Enriched Reduced Model Accelerated Level Set Topology optimization

In this work, we develop level-set topology optimization methods accelerated by projection-based reduced-order models (ROM) constructed on the fly. We extend existing trust-region-based ROM-accelerated topology optimization methods, which are restricted to density-based topology optimization, to level-set cut finite element methods (FEMs), which provide accurate geometry representation and avoid so-called ``ersatz materials'' or ``passive elements''. One challenge to apply ROM to topology optimization based on cut FEM is that the support of the solution snapshots changes with the geometry, which makes the construction of reduced basis difficult particularly near the domain boundaries. To overcome the challenge, we introduce a family of enriched reduced models, which enrich the reduced basis using finite element basis near part or all of the boundaries. We devise various methods to specify the enrichment regions. We assess the methods using two-dimensional structural topology optimization problems. We observe that a multi-stage algorithm which adaptively selects the enrichment region considerably reduces the computational time, especially as the full order model cost increases.M.A.S