Speaker
Description
In this talk, we will discuss a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as (port-)Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or with dissipation and hence plays a crucial role in the description of the physical properties of the system. We propose to combine empirical interpolation (EIM) with parameter sampling to approximate the parametric nonlinear gradients mapped into a suitable reduced space. Whenever the evolution of the nonlinear gradients require high-dimensional EIM approximation spaces, an adaptive strategy is performed. This consists in updating the hyper-reduced function via a low-rank correction of the EIM basis. Numerical tests on parametric Hamiltonian systems will be shown to demonstrate the improved performances of the hyper-reduced model compared to the full and reduced models.
This is joint work with F. Vismara (TU Eindhoven).
