Space‐local reduced‐order bases for accelerating reduced‐order models through sparsity

Abstract

AbstractProjection‐based model order reduction (PMOR) methods based on linear or affine approximation subspaces accelerate numerical predictions by reducing the dimensionality of the underlying computational models. The state of the art of PMOR includes approximation methods based on state‐local subspaces—that is, subspaces associated with different regions of the solution manifold—and methods based on adaptive reduced‐order bases. For challenging applications such as those associated with highly nonlinear problems, such methods accelerate traditional PMOR by controlling the dimension of the reduced‐order basis (ROB) and associated projection‐based reduced‐order model (PROM). This article proposes an alternative as well as complementary approach for accelerating PMOR based on introducing sparsity into the ROB, in order to enhance the computational efficiency of the associated PROM. Specifically, the proposed approach introduces sparsity in PMOR by partitioning the computational domain rather than, or in addition to, the solution manifold, and therefore leads to the concept of a space‐local ROB. This concept is compatible with both concepts of a state‐local ROB and hyperreduction. It is demonstrated for two computational fluid dynamics problems in turbulent flow applications. Acceleration factors of the order of 1.5 relative to traditional PMOR and CPU time speedup factors of several orders of magnitude relative to high‐dimensional models are reported.