Computational bottlenecks for PROMs: Precomputation and hyperreduction

For many applications, the projected quantities arising from projectionbased model order reduction (PMOR) must be repeatedly recomputed due to, for example, nonlinearities or parameter dependence. Such repetitive computations constitute a performance bottleneck. Specifically, they limit the ability of a projectionbased reduced-order model (PROM) to deliver the coveted speedup factor. This chapter reviews several state-of-the-art approaches for mitigating this issue and organizes them into two categories. Methods in the first category divide the computation of projections, whenever possible, into two parts: one that is responsible for the aforementioned bottleneck but can be precomputed offline and another part that must be repeatedly performed online but whose computational complexity scales only with the dimension of the PROM. Methods in the second category are known as hyperreduction methods: They achieve the desired computational efficiency by approximating either the quantity to be projected, or the result of the projection. The significance of hyperreduction for PMOR is highlighted using four numerical applications that are representative of academic and real-world problems.