Multipreconditioning with application to two-phase incompressible navier–stokes flow

We consider the use of multipreconditioning to solve linear systems when more than one preconditioner is available but the optimal choice is not known. In particular, we consider a selective multipreconditioned GMRES algorithm where we incorporate a weighting that allows us to prefer one preconditioner over another. Our target application lies in the simulation of incompressible two-phase flow. Since it is not always known if a preconditioner will perform well within all regimes found in a simulation, we also consider robustness of the multipreconditioning to a poorly performing preconditioner. Overall, we obtain promising results with the approach.