Preconditioners for Multilinear Problems Arising in Parametric Partial Differential Equations

ABSTRACT This work deals with the set up of preconditioning methods for multilinear problems emerging from the discretisation of parametric Partial Differential Equations. We are going to focus, here, on linear problems. We will investigate three different preconditioning strategies. Some theoretical results are presented in order to assess the properties of these preconditioners and understand their limitations. We present several numerical experiments on three‐dimensional parametric PDEs.