On-the-fly dual reduction for time-dependent topology optimization

A new model reduction approach is presented for time-dependent topology optimization of elastodynamic problems. Two salient features the are on-the-fly and dual reduction. That is, snapshots reduced basis obtained during rather than through off-line training; primal adjoint equations independently. For reduction, we use two complementary dynamic sampling strategies snapshots: nearest nf full-order solutions rolling transient ensemble nt solutions. apply proper orthogonal decomposition Galerkin procedure independently to Central our strategy continuous obtain so that can be along side equation The residuals governing used determine whether (FOM) based should used. Two-dimensional three-dimensional numerical examples on elastodynamics problems presented. Our results demonstrate dual-reduction leads orders magnitude improvement in FOM (in terms number solution procedures being invoked) data storage required solve backward compute sensitivity).