Discrete empirical interpolation and unfitted mesh FEMs: application in PDE-constrained optimization

In this work, we investigate the performance CutFEM as a high fidelity solver well construct competent and economical reduced order for PDE-constrained optimization problems in parametrized domains that live fixed background geometry mesh. Its effectiveness reliability will be assessed through its application numerical solution of quadratic with elliptic equations constraints, examining an archetypal case. The reduction strategy via Proper Orthogonal Decomposition suitable FE snapshots, using aggregated state adjoint test space, while efficiency offline-online decoupling ensured by means Discrete Empirical Interpolation optimality system matrix right-hand side, enabling thus rapid resolution model each new spatial configuration.