Fast solvers for EVSS formulations of viscoelastic flows

Numerical simulations of viscoelastic flow problems require the solution of large, typically sparse, systems of equations which inherit the (highly) nonlinear coupling of the original PDE model. Recent approaches, such as the elastic viscous split stress (EVSS) methods, while allowing more flexibility and the treatment of complex rheological models come at the cost of increased problem size. At the same time, there is an evident lack of efficient solution techniques. In this work we introduce and analyze a class of implicit iterative solvers based on a Schur complement approach. The technique is based on identifying a suitable decoupling of the original system of PDE through an approximation to a Schur complement operator. We illustrate our approach on discretizations of EVSS formulations of Oldroyd-type fluid models.