  We consider several methods for generating initial guesses when iteratively
solving sequences of linear systems, showing that they can be implemented
efficiently in GPU-accelerated PDE solvers, specifically solvers for
incompressible flow. We propose new initial guess methods based on stabilized
polynomial extrapolation and compare them to the projection method of Fischer
[15], showing that they are generally competitive with projection schemes
despite requiring only half the storage and performing considerably less data
movement and communication. Our implementations of these algorithms are freely
available as part of the libParanumal collection of GPU-accelerated flow
solvers.
