensional analysis together with
numerical experiments for large scale 2D acoustic models show superior
approximation properties of preconditioned RKS compared with the standard RKS
model-order reduction. The preconditioned RKS results in a reduction of the
frequency sampling well below the Nyquist-Shannon rate, a weak dependence of
the RKS size on the number of inputs and outputs for
multiple-input/multiple-output (MIMO) problems, and, most importantly, in a
significant coarsening of the finite-difference grid used to generate the RKS.
A prototype implementation indicates that the preconditioned RKS algorithm is
competitive in the modern high performance computing environment.
