PREIM for nonlinear parabolic problems

The purpose of PREIM (Progressive RB-EIM) is to reduce the offline costs of nonlinear parabolic reduced order models with accurate RB approximations in the online stage. The key idea is a progressive enrichment of both the EIM approximation and the RB space, in contrast to the standard approach where the EIM approximation and the RB space are built separately. PREIM uses high-fidelity computations whenever available and RB computations otherwise. Another key feature of each PREIM iteration is to select twice the parameter in a greedy fashion, the second selection being made after computing the high-fidelity solution for the firstly selected value of the parameter.